Active Equity Investing - Portfolio Construction (Skipped)

INTRODUCTION

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Active equity investing is based on the concept that a skilled portfolio manager can both identify and differentiate between the most attractive securities and the least attractive securities—typically relative to a pre-specified benchmark. If this is the case, why is a portfolio—a collection of securities—even necessary? Why shouldn’t the portfolio manager just identify the most attractive security and invest all assets in this one security? Or in a long/short context, why not buy the “best” security and sell the “worst” one? Although very simple, this one-stock approach is not likely to be optimal or even feasible. No manager has perfect foresight, and her predictions will likely differ from realized returns. What she predicted would be the “best security” may quite likely turn out not to be the best. Active equity portfolio managers, even those with great skill, cannot avoid this risk. Security analysis is the process for ranking the relative attractiveness of securities, whereas portfolio construction is about selecting the securities to be included and carefully determining what percentage of the portfolio is to be held in each security—balancing superior insights regarding predicted returns against some likelihood that these insights will be derailed by events unknown or simply prove to be inaccurate.

Active managers rely on a wide array of investment strategies and methodologies to build portfolios of securities that they expect to outperform the benchmark. The challenges faced by active managers are similar whether they manage long-only traditional strategies, systematic/quantitative strategies, or long/short opportunistic strategies. Managers may differ in their investment style, operational complexity, flexibility of investment policy, ability to use leverage and short positions, and implementation methodologies, but predictions about returns and risk are essential to most active equity management styles.

In Section 2, we introduce the “building blocks” of portfolio construction, and in Sections 3–5, we discuss the different approaches to portfolio construction. In Sections 6–9, we discuss risk budgeting concepts relevant to portfolio construction and the measures used to evaluate portfolio risk. Section 10 looks at how issues of scale may affect portfolio construction. Section 11 addresses the attributes of a well-constructed portfolio. Section 12 looks at certain specialized equity strategies and how their approaches to portfolio construction may differ from a long-only equity strategy. The reading concludes with a summary.

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BUILDING BLOCKS OF ACTIVE EQUITY PORTFOLIO CONSTRUCTION

Learning Outcome

• describe elements of a manager’s investment philosophy that influence the portfolio construction process

Investors who pursue active management are looking to generate portfolio returns in excess of benchmark returns (adjusted for all costs) for an appropriate level of risk. The excess return—also called active return (RA)—of an actively managed portfolio is driven by the difference in weights between the active portfolio and the benchmark. It can be mathematically expressed as

$RA=∑i=1NΔWiRi$𝑅𝐴=∑𝑖=1𝑁𝛥𝑊𝑖𝑅𝑖1where

Ri = the return on security i and

ΔWi = the difference between the portfolio weights WPi and the benchmark weights WBi. ΔWi is also referred to as the active weight.

An active manager will generate positive active returns if:

The gains generated by	are, on average, >	The losses generated by
overweighting the securities that outperform the benchmark and underweighting the securities that underperform the benchmark.	underweighting the securities that outperform the benchmark and overweighting the securities that underperform the benchmark.

Fundamentals of Portfolio Construction

Conceptually, a manager can generate active returns by

• strategically adjusting the active weights of the securities to create long-term exposures to rewarded risks that are different from those of his benchmark;

• tactically adjusting the active weights of the securities using his skills/expertise in identifying mispricing in securities, sectors, rewarded risks, and so on, to generate alpha that cannot be explained by long-term exposure to rewarded risks; and

• assuming excessive idiosyncratic risk that may result in lucky or unlucky returns.

Historically, any excess return over the benchmark was often termed “alpha.” More sophisticated investors then moved to evaluating managers on the basis of excess risk-adjusted returns, where risk was assessed relative to a cap-weighted index. The information ratio became an important measure of the manager’s value-added. Today, research supports the argument that much of what was historically viewed as alpha is, in fact, “alternative beta”—exposure to rewarded risks (often referred to as “priced factors” or “rewarded factors”) that can be obtained at much lower cost.1 In this reading, we use “rewarded factors” as a generic term that refers specifically to investment risks for which investors expect to be compensated through a long-run return premium, such as exposure to market risk and liquidity risk. The existence of numerous rewarded factors is well documented in the literature and supported by strong empirical evidence. The recognition of this phenomenon is fundamentally altering the investment management industry, with large asset owners negotiating fee structures that compensate active managers for returns above and beyond those that can be generated by simple exposure to rewarded factors.2

These three sources of active return remain the same whether a manager follows a fundamental/discretionary or quantitative/systematic approach, a bottom-up or top-down strategy, or a style such as value or growth at a reasonable price. Of course, the proportion of return sourced from exposure to rewarded factors, alpha, and luck will vary among managers and portfolio management approaches. Equation 2 expresses the decomposition of ex post active returns in terms of these components:

$RA=∑(βpk−βbk)×Fk+(α+ε)$𝑅𝐴=∑(𝛽𝑝𝑘−𝛽𝑏𝑘)×𝐹𝑘+(𝛼+𝜀)2where

βpk = the sensitivity of the portfolio (p) to each rewarded factor (k)

βbk = the sensitivity of the benchmark to each rewarded factor3

Fk = the return of each rewarded factor

(α + ε) = the part of the return that cannot be explained by exposure to rewarded factors. The volatility of this component is very much dependent on how a manager sizes individual positions in his portfolio. The alpha (α) is the active return of the portfolio that can be attributed to the specific skills/strategies of the manager—skills such as security selection and factor timing. ε is the idiosyncratic return, often resulting from a random shock, such as a company announcing unexpected earnings. It could also be called noise or luck (good or bad). Although managers generate returns above or below those that can be explained by the exposure to rewarded factors, it is very difficult to isolate how much of this return differential can be attributed to alpha/skill or to noise/luck.4

Although not all active managers expressly employ a factor methodology in creating active returns, the growth of exchange-traded funds, coupled with the disappointing after-fee performance of many active managers, is expanding the factor-based view of the investment landscape. It is important to understand the components of active returns (exposure to rewarded risks, alpha, and luck) and how Equation 2 explicitly or implicitly relates to various management styles and approaches.

To illustrate, let’s consider two hypothetical managers: a systematic manager (Quanto) and a discretionary manager (Evolo). Each claims to have a “Value” orientation.

Quanto estimates the “Value” characteristics of each security in his investment universe using such proxies as the ratios of price to book and forward earnings to price. He then uses a systematic allocation methodology that determines the specific active weights that can be expected to deliver the desired exposure to the Value factor. Quanto holds a large number of securities to limit the impact of idiosyncratic risks on performance. Quanto attempts to outperform the benchmark by choosing factor exposures that differ from those of the benchmark.

Evolo has developed a comprehensive measure of value using a forward-looking free cash flow model. This allows Evolo to compare her own estimates of security valuation to the current market price for each security covered by the firm. The manager uses her judgment to determine the appropriate active weights based on her own level of confidence in each estimate. She runs a concentrated portfolio because she believes she has an edge in setting the appropriate active weights.

Although Evolo is not using a systematic approach to determine the active security weights and the overall portfolio exposure to the Value factor, she is driven by a Value philosophy and is exposed to the Value factor. Her returns will be driven in part by this factor exposure, even if she has never seen Equation 2. Indeed, if her portfolio is not exposed to the Value factor, clients and consultants may question her claim to run a value-oriented portfolio. If Evolo has developed a better Value proxy than her competitors and if she is skilled at identifying the best and worst securities and setting appropriate active weights, part of her active return will be attributed to her alpha skills. Because Evolo runs a more concentrated portfolio, the portion of her active performance attributed to idiosyncratic risk will likely be greater.

Building Blocks Used in Portfolio Construction

This section introduces the three main building blocks of portfolio construction—rewarded factor weightings, alpha skills, and position sizing (shown in Exhibit 1)—and explains how each relates to the three broad sources of active returns. A fourth critical component of portfolio construction, breadth of expertise, is necessary to assemble these three building blocks into a successful portfolio construction process.

Exhibit 1:

Building Blocks Used in Portfolio Construction

First Building Block: Overweight or Underweight Rewarded Factors

Let’s begin by considering the market portfolio as our benchmark. The market portfolio encompasses all securities, and the weight of each security is proportional to its market capitalization. Our benchmark would have an exposure (or beta, β) of 1 to the Market factor and no net exposure to other rewarded factors, such as Size, Value, and Momentum.5

However, most individual securities have a β less than or greater than 1 to the Market factor and most will also have a non-zero exposure to the other factors. Indeed, one way an active manager can try to add value over and above the market portfolio is to choose, explicitly or implicitly, exposures to rewarded risks that differ from those of the market.

Practically speaking, most investors use narrower market proxies as a benchmark: the S&P 500 Index for a US mandate, the FTSE 100 Index for a UK mandate, or the MSCI All Country World Index (ACWI)6 for a global mandate, for example. These indexes, although quite broad, do not include all securities that are publicly traded. Thus, these well-known indexes may not have a β of exactly 1 to the Market factor and could very well have a net exposure to other rewarded factors. For example, although most large-cap indexes usually have a β close to 1 to the Market factor, they usually have a negative sensitivity to the Size factor, indicating their large-cap tilt. When a manager is creating an exposure to a rewarded risk, the exposure must be established relative to that of his benchmark to achieve an expected excess return.

The growing understanding of rewarded factors is profoundly changing the view of active and passive investing. There are many investment products that allow investors to directly access such factors as Value, Size, Momentum, and Quality, and the bar for active managers is rising: An active value manager not only needs to outperform a passive value benchmark but may also need to outperform a rules-based value-tilted product. In the following discussion, we illustrate the concept of returns to factors and the application of this concept to portfolio management.

Exhibit 2 illustrates the factor exposures of the Russell 1000 Index, the Russell 1000 Value Index, and a discretionary mid-cap value fund (using the four Fama–French and Carhart factors) over a discrete 26-year period. The performance of the actively managed fund is presented before the deduction of fees to make the comparison with benchmark returns fair.

The average monthly performance of each factor is specified in the last column.7 All four factors showed positive returns over the period. Most regression coefficients are statistically significant at the 5% level (not shown); the momentum coefficients of the Russell 1000 and the Russell 1000 Value are the exceptions.

Exhibit 2:

Risk Factor Exposure

	Russell 1000 Index	Russell 1000 Value Index	Value Fund	Factor Performance US Market
Monthly performance in excess of the risk-free rate	0.64%	0.66%	0.40%	—
	β to specified factor:
Market*	0.99	0.92	0.90	0.64%
Size	−0.16	−0.23	0.13	0.16%
Value	0.02	0.41	0.59	0.18%
Momentum	−0.01	0.13	0.09	0.61%
“Alpha” (monthly)	0.05%	−0.05%	−0.35%	—
R2	0.99	0.95	0.74

* As mentioned in footnote 3, the Market factor is built from a much larger universe of securities than are traditional benchmarks, such as the Russell 1000. Therefore, we should not expect the β of indexes to the Market factor to be necessarily equal to one.

Note: All data are measured in US dollars.

Sources: Factor data for the United States are from AQR Capital Management, market data are from Bloomberg, and calculations are from the authors.

The Russell 1000 Index has a Market β close to 1, a negative exposure to the Size factor (indicating it has a large-cap tilt), and almost no sensitivity to the Value and Momentum factors. This is what we would expect for a capitalization-weighted large-cap index. In comparison, the Russell 1000 Value Index has a lower Market β and a significant exposure to the Value factor, also in line with expectations. Finally, the mid-cap value fund has positive exposure to the Size factor (consistent with its mid-cap tilt) and a very significant exposure to the Value factor.

In these regression specifications, there is still a component of return that cannot be explained by the rewarded factors alone. It is often labeled “alpha.” This may be true alpha, or it may be simply noise/luck. The two indexes have a relatively small alpha, whereas the value fund has a significantly negative alpha of −0.35% per month. An alpha of this magnitude is unlikely to be explained by a small misspecification in the factor model. An investor considering this fund would need to investigate the causes of this negative alpha.

In Exhibit 3, we show the sources of performance of each product in terms of its exposure to each of the four factors and its respective alpha. In all cases, the Market factor is the dominant source of performance. The Value and Momentum factors did contribute positively to performance for the Russell 1000 Value, but much of this performance was lost because of the large-cap tilt and the negative alpha. The value fund did get a significant performance boost from the Value tilt, but much of it was lost to the very poor alpha in this period.

Exhibit 3:

Sources of Performance (February 1990–December 2016)

Source of Performance	Russell 1000	Russell 1000 Value	Value Fund
Market	0.63%	0.59%	0.57%
Size	−0.03%	−0.04%	0.02%
Value	0.00%	0.08%	0.11%
Momentum	−0.01%	0.08%	0.05%
Alpha	0.05%	−0.05%	−0.35%
Total monthly performance	0.64%	0.66%	0.40%

Source: Calculations by authors.

These examples illustrate the components of Equation 2. Irrespective of the manager’s investment approach—whether she explicitly targets factors or focuses only on securities she believes to be attractively priced—her portfolio performance can be analyzed in terms of factors. Some portion of returns will not be explained by factors, which may be attributable to

• the unique skills and strategies of the manager (alpha),

• an incomplete factor model that ignores relevant factors, or

• exposure to idiosyncratic risks that either helped or hurt performance.

The next section discusses the alpha skills building block.

Second Building Block: Alpha Skills

In principle, there are many approaches that can be used to generate alpha, but in practice, generating positive alpha in a zero-sum game environment (before fees) is a challenge.8 Furthermore, the alpha generated by active managers must be sufficient to cover the higher fees usually associated with active management.

Let’s initially consider rewarded factors. With exposures to rewarded factors increasingly accessible via rule-based indexes, simple static exposure to known rewarded factors is no longer widely considered a source of alpha. However, successfully timing that exposure would be a source of alpha. For example, some managers believe part of their skill emanates from an understanding of when rewarded factor returns might be greater than or less than their average returns (factor timing). Hence, in periods when the market return is negative, a manager with an exposure (β) to the Market factor substantially less than 1 will outperform the market and will probably also outperform many other managers. Similarly, a beta greater than 1 in a rising market would drive strong portfolio performance relative to the market. Exposure to the Market factor can be adjusted by investing in securities having, on average, Market betas less than or greater than 1.

Exhibit 4 shows the cumulative value of $100 invested in both the Russell 1000 Growth Index and the Russell 1000 Value Index over a 10-year period ending in 2020. The Growth index produced superior performance over the full 10-year time span.9

Exhibit 4:

Cumulative Value—Russell 1000 Growth and Russell 1000 Value

Source: Morningstar Direct, October 2021).

In principle, alpha can also be generated from timing exposure to unrewarded factors, such as regional exposure, sector exposure, the price of commodities, or even security selection. For example, there is no theoretical basis supporting an expectation that a portfolio with greater-than-benchmark sensitivity to oil prices will be rewarded in the long term. Oil price fluctuations are certainly a risk, but oil price is not a rewarded factor. However, a manager who held a very specific view about the future of oil prices and correctly anticipated the decline in the price of oil that started in June 2014 and ended in March 2016 would have had a strong incentive to reduce his exposure to the energy sector and especially to smaller, less integrated, and more indebted energy companies, which performed poorly as a result of the price movement. A discretionary manager might refer to these as thematic exposures. Although oil prices are not a rewarded “factor,” his skill in timing that exposure would have been amply rewarded. The literature thus far has found little evidence of an ability to consistently time rewarded factors, but it is conceivable that a skillful manager could have identified a factor that has yet to be recognized by the academic or investment community.

In summary, active returns arising from skillful timing of exposure to rewarded factors, unrewarded factors, or even other asset classes (such as cash) constitute a manager’s alpha—the second building block.

Third Building Block: Sizing Positions

Position sizing is about balancing managers’ confidence in their alpha and factor insights while mitigating idiosyncratic risks. Although position sizing influences all three components of Equation 2, its most dramatic impact is often on idiosyncratic risk. For example, consider a manager seeking to create a greater exposure to the Value and Size factors. She could achieve the same average exposure (beta) to these factors by allocating her portfolio to 20 securities or 200 securities. However, the level of idiosyncratic risk and the potential impact of luck on performance will be much greater in the concentrated portfolio. In concentrated portfolios, the volatility of the active return

$(σRA)$(𝜎𝑅𝐴)attributed to idiosyncratic risks (σε) will likely be more significant. In other words, there may be greater deviations between realized portfolio returns and expected returns.

A manager’s choices with respect to portfolio concentration are a function of his beliefs regarding the nature of his investment skill. The factor-oriented manager believes that she is skilled at properly setting and balancing her exposure to rewarded factors. She targets specific exposure to factors (the

$∑(βpk−βbk)×Fk$∑(𝛽𝑝𝑘−𝛽𝑏𝑘)×𝐹𝑘part of Equation 2) and maintains a diversified portfolio to minimize the impact of idiosyncratic risk. The stock picker believes that he is skilled at forecasting security-specific performance over a specific horizon and expresses his forward-looking views using a concentrated portfolio, assuming a higher degree of idiosyncratic risk (the α + ε part of Equation 2).

Diversification, Volatility, and Idiosyncratic risk

The stock picker must carefully consider influences that can substantially alter the absolute or relative risk profile of his portfolio. Consider, for example, the absolute volatility of the Russell 1000 Index and its underlying securities over the 12 months ending in October 2016. During this period:

• the index had an annualized daily volatility of 15.7%;

• the weighted average volatility of all securities in the index was substantially higher, about 26.7%;

• the average volatility of the 100 smallest securities in the index was approximately 41%;

• the average volatility of the 100 largest securities in the index was approximately 24%.

This disparity in individual stock volatility illustrates the potential of diversification. A concentrated portfolio is unlikely to achieve the low volatility of the Russell 1000 unless the manager specifically emphasizes investing in stocks that have a lower average volatility than that of the average security in the index.

Exhibit 5 illustrates the effect of diversification on total portfolio risk at two different levels of average individual stock volatility. (We use the standard deviation of returns as our measure of risk here.) Total portfolio volatility is a function of the average individual stock volatility and the number of securities in the portfolio. The calculations assume an average cross correlation of 0.24, consistent with the historical average correlation for Russell 1000 securities since 1979.

Exhibit 5:

Total Portfolio Volatility as a Function of Concentration and Single Stock Volatility10

	Single Stock Volatility
25%	30%
Number of Securities	Portfolio Volatility
10	14.1%	16.9%
30	12.9%	15.5%
50	12.6%	15.2%
100	12.4%	14.9%
500	12.3%	14.7%

Examining this table closely, we can see that diversification is a powerful tool but that it has its limitations. Even the most diversified portfolio of high-volatility stocks (the 500-stock portfolio with an average single-stock volatility of 30%) cannot achieve the same level of volatility inherent in the portfolios of lower-volatility stocks. Even the most concentrated portfolio of lower-volatility stocks displays a portfolio volatility lower than that of the highly diversified portfolio of higher-volatility stocks.

The concentrated portfolio, however, bears higher idiosyncratic risk, which can substantially influence portfolio performance. The manager’s choices with respect to the magnitude of his active weights and the volatility of the securities with the highest active weights will be significant determinants of the portfolio’s active return and active risk.

Active risk is a measure of the volatility of portfolio returns relative to the volatility of benchmark returns. It is expressed as follows:

Active risk (σRA)=∑t=1T(RAt)2T−1‾‾‾‾‾‾‾‾‾‾⎷Active risk (𝜎𝑅𝐴)=∑𝑡=1𝑇(𝑅𝐴𝑡)2𝑇−13where RAt represents the active return at time t and T equals the number of return periods. Active risk is often referred to as “tracking error.”

All else being equal, a 1.0% allocation to a security that has a 0.2% weighting in the benchmark (Security A) will have a greater effect on the active risk of the portfolio than a 2.0% allocation to a security that has a 2.5% weighting in the benchmark (Security B). Despite the overall smaller position size of Security A, the active decision the manager made with respect to the weighting of Security A (an 80 bp difference from the benchmark weight) is significantly larger than the active decision with respect to the weight of Security B (a 50 bp difference). If Security A also has a higher volatility than Security B, the effect of the active decision will be magnified.

Similarly, all else equal, an active weight of 1.0% on a single security will have a greater impact on active risk than will an active weight of 0.2% on five separate securities. The imperfect cross correlations of active returns of the basket of five stocks would contribute to lowering the level of active risk.

To summarize, a manager’s choice with respect to position sizing is influenced by her investment approach and the level of confidence she places on her analytic work. On the one hand, the stock picker with high confidence in her analysis of individual securities may be willing to assume high levels of idiosyncratic risk. This is consistent with her emphasis on the “α + ε” part of Equation 2. On the other hand, a manager focused on creating balanced exposures to rewarded factors is unlikely to assume a high level of idiosyncratic risk and is, therefore, quite likely to construct a highly diversified portfolio of individual securities.

Integrating the Building Blocks: Breadth of Expertise

The three foregoing building blocks encompass all of Equation 2, which we used to describe the sources of a manager’s active returns:

• exposure to rewarded risks,

• timing of exposures to rewarded and unrewarded risks, and

• position sizing and its implications for idiosyncratic risk.

A manager may be more or less successful at combining these three sources of return into a portfolio. Success is a function of a manager’s breadth of expertise. Broader expertise may increase the manager’s likelihood of generating consistent, positive active returns.

The importance of breadth of expertise is implicit in the fundamental law of active management (covered extensively in the Level II reading “Analysis of Active Portfolio Management”), which implies that confidence in a manager’s ability to outperform his benchmark increases when that performance can be attributed to a larger sample of independent decisions. Independent decisions are not the same thing as individual securities. Independent decisions are uncorrelated decisions, much like two uncorrelated stocks are diversifying. Thus, overweighting both General Motors and Toyota, two auto companies, relative to their benchmark weights are not fully independent decisions because much of their respective returns are driven by common influences—the strength of consumer spending, the price of gasoline, and the price of steel and aluminum, for example. In evaluating portfolio construction, one must distinguish between the nominal number of decisions a manager makes about his active weights and the effective number of independent decisions. Without truly independent decisions, performance may be influenced more significantly by common exposures to specific factors.11 According to the fundamental law, the expected active portfolio return E(RA) is determined by the following:12

$E(RA)=ICBR‾‾‾√σRATC$𝐸(𝑅𝐴)=𝐼𝐶𝐵𝑅𝜎𝑅𝐴𝑇𝐶4where

IC = Expected information coefficient of the manager—the extent to which a manager’s forecasted active returns correspond to the managers realized active returns

BR = Breadth—the number of truly independent decisions made each year

TC = Transfer coefficient, or the ability to translate portfolio insights into investment decisions without constraint (a truly unconstrained portfolio would have a transfer coefficient of 1)

$σRA$𝜎𝑅𝐴= the manager’s active risk

For example, assuming an active risk of 6% (which many institutional investors would consider to be high), a transfer coefficient of 0.25 (representative of a constrained long-only investor), and an information coefficient of 0.10, the manager could expect to generate an active return of 15 bps yearly, on average, if she makes a single independent decision. If the manager wanted to achieve excess return of 1%, she would need to make approximately 40 fully independent decisions. Even if a manager does have positive information and transfer coefficients, it does not necessarily follow that excess return will be positive every year. A horizon of many years is required to have a reasonable probability of generating the expected excess return. However, a larger number of independent decisions will increase the probability of outperforming over a shorter horizon.

What is the implication of making multiple independent decisions? Assume two managers hold similarly diversified portfolios in terms of the number of securities and that both managers have outperformed the market over a specific period. Manager A has a pure value style and favors securities that have a low price-to-book ratio (a single valuation metric), whereas Manager B has a multidimensional, factor-based approach. Manager B’s approach includes considerations related to valuation, price momentum, growth, balance sheet sustainability, quality of management, and so on, and considers a much larger set of metrics for each dimension (such as several metrics for valuation). Manager A’s performance is largely attributed to a single dimension: his narrowly defined value bias. Although he holds 100 securities, he did not make 100 independent decisions.13

Manager B may not have 100 independent decisions embedded in her portfolio, but she likely has more than Manager A. Thus, the historical performance of Manager B may be a more reliable indicator of her ability to outperform in the future because her portfolio construction process integrates several dimensions and metrics, as well as their interactions. Her performance is less likely to be explained by how the market has recently favored a specific management style.

Let’s take this example a bit further. Suppose Manager A makes 20 independent decisions and Manager B makes 40 independent decisions. Assume they both have the same information coefficient (0.2), the same active risk (4%), and the same transfer coefficient (0.6). What would be the expected active return of each manager? Using Equation 4:

Manager 1	$0.2×20‾‾‾√×4$0.2×20×4%×0.6=2.15%
Manager 2	$0.2×40‾‾‾√×4$0.2×40×4%×0.6=3.04%

What if Manager A’s information coefficient was only 0.1? How many independent decisions would the manager need to make to generate the same 2.15% expected active return?

$0.1×x√×4$0.1×𝑥×4%×0.6=2.15%

x ≈ 80

Assuming Manager A maintains a concentrated portfolio of twenty securities, what information coefficient would be required for Manager A to match the expected performance of Manager B?

$x×20‾‾‾√×4$𝑥×20×4%×0.6=3.04%

x ≈ 0.28

Equation 4 illustrates the importance of breadth of expertise. As a practical matter, long-term success is not achieved by being right all the time but, rather, by being right often through small victories achieved consistently over long periods.

EXAMPLE 1

The Building Blocks of Asset Management

1. Proteus was launched as an asset management firm 20 years ago, after receiving assets of $100 million from a seed investor. Today, the firm has grown into a large organization with more than $30 billion in assets. Although the investment process has evolved, the firm has remained true to its core philosophy. It has also delivered strong risk-adjusted performance to its investors.

   Proteus’s emphasis has always been to invest in quality companies, appropriately priced, which are benefiting from positive and sustained price momentum. Although fairly agnostic in terms of portfolio weights compared with benchmark weights, the managers of Proteus believe in avoiding extreme views. For example, sector deviations are limited to between 80% and 120% of benchmark weights plus or minus 500 bps; for example, a sector with a 20% weight in the index could have a weight in the portfolio ranging from 11% [(0.8 × 20%) − 5%] to 29% [(1.2 × 20%) + 5%]. An individual security position can be no more than the lesser of (1) 10 times its weight in the index or (2) its weight in the index + 1%. On average, Proteus’s portfolios hold between 120 and 150 securities. The active risk is above 5%.

   As the firm grew in experience, research, and resources, the process of defining and measuring what is a quality company, appropriately priced, and benefiting from positive momentum evolved. Initially, the firm avoided companies that were the most indebted within their sector and favored those that generated strong cash flows to sales. It also favored companies that had a lower price-to-book value and had positive price momentum in the last 12 months.

   Today, Proteus still emphasizes quality, valuation, and price momentum but has considerably improved how those characteristics are measured and weighed. It now evaluates 45 metrics related to the financial health of the companies, the quality of its financial reporting, its valuation within its sector, and its short- and medium-term price momentum. It also developed its own weighting mechanism to appropriately weight each metric. The managers at Proteus believe their competitive advantage is the effort they invest in identifying, measuring, and weighing these metrics.

   Discuss the contributions of rewarded factors, alpha skills, position sizing, and breadth of expertise for Proteus.

   Solution:

   Overall, Proteus has integrated all the primary dimensions of the investment process.

   • Rewarded factors: Proteus recognizes the existence of rewarded factors, and it has significantly enhanced its measures of Quality, Value, and Momentum over time.

   • Alpha skills: Given the commercial success of Proteus as a firm, we might safely assume that there is an alpha component in the process.

   • Position sizing: Position size limits are integrated into the investment process to ensure diversification limits idiosyncratic risks.

   • Breadth of expertise: Proteus has 20 years of experience refining and improving an investment process based on a consistent investment philosophy.

https://study.cfainstitute.org/app/cfa-institute-program-level-iii-for-august-2024#read/study_task/2564193/portfolio-construction-approaches-1 PORTFOLIO CONSTRUCTION APPROACHES

Learning Outcome

• discuss approaches for constructing actively managed equity portfolios

Portfolio construction is part art and part science. It is about investment philosophy and the implementation of that philosophy. It requires an understanding of the technical principles of portfolio construction, filtered through a manager’s core beliefs regarding her ability to add value using the building blocks discussed earlier:

• Factor exposures: How does she create her factor exposures? Does the manager believe she is skilled at extracting return premiums from rewarded factors? Or are her exposures to rewarded factors a residual of her in-depth research into the securities’ fundamentals?

• Timing: Does she believe that she has skill in generating alpha through timing of portfolio exposures to rewarded and unrewarded factors or to security selection uncorrelated with exposures to either rewarded or unrewarded factors?

• Position sizing: How does she size portfolio positions? Is she confident about her expected return forecasts, and therefore runs a high-conviction portfolio? Or does she seek to reduce idiosyncratic risk by running a highly diversified portfolio?

• Breadth or depth: Does she rely on a specialized but narrower skill set or on a greater breadth of expertise?

A manager’s portfolio construction process should reflect her beliefs with respect to the nature of her skills in each of these areas. The majority of investment approaches can be classified as either

• systematic or discretionary (the degree to which a portfolio construction process is subject to a set of predetermined rules or is left to the discretionary views of the manager)

and

• bottom-up or top-down (the degree to which security-specific factors, rather than macroeconomic factors, drive portfolio construction).

In addition, these approaches can vary in the extent to which they are benchmark aware versus benchmark agnostic. Each manager’s investment approach is implemented within a framework that specifies the acceptable levels of active risk and Active Share relative to a clearly articulated benchmark. (Active Share is a measure of how similar a portfolio is to its benchmark.) A manager may emphasize these dimensions to varying degrees as he attempts to differentiate his portfolio from the benchmark.

The Implementation Process: The Choice of Portfolio Management Approaches

We previously identified three primary building blocks that managers can use in constructing a portfolio that reflects their core beliefs. Let’s look at these in a little more detail, beginning with the systematic–discretionary continuum.

Systematic vs. Discretionary

How are a manager’s beliefs regarding rewarded factor exposures, timing of factor exposures, exposure to unrewarded factors, and willingness to assume idiosyncratic risk reflected in a systematic investment process and in a discretionary investment process?

• Systematic strategies are more likely to be designed around the construction of portfolios seeking to extract return premiums from a balanced exposure to known, rewarded factors.

• Discretionary strategies search for active returns by building a greater depth of understanding of a firm’s governance, business model, and competitive landscape, through the development of better factor proxies (e.g., a better definition of Quality), or through successful timing strategies. Factor timing is a challenging endeavor, and few factor-based systematic strategies have integrated a factor timing approach.

• Systematic strategies typically incorporate research-based rules across a broad universe of securities. For example, a simple systematic value methodology could filter out the 50% of securities that have the highest price-to-book ratio and then equally weight the remaining securities, leading to small individual portfolio positions. A more comprehensive approach might integrate a much larger number of considerations and balance total portfolio risk equally across them.

• Discretionary strategies integrate the judgment of the manager, usually on a smaller subset of securities. While a discretionary value manager might also rely on financial metrics to estimate the value characteristics of each security, she is likely to use her judgment to evaluate the relative importance of this information and assign appropriate weights to each security. A discretionary manager is also likely to integrate nonfinancial variables to the equation, such as the quality of management, the competitive landscape, and the pricing power of the firm. (Systematic strategies also integrate judgment, but their judgment is largely expressed up front through the design of the strategy and the learning process that comes with its implementation.)

• Systematic strategies seek to reduce exposure to idiosyncratic risk and often use broadly diversified portfolios to achieve the desired factor exposure while minimizing security-specific risk.

• Discretionary strategies are generally more concentrated portfolios, reflecting the depth of the manager’s insights on company characteristics and the competitive landscape.

• Systematic strategies are typically more adaptable to a formal portfolio optimization process. The systematic manager must, however, carefully consider the parameters of that optimization. What objective function is he seeking to maximize (information ratio, Sharpe ratio, index or factor exposure, etc.) or minimize (volatility, downside risk, etc.)? Will elements of his investment style (such as performance and valuation metrics) be incorporated into the objective function or into the constraints?

• Discretionary portfolio managers typically use a less formal approach to portfolio construction, building a portfolio of securities deemed attractive, subject to a set of agreed-upon risk constraints.

Bridging the Divide

The philosophical divide between systematic and discretionary managers seems to be shrinking. Systematic and discretionary strategies were commonly differentiated in terms of their breadth and depth (discretionary managers conducting more in-depth research on a sub-set of the securities universe) and systematic managers having more breadth (less in-depth research across the entire universe of securities). Although this remains generally true today, research and technology have been narrowing the gap. Advancements in and the accessibility of technology, together with the greater range of quality data available, are allowing discretionary managers to extend their in-depth analyses across a broader universe of securities. Technology also allows systematic managers to design strategies that can capture risk premiums in rewarded factors, a source of active returns that was previously considered to be part of the alpha of discretionary managers.

Bottom-Up vs. Top-Down

A top-down approach seeks to understand the overall geo-political, economic, financial, social, and public policy environment and then project how the expected environment will affect countries, asset classes, sectors, and then securities. An investment manager who projects that growth companies will outperform value companies, that financials will outperform industrials, that the US market will outperform the European market, that oil prices will increase, or that cash will outperform equity and then targets individual securities and/or a cash/stock allocation to reflect these views is following a top-down approach.

A manager following a bottom-up approach develops his understanding of the environment by first evaluating the risk and return characteristics of individual securities. The aggregate of these risk and return expectations implies expectations for the overall economic and market environment. An investment manager who expects Ford to outperform GM, AstraZeneca (a bio-pharmaceutical company) to outperform Ford, and Sony to outperform AstraZeneca and builds a portfolio based on these stock-specific forecasts is following a bottom-up approach. Although the resulting portfolio will contain an implicit expectation for sector, style, and country performance, this is nonetheless a bottom-up approach.

• Both top-down and bottom-up strategies typically rely on returns from factors. However, top-down managers are more likely to emphasize macro factors, whereas bottom-up managers emphasize security-specific factors.

• A top-down investment process contains an important element of factor timing. A manager who opportunistically shifts the portfolio to capture returns from rewarded or unrewarded factors, such as country, sectors, and styles, is following a top-down investment process. They may also embrace the same security characteristics sought by bottom-up managers as they translate their macro views into security-specific positions. A top-down investment process is also more likely to raise cash opportunistically when the overall view of the Market factor is unfavorable.

• Bottom-up managers may embrace such styles as Value, Growth at Reasonable Price, Momentum, and Quality. These strategies are often built around documented rewarded factors, whether explicitly or implicitly.

• A top-down manager is likely to run a portfolio concentrated with respect to macro factor exposures. Bottom-up managers and top-down managers can run portfolios that are either diversified or concentrated in terms of securities. Both a bottom-up stock picker and a top-down sector rotator can run concentrated portfolios. Both a bottom-up value manager and a top-down risk allocator can run diversified portfolios.

Some managers will incorporate elements of both top-down and bottom-up investment approaches.

A Summary of the Different Approaches

While most managers make some use of all the building blocks, we can make some general assertions about the relative importance and use of these building blocks to each of the implementation choices. They are summarized in the four quadrants of Exhibit 6.

Exhibit 6:

Approaches and Their Use of Building Blocks

• Exposure to rewarded factors can be achieved with either a systematic or discretionary approach.

• Bottom-up managers first emphasize security-specific factors, whereas top-down managers first emphasize macro factors.

• Factor timing is more likely to be implemented among discretionary managers, especially those with a top-down approach.

• Systematic managers are unlikely to run concentrated portfolios. Discretionary managers can have either concentrated or diversified portfolios, depending on their strategy and portfolio management style.

• In principle, a systematic top-down manager would emphasize macro factors and factor timing and would have diversified portfolios. However, there are few managers in this category.

https://study.cfainstitute.org/app/cfa-institute-program-level-iii-for-august-2024#read/study_task/2564203/measures-of-benchmark-relative-risk-1

MEASURES OF BENCHMARK-RELATIVE RISK

Learning Outcomes

• discuss approaches for constructing actively managed equity portfolios

• distinguish between Active Share and active risk and discuss how each measure relates to a manager’s investment strategy

Managers have very specific beliefs about the level of security concentration and the absolute or relative risk that they (and their investors) are willing to tolerate. Relative risk is measured with respect to the benchmark that the manager has adopted as representative of his investment universe. We know that a manager must have active weights different from zero in order to outperform his benchmark. How do we measure these weights?

There are two measures of benchmark-relative risk used to evaluate a manager’s success—Active Share and active risk—and they do not always move in tandem. A manager can pursue a higher Active Share without necessarily increasing active risk (and vice versa).

Active Share is easier to calculate than active risk; one only needs to know the weight of each security in the portfolio and the weight of the security in the benchmark. The formula for Active Share is shown in Equation 5. It measures the extent to which the number and sizing positions in a manager’s portfolio differ from the benchmark.

$Active Share=12∑i=1n∣∣Weightportfolio,i−Weightbenchmark,i∣∣$Active Share=12∑𝑖=1𝑛|Weight𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜,𝑖−Weight𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘,𝑖|5where n represents the total number of securities that are in either the portfolio or the benchmark.

The Active Share calculation involves no statistical analysis or estimation; it is simple arithmetic. Active Share is a measure of the differentiation of the holdings of a portfolio from the holdings of a chosen benchmark portfolio. It measures the proportion of a portfolio’s holdings that is different from the benchmark for that portfolio. The Active Share is 0 for a portfolio that matches the benchmark and 100% for a portfolio that shares no investments with those of the benchmark. The percentage of portfolio assets deployed in the same way as the benchmark is equal to 100% minus the portfolio’s Active Share. For example, an Active Share of 80% implies that 20% of the portfolio capital was invested in a similar way as the index. There are only two sources of Active Share:

• Including securities in the portfolio that are not in the benchmark

• Holding securities in the portfolio that are in the benchmark but at weights different than the benchmark weights

If two portfolios are managed against the same benchmark (and if they invest only in securities that are part of the benchmark), the portfolio with fewer securities will have a higher level of Active Share than the highly diversified portfolio. A portfolio manager has complete control over his Active Share because he determines the weights of the securities in his portfolio.

Active risk is a more complicated calculation. Like Active Share, active risk depends on the differences between the security weights in the portfolio and the security weights in the benchmark. There are two different measures of active risk. One is realized active risk, which is the actual, historical standard deviation between the portfolio return and the benchmark return as described in Equation 3. This number relies on historical returns and is easy to calculate. But portfolio construction is a forward-looking exercise, and in this context, the relevant measure is predicted active risk, which requires a forward-looking estimate of correlations and variances.14 As the accuracy of the forward-looking estimates of correlations and variances improves, the likelihood of better portfolio outcomes also improves.

The variance–covariance matrix of returns is very important in the calculation of active risk. Although portfolios that have higher active risk tend to have higher Active Share (and vice versa), this is not always the case. For example, underweighting one bank stock to overweight another bank stock will likely have less effect on active risk than underweighting one bank stock and overweighting an information technology stock. Active risk is affected by the degree of cross correlation, but Active Share is not. Active Share is not concerned with the efficiency of diversification.15 If the extent of underweighting and overweighting is the same in the bank/bank over-/underweight and in the bank/technology over-/underweight, the effect on Active Share would be identical. The effect on active risk would be different, however, because the correlation of the bank/technology pair is most likely lower than the correlation of the bank/bank pair. This highlights an important difference in Active Share versus active risk. A portfolio manager can completely control Active Share, but she cannot completely control active risk because active risk depends on the correlations and variances of securities that are beyond her control. Recall that in Equation 2, we decomposed active return into returns to factors, alpha, and idiosyncratic risk.

$σRA=σ2(∑(βpk−βbk)×Fk)+σ2e‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√$𝜎𝑅𝐴=𝜎2(∑(𝛽𝑝𝑘−𝛽𝑏𝑘)×𝐹𝑘)+𝜎𝑒26

Here, we show that the active risk of a portfolio

$(σRA)$(𝜎𝑅𝐴)is a function of the variance attributed to the factor exposure$σ2(∑(βpk−βbk)×Fk)$𝜎2(∑(𝛽𝑝𝑘−𝛽𝑏𝑘)×𝐹𝑘)and of the variance attributed to the idiosyncratic risk$(σ2e)$(𝜎𝑒2).16 Although realized active risk will almost never be identical to predicted active risk, existing risk forecasting methodologies allow the manager to predict active risk over a short horizon with a high level of accuracy. Managers can then control the level of active risk through portfolio structure.

Sapra and Hunjan (2013) derived a relationship between active risk, Active Share, and factor exposure for an unconstrained investor, assuming a single-factor model. They found that

• high net exposure to a risk factor will lead to a high level of active risk, irrespective of the level of idiosyncratic risk;

• if the factor exposure is fully neutralized, the active risk will be entirely attributed to Active Share;

• the active risk attributed to Active Share will be smaller if the number of securities is large and/or average idiosyncratic risk is small; and

• the level of active risk will rise with an increase in factor and idiosyncratic volatility (such as occurred in 2008).17

These observations are very intuitive: Active risk increases when a portfolio becomes more uncorrelated with its benchmark. As discussed previously, although overweighting or underweighting GM relative to Ford will generate some Active Share, it will typically not generate much active risk. However, overweighting or underweighting energy firms versus financial firms, small-cap firms versus large-cap firms, or growth firms versus value firms will certainly contribute more to active risk.

So how do we use these two measures to discriminate between different portfolio management approaches and management styles? Using the observations from Sapra and Hunjan (2013), we could characterize a manager as

• factor neutral, factor diversified, or factor concentrated and as

• diversified (with low security concentration and low idiosyncratic risk) or concentrated (with high security concentration and high idiosyncratic risk).18

Exhibit 7 illustrates how various combinations of factor exposure and idiosyncratic risk affect Active Share and active risk.19

Exhibit 7:

Investment Styles, Active Share, and Active Risk

*A closet indexer is defined as a fund that advertises itself as being actively managed but is substantially similar to an index fund in its exposures.

Using this framework, we can classify most equity strategies in terms of active risk and Active Share by analyzing the specific management style of the manager. For example, most multi-factor products have a low concentration among securities, often holding more than 250 positions (the purpose of these products is to achieve a balanced exposure to risk factors and minimize idiosyncratic risks). They are diversified across factors and securities. Thus, they typically have a high Active Share, such as 0.70, but they have reasonably low active risk (tracking error), often in the range of ±3%.

The concentrated stock picker, in contrast, has both a high Active Share (typically above 0.90) and a high active risk (such as 8%–12% or higher).20 (The average active manager owns about 100 stocks, and fewer than 20% of managers own more than 200 stocks.) It follows, then, that the level of idiosyncratic risk in the average active discretionary portfolio is greater than that of the average multi-factor fund, with its 250+ positions. Therefore, on average, we could expect the portfolio of a typical discretionary manager to display higher active risk.

Consequently, a manager can increase his degree of control over the level of Active Share and/or active risk in his portfolio by decreasing his security concentration. For example, it would not be uncommon for a sector rotator—typically a high-active-risk strategy—to have an active risk above 8%. If he chooses to run a concentrated portfolio, he might also have high Active Share. Or he can diversify his portfolio and reduce his Active Share.21

Petajisto (2013) provided examples of funds of different styles and their corresponding active risk and Active Share; see Exhibit 8. The risk tolerance and portfolio construction approach of each manager is partially revealed by his Active Share and active risk. Exhibit 9 presents the same information but plots it in the Active Share/active risk dimension using the format of Exhibit 7.

Exhibit 8:

Active Risk, Active Share, and Portfolio Styles Examples

Name of Fund	Style/Comments	Active Risk	Active Share
Vanguard Index Fund	Indexed	0.0%	0.00
RiverSource Disciplined Equity Fund	Large-Cap Growth (Small active weight, limited factor timing)	4.4%	0.54
T. Rowe Price Mid-Cap Value Fund	Mid-Cap Value (Limited active weights on sectors but significant stock picking)	5.4%	0.93
AIM Constellation Fund	Large-Cap Growth (Significant sector bets )	9.7%	0.66
GMO Quality Fund	Mega-Cap Core (Timing on a number of factors and cash)	12.9%	0.65
Sequoia	Stock Picker (Highly concentrated positions)	14.1%	0.97

Source: Petajisto (2013).

Exhibit 9:

Active Risk, Active Share, and Portfolio Styles

Active risk and Active Share provide information about the level of managers’ activism against their benchmark, but there is little research on the relative efficiency of different asset management styles translating higher active risk or Active Share into higher active returns. However, many investors are using Active Share to assess the fees that they pay per unit of active management. For example, a fund with an Active Share of 0.25 (a closet indexer) would be considered expensive relative to a fund with an Active Share of 0.75 if both funds were charging the same fees.

Not all investment products neatly fall into the categorization we have just presented. Niche equity strategies, such as statistical arbitrage, event-driven investing, and activist investing, focus on generating alpha returns generally without regard to factor exposures or factor timing. These strategies do, however, typically assume a high level of idiosyncratic risk.

EXAMPLE 2

Portfolio Construction—Approaches and Return Drivers

1. You are evaluating two equity managers. Explain how Manager A, with his high level of Active Share, is able to achieve such a low active risk. What are the implications for Manager B’s performance relative to that of Manager A?

   	Manager A	Manager B
   Active Share	0.73	0.71
   Active risk	2.8%	6.0%
   Number of positions	120	125

   Solution to 1:

   Managers A and B have a similar number of positions and similar Active Share. Manager B has much higher active risk. A high Active Share says only that a manager’s security-level weights are quite different from those of the index. A 0.5% underallocation to one security and a 0.5% over-allocation to another security will have the same impact on Active Share whether these two securities are in the same sector or in different sectors. Given similar levels of Active Share, it is likely that Manager B’s active risk is driven by active decisions at the sector level rather than at the security level. Clearly, they implement very different investment strategies. Although we cannot draw a direct conclusion about the ability of Manager B to outperform Manager A, we can assume that the realized outcomes of Manager B are likely to be much more dispersed about the benchmark (both in positive and negative directions) given the higher level of active risk.

2. Discuss the drivers of return for Managers A and B.

   	Manager A	Manager B	Factor Returns
   Monthly performance in excess of the risk-free rate	0.65%	0.65%
   “Alpha” (monthly)	0.00%	0.20%
   Beta to:
   Market*	0.99	1.05	0.45%
   Size	0	−0.2	0.20%
   Value	0.15	0.05	0.35%
   Momentum	0.25	0	0.60%
   R-squared	0.99	0.78

   * Market factor is built from a much larger universe of securities than traditional benchmarks such as the Russell 1000. Therefore, we should not expect the β of indexes to the Market factor to be necessarily equal to one.

   Solution to 2:

   Both managers generated the same absolute return, but they achieved their performance in very different ways. All of Manager A’s performance can be explained from exposure to rewarded factors. There is no alpha, and the high R2 shows that the four factors explain much of the monthly variability in returns. Manager A did outperform the Market factor by 20 bps (0.65% − 0.45%). The excess return can be attributed to the significant exposure (0.25) to the strong-performing Momentum factor (0.60%). Exposure to the Value factor explains the balance.

   Manager B generated significant alpha (20 bps per month). The relatively low R2 indicates that much of the variability of returns is unexplained by the factors. Manager B’s performance must, therefore, be attributed to either her alpha skills or idiosyncratic risks that favored the manager’s investment approach during the period.

3. Based on the information provided below regarding four managers benchmarked against the MSCI World Index, identify the manager most likely to be a:

   1. closet indexer.

   2. concentrated stock picker.

   3. diversified multi-factor investor.

   4. sector rotator.

   Justify your response.

   Manager Constraints:	A	B	C	D
   Target active risk	10%	1%	4%	7%
   Max. sector deviations	0%	3%	10%	15%
   Max. risk contribution, single security	5%	1%	1%	3%

   Solution to 3:

   Manager B is a closet indexer. The low targeted active risk combined with the narrow sector deviation constraint indicates that the manager is making very few active bets.

   Manager A is likely a concentrated stock picker. The 10% active risk target indicates a willingness to tolerate significant performance deviations from the market. The 5% limit on a single security’s contribution to portfolio risk indicates he is willing to run a concentrated portfolio. The unwillingness to take sector deviations combined with the high tolerance for idiosyncratic risk indicates that the manager likely focuses on stock selection and is, therefore, a stock picker.

   Manager C limits single-security risk contribution to no more than 1%, which implies a highly diversified portfolio. The significant sector deviations despite this high diversification are often indicative of a multi-factor manager. The relatively low tracking error further supports the argument that Manager C is a multi-factor manager.

   Manager D has characteristics consistent with a sector rotator. The significant active risk and high tolerance for sector deviations and security concentration are what one would expect to find with a sector rotator.

4. Discuss the main differences between top-down and bottom-up portfolio management approaches and how they relate to two of the building blocks: exposure to rewarded factors and alpha.

   Solution to 4:

   Factor exposure.

   Bottom-up managers look at characteristics of securities to build their portfolios. The factor exposure inherent in their portfolios may be intentional, or it may be a by-product of their security selection process. Top-down managers articulate a macro view of the investment universe and build a portfolio emphasizing the macro factors that reflect those views. Although their macro views could then be translated into security views using a bottom-up approach, their performance will likely be dominated by their macro-level factor exposures.

   Alpha.

   In the context of Equation 2, the alpha of bottom-up managers is most likely attributable to their security selection skills. Some portion of their active return can also be explained through exposure to rewarded factors. Top-down managers’ alphas are largely derived from factor timing.

https://study.cfainstitute.org/app/cfa-institute-program-level-iii-for-august-2024#read/study_task/2564213/objectives-and-constraints-1

OBJECTIVES AND CONSTRAINTS

Learning Outcomes

• discuss approaches for constructing actively managed equity portfolios

• distinguish between Active Share and active risk and discuss how each measure relates to a manager’s investment strategy

The simplest conceptual way to think about portfolio construction is to view it as an optimization problem. A standard optimization problem has an objective function and a set of constraints. The objective function defines the desired goal while the constraints limit the actions one can take to achieve that goal. Portfolio managers are trying to achieve desirable outcomes within the bounds of permissible actions. The nature of the objective function and the nature and specifics of the constraints can be indicative of an investment manager’s philosophy and style.

A common objective function in portfolio management is to maximize a risk-adjusted return. If risk is being measured by predicted active risk, then the objective function is seeking to maximize the information ratio (the ratio of active return to active risk). If risk is being measured by predicted portfolio volatility, then the objective function is seeking to maximize the Sharpe ratio (the ratio of return in excess of the risk-free rate to portfolio volatility). Ideally, these objective functions would specify net returns—adjusted for the costs associated with implementation.

Typical constraints in the portfolio optimization problem may include limits on geographic, sector, industry, and single-security exposures and may also specify limits on transaction costs (to limit turnover and/or help manage liquidity issues). They may also include limits on exposure to specific factors; for example, the investment process may specify a required minimum market capitalization for any single security or a minimum weighted average capitalization for the portfolio as a whole. Or it may specify a maximum price-to-book ratio for any single security or a maximum weighted average price-to-book ratio for the portfolio. Constraints can be defined relative to the benchmark or without regard to it. Setting constraints that properly express the risk dimensions being monitored, the desired level of risk taking, and the preferred portfolio structure while still allowing sufficient flexibility to achieve the risk and return goals is a challenging task. In principle, the active equity manager’s portfolio is the final blend that maximizes the objective function subject to the portfolio constraints.

Not all portfolio managers engage in such a formalistic, scientific approach to portfolio construction. The objectives and constraints of systematic managers are explicitly specified, whereas those of discretionary managers are less explicitly specified. However, most managers at least conceptually optimize their portfolios using the expected returns for each security, their own view of risk, and constraints imposed by the stated portfolio construction process or by the client. For our purposes, it is useful to frame the problem in this technical manner to provide a framework for discussion of the portfolio construction process.

Objectives and constraints may be stated in absolute terms or relative to a benchmark. Exhibit 10 illustrates two generic objective functions—one that is absolute and one that is relative. Each is subject to a few specific constraints.

Exhibit 10:

Objective Functions and Constraints

	Absolute Framework	Relative Framework
Objective Function:	Maximize Sharpe Ratio	Maximize Information Ratio
Constraint
Individual security weights (w)	wi ≤ 2%	|wip − wib| ≤ 2%
Sectors weights (S)	Si ≤ 20%	|Sip − Sib| ≤ 10%
Portfolio volatility (σ)	σp < 0.9 σb	—
Active risk (TE)	—	TE ≤ 5%
Weighted average capitalization (Z)	Z ≥ 20bn	Z ≥ 20bn

• The absolute approach seeks to maximize the Sharpe ratio; the relative approach seeks to maximize the information ratio.

• The absolute approach limits any single security position to no more than 2% of the portfolio and any single sector to no more than 20% of the portfolio; the relative approach imposes a constraint that a security must remain within ±2% of its index weight and sector weights must remain within ±10% of the index weights.

• The absolute approach imposes a portfolio volatility limit equal to 90% of the estimated benchmark volatility and imposes a minimum weighted average security capitalization of $20 billion; the relative approach imposes a 5% active risk limit and the same capitalization constraint.

• Managers can also combine relative and absolute constraints in the same framework, such as limiting sector deviations against a benchmark while imposing absolute limits on security positions.

Other optimization approaches specify their objectives in terms of the risk metrics, such as portfolio volatility, downside risk, maximum diversification, and drawdowns. These approaches do not integrate an explicit expected return component. However, they do implicitly create an exposure to risk factors. For example, products built using a risk-based objective function (such as minimum variance or maximum diversification)22 often exhibit a Market beta below 1.0 and have a statistically significant exposure to the Value factor and to the low-minus-high-β factor.23 This occurs because an objective function that seeks to manage or minimize risk will tend to favor value and low-beta securities.

Finally, not all objective functions are explicitly concerned with risk or returns. For example, Equation 7 shows an explicit objective function that might be specified by a quantitative manager seeking to maximize exposure to rewarded factors:

$MAX(∑i=1N13Sizei+13Valuei+13Momentumi)$MAX(∑𝑖=1𝑁13Size𝑖+13Value𝑖+13Momentum𝑖)7where Sizei, Valuei, and Momentumi are standardized24 proxy measures of Size, Value, and Momentum for security i.25 The portfolio may also be subject to additional constraints similar to those in Exhibit 10.

Of course, articulating an explicit objective of maximizing the Sharpe ratio or the information ratio or minimizing a given risk measure implies that we have information about expected returns and expected risk. Some managers—typically discretionary managers—do not make explicit return and risk forecasts and instead seek to “maximize” their exposure to securities having specific characteristics. Embedded in their investment process is an implicit return-to-risk objective.

For example, the objective function of a discretionary manager may be expressed in a mission statement such as: “We are a deep value manager in large-cap US equity with a concentrated, best ideas style.” They then identify securities possessing deep value characteristics (as they define value). The portfolio construction process will balance security concentration and sector exposure as the manager seeks to maximize the return at an acceptable level of risk. The allocation may be driven by the manager’s judgment about the risk and return trade-offs, or a formal risk management protocol may be used to drive the allocation process, or a feedback mechanism may be put in place to ensure that constraints are being respected as the portfolio is being assembled or rebalanced by the manager.

When an explicit objective function is not used, many heuristic methodologies can be considered to determine security weighting in a portfolio. We list a few examples below.

• Identify securities that have the desired characteristics and weight them relative to their scoring on these characteristics. For example, a security with a price-to-book ratio of 8 would have half the weight of a security with a price-to-book ratio of 4.

• Identify securities that have the desired characteristics and weight them per their ranking or risk on these characteristics. For example, if there are five securities ranked on their price-to-book ratios, the security with the lowest price-to-book ratio would constitute 33% of the portfolio value [5/(5 + 4 + 3 + 2 + 1)] and the security with the highest price-to-book ratio would constitute 6.7% of the portfolio value [1/(5 + 4 + 3 + 2 + 1)].

• Identify stocks that have the desired characteristics, rank them according to how strongly they adhere to these characteristics, select the top x% of these stocks, and assign them portfolio weights based on one of several methodologies, such as equal weight, equal risk, scoring, or ranking on these characteristics. For example, if there are 1,000 securities in an index, the 500 securities with the lowest price-to-book ratios could be selected. Each security would then be weighted using the chosen methodology.

Although these alternative methodologies may be intuitively appealing, they may not allocate active risk as efficiently as a formal optimization framework would. The constraints and objective function will be strongly reflective of the philosophy and style of a manager. For example, a stock picker is likely to have fewer and more permissive constraints on security weights than a multi-factor manager seeking to minimize idiosyncratic risks. A manager specializing in sector rotation will have more permissive constraints with respect to sector concentration than a value manager.

EXAMPLE 3

Approaches to Portfolio Construction

1. Marc Cohen is a portfolio manager whose primary skill is based on having a good understanding of rewarded sources of risk. He does not believe in factor timing. Sophie Palmer is a portfolio manager who believes she has skill in anticipating shifts in sector performance. She does not profess to have skill in individual security selection but tolerates significant deviations in sector exposure. Sean Christopher is a stock picker running a high-turnover strategy based on recent movements in market price among the Russell 1000 stock universe. He is highly sector and size agnostic and has significant active risk. Discuss the expected profile of each manager in terms of

   • the sensitivity of their performance to risk factors,

   • the level of security concentration, and

   • the contribution of idiosyncratic risk to the total active risk of their portfolios.

   Solution:

   We should be able to explain a large part of Cohen’s excess return using the performance of rewarded factors. We would not expect alpha to be a significant component of his performance. His exposure to risk factors would be relatively stable across time periods because he does not believe in factor timing. Because his primary emphasis is on long-term exposure to risk factors, he would hold a highly diversified portfolio to minimize idiosyncratic risk. As a multi-factor manager running a diversified portfolio, his active risk should be relatively low.

   Palmer’s performance is likely to be explained by tactical exposures to sectors, which we have said are unrewarded risks, rather than static exposures to known rewarded factor returns. Her excess performance against her benchmark will likely be attributed to alpha. With no professed skill in security selection, she is likely to hold a large number of securities in each sector to minimize idiosyncratic risk. The active risk arising from her sector weightings will overshadow the active risk from security weightings. Her active risk is likely to be higher than that of Marc Cohen.

   Christopher’s portfolio is more difficult to assess. His focus on recent price movements indicates a sensitivity to the Momentum factor, although the sensitivity to this factor may depend on the time horizons and methodologies he uses to measure price momentum. He is size agnostic and may at times have exposure to the Size factor, a smaller-cap bias. With the information given, we cannot make an inference regarding the diversification of his portfolio. As a discretionary manager, he is to run a concentrated portfolio in order to more closely monitor his positions. However, if he makes extensive use of quantitative tools in monitoring his portfolio, he may be able to hold a more diversified portfolio. His active risk will be high, and his performance is likely to have a significant alpha component, whether positive or negative.

EXAMPLE 4

Approaches to Portfolio Construction

1. Manager A uses a scoring process and seeks to maximize the portfolio score based on the factor characteristics of individual securities. His purpose is not to time factor exposure but to achieve an appropriate diversification of factor risks. His approach is fully systematic, and he has a tracking error constraint of less than 4%. No one position can be greater than 2%, irrespective of its benchmark weight.

   Manager B has a strong fundamental process based on a comprehensive understanding of the business model and competitive advantages of each firm. However, Manager B also uses sophisticated models to make explicit three-year forecasts of the growth of free cash flow to determine the attractiveness of each security’s current valuation. A committee of portfolio managers meets once a month to debate the portfolio allocation. The manager has a large staff of portfolio managers and analysts and thus can maintain wide coverage of companies within each industry. Individual positions are constrained to the lower of (1) benchmark weight + 2% or (2) five times the benchmark weight.

   Manager C specializes in timing sector exposure and has little appetite for idiosyncratic risks within sectors. Using technical analyses and econometric methodologies, she produces several types of forecasts. The manager uses this information to determine appropriate sector weights. The risk contribution from any single sector is limited to 30% of total portfolio risk. The final decision on sector allocations rests with the manager.

   Discuss each manager’s implementation approach, security selection approach, portfolio concentration, objective function, and constraints.

   Solution:

   Manager A is best characterized as a systematic, bottom-up manager.

   • Implementation approach. An implementation approach that is fully quantitative (allocations are unaffected by a portfolio manager’s judgment) is systematic.

   • Security selection approach. A scoring process that ranks individual securities based on their factor characteristics is a bottom-up approach.

   • Concentration. Although the limit of no more than 2% of the portfolio in any single position means the portfolio could hold as few as 50 securities, the tracking error constraint of 4% indicates that the portfolio is likely diversified.

   • Objective function. A process that aims to maximize the portfolio’s score based on the factor characteristics of single securities is an example of an explicit objective function.

   • Constraints. The tracking error constraint of less than 4% is a relative constraint function. The limit on any single position to no more than 2% of the portfolio is an absolute—not a relative—constraint. It does not depend on benchmark weights.

   The following table summarizes this information for all three managers:

   	Manager A	Manager B	Manager C
   Implementation approach	Systematic	Discretionary	Discretionary
   Security selection approach	Bottom-up	Bottom-up	Top-down
   Portfolio concentration	Diversified	Diversified	Security diversified Factor concentrated
   Objective function	Explicit	Explicit	Explicit
   Constraints	Relative and absolute	Relative	Absolute

https://study.cfainstitute.org/app/cfa-institute-program-level-iii-for-august-2024#read/study_task/2564223/absolute-vs-relative-measures-of-risk-1 ABSOLUTE VS. RELATIVE MEASURES OF RISK

Learning Outcomes

• discuss the application of risk budgeting concepts in portfolio construction

• discuss risk measures that are incorporated in equity portfolio construction and describe how limits set on these measures affect portfolio construction

Risk budgeting is a process by which the total risk appetite of the portfolio is allocated among the various components of portfolio choice. As an example, if the portfolio manager has an ex ante active risk budget explicitly provided by the client, with risk budgeting, she seeks to optimize the portfolio’s exposures relative to the benchmark to ensure that the choices she makes among stocks, sectors, or countries make efficient use of the active risk budget. But ex ante active risk is just one possible measure of risk. An effective risk management process requires that the portfolio manager do the following:

• Determine which type of risk measure is most appropriate to her strategy.

  • For example, a long/short equity manager benchmarked against a cash plus target will usually prefer an absolute risk measure (such as total volatility of portfolio returns), whereas a long-only equity manager benchmarked against a capitalization-weighted index may prefer a relative risk measure (such as active risk).

• Understand how each aspect of the strategy contributes to its overall risk.

  • Total portfolio variance may be dominated by exposure to rewarded risk factors or by allocations to countries, sectors, or securities. If these exposures are dynamic, the timing of portfolio exposures also introduces risk. An important step in risk budgeting is to understand what drives a portfolio’s risk and to ensure the portfolio has the right kinds of specific risks.

• Determine what level of risk budget is appropriate.

  • Targeted levels of risk vary widely among managers and strategies. Although there are general principles that limit the level of advisable risk in a specific strategy, it is also very much a policy issue.

• Properly allocate risk among individual positions/factors.

  • Whether the risk measure is absolute or relative, managers must efficiently allocate their targeted risk budget.

Absolute vs. Relative Measures of Risk

The choice between an absolute and a relative risk portfolio management orientation is driven by the mandate of the manager and the goals of investors. If the mandate is to outperform a market index over a horizon, such as three years, then the manager will focus on active risk. If the investment objective is expressed in terms of total returns, then the manager will likely focus on the volatility of portfolio returns.

Managers’ beliefs about how they add value can influence the choice between an absolute and a relative risk measure. Some managers may believe that the benchmark-relative constraints so common in the world of investment management today inhibit the ability of their investment approach to realize its full potential. To address this issue, they may prefer either an absolute risk measure or a relative risk measure with a wide range of allowed deviations. An absolute risk measure is just that: Whatever the risk threshold, the portfolio risk must remain at or below that level. The manager is free to construct his portfolio without regard to the characteristics of the benchmark. A relative risk measure with wide bands around a central target implies a benchmark-relative approach with significant degrees of freedom to diverge from the characteristics of the benchmark. Ultimately, however, risk and reward will be measured relative to that benchmark. Although some large institutional investors have adopted investment strategies in recent years that are agnostic to the benchmark (an absolute/total return approach) or have had a very high active risk target in a benchmark-relative framework, most assets under management are managed under benchmark-relative mandates. Irrespective of whether a manager focuses on absolute risk or relative risk, the risks he chooses to take should be related to his perceived skills. All other risk should be diversified or minimized. For example,

• market timers should be concerned with timing their factor exposure,

• sector rotators should be concerned with timing their sector exposure, and

• multi-factor managers should be concerned with balancing their factor exposure.

The first step in determining how risk should be allocated is understanding the generic drivers of absolute and relative portfolio risk.

Causes and Sources of Absolute Risk

We start with the following fundamental principles:

• If a manager adds a new asset (such as a security) to his portfolio that has a higher covariance with the portfolio than most current securities, total portfolio risk will rise. (A high covariance with the existing portfolio can be driven by a high variance or a higher correlation of the new security with the portfolio.)

• If a manager replaces an existing security with another security that has a higher covariance with the portfolio than that of the security being replaced, total portfolio risk will rise.

These principles also work in reverse. Consider the three-asset portfolio in Exhibit 11.

Exhibit 11:

Absolute Risk Attribution

	Portfolio Weight	Standard Deviation	Correlation		Portfolio Risk Attribution
Asset A	Asset B	Asset C		Contribution to Portfolio Variance
							Absolute	%
Asset A	40%	20%	1	0.40	0.20		0.008416	59.22%
Asset B	50%	12%	0.40	1	0.20		0.005592	39.35%
Asset C	10%	6%	0.20	0.20	1		0.000204	1.44%
Portfolio	100%	11.92%	0.88	0.78	0.20		0.014212	100%

	Covariance
	Asset A	Asset B	Asset C
Asset A	0.040000	0.009600	0.002400
Asset B	0.009600	0.014400	0.001440
Asset C	0.002400	0.001440	0.003600
Portfolio	0.020926	0.011129	0.001427

Portfolio variance is a function of the individual asset returns and the covariance of returns between assets. In this example, the total variance is 0.014212, which equates to a portfolio standard deviation of 11.92%. Equation 8 expresses the calculation of total portfolio variance (Vp), and Equation 9 determines the contribution of each asset to portfolio variance (CVi).

$Vp=∑i=1n∑j=1nxixjCij$𝑉𝑝=∑𝑖=1𝑛∑𝑗=1𝑛𝑥𝑖𝑥𝑗𝐶𝑖𝑗8$CVi=∑j=1nxixjCij=xiCip$𝐶𝑉𝑖=∑𝑗=1𝑛𝑥𝑖𝑥𝑗𝐶𝑖𝑗=𝑥𝑖𝐶𝑖𝑝9where

xj = the asset’s weight in the portfolio

Cij = the covariance of returns between asset i and asset j

Cip = the covariance of returns between asset i and the portfolio

In other words, the contribution of an asset to total portfolio variance is equal to the product of the weight of the asset and its covariance with the entire portfolio. For example, Asset A’s contribution to total portfolio variance is calculated as follows:

Weight of Asset A × Weight of Asset A × Covariance of Asset A with Asset A	0.40 × 0.40 × 0.04
+ Weight of Asset A × Weight of Asset B × Covariance of Asset B with Asset A	+ 0.40 × 0.50 × 0.0096
+ Weight of Asset A × Weight of Asset C × Covariance of Asset C with Asset A	+ 0.40 × 0.10 × 0.0024
= Asset A’s contribution to total portfolio variance	= 0.008416

The proportion of total portfolio variance contributed by Asset A is, therefore, 0.008416/0.014212 = 59.22%. Asset A, which has an allocation of 40%, accounts for nearly 60% of total portfolio variance. This is not surprising, because the correlation of Asset A with the portfolio is 0.88. Asset B contributes 39.35% of total portfolio variance, and Asset C contributes 1.44%.

As you read the foregoing discussion, you naturally thought of Assets A, B, and C as securities, but the “assets” might also be sectors, countries, or pools of assets representing risk factors (Value versus Growth, Small versus Large). Hence, if a manager specializes in sector rotation and replaces an allocation to one sector with an allocation to another sector having a higher covariance with the portfolio, total portfolio risk will increase.

We have explained risk by looking at how a single asset contributes to total portfolio variance, but a manager might also seek to understand how his portfolio variance can be attributed to factor exposures versus that which is unexplained by these factors. As we noted earlier, the risks a manager chooses to take should be related to his perceived skills. If the manager’s skills can be attributed to certain factors, then he would want to minimize the level of portfolio risk not explained by those factors. The segmentation of absolute portfolio variance into these two components—variance attributed to factor exposure and variance unexplained—is expressed by Equation 10:26

$Vp=Var(∑i=1K(βip×Fi))+Var(εp)$𝑉𝑝=Var(∑𝑖=1𝐾(𝛽𝑖𝑝×𝐹𝑖))+Var(𝜀𝑝)10

If the manager’s portfolio were the market portfolio, all the variance of the portfolio returns would be explained by a beta of 1 to the Market factor. Idiosyncratic risks would be fully diversified. However, as we move away from the market portfolio, total portfolio variance will be influenced by other factor exposures and other risks unexplained by factors.27

Exhibit 12 presents the risk factor attribution (as measured by the variance of returns) of the three products presented earlier in Exhibit 2: the Russell 1000 Index, the Russell 1000 Value Index, and a Value fund. Exhibit 12 shows that more than 100% of the absolute risk of the Russell 1000 Index is explained by the Market factor. The size exposure (the large-cap tilt of the Russell 1000 relative to the market) has a slight negative contribution to total risk.

The risk of the Russell 1000 Value Index is also dominated by the Market factor, and unsurprisingly, the Value factor explains 12.5% of total risk.

The Value fund appears to have much idiosyncratic risk. Its sensitivity to the Market factor is only 57.7%, whereas the Value factor accounts for 18.1% of total risk. Overall, the four factors account for slightly more than 74% of total portfolio risk, and almost 26% remains unexplained. The percentage of total variance that is explained corresponds to the R2 of the regressions as reported in Exhibit 2.

Exhibit 12:

Absolute Risk Factor Attribution28

	Russell 1000 Index	Russell 1000 Value Index	Value Fund
Market	100.4%	88.9%	57.7%
Size	−1.8%	−1.6%	1.8%
Value	0.2%	12.5%	18.1%
Momentum	0.5%	−5.2%	−3.5%
Total explained risk	99.3%	94.6%	74.1%
Total unexplained risk	0.7%	5.4%	25.9%
Total absolute risk (standard deviation annualized)	14.5%	14.2%	18.0%

Source: Calculations by authors.

Causes and Sources of Relative/Active Risk

Relative risk becomes an appropriate measure when the manager is concerned with her performance relative to a benchmark. One measure of relative risk is the variance of the portfolio’s active return (AVp):

$AVp=∑i=1n∑j=1n(xi−bi)(xj−bj)RCij$𝐴𝑉𝑝=∑𝑖=1𝑛∑𝑗=1𝑛(𝑥𝑖−𝑏𝑖)(𝑥𝑗−𝑏𝑗)𝑅𝐶𝑖𝑗11where

xi = the asset’s weight in the portfolio

bi = the benchmark weight in asset i

RCij = the covariance of relative returns between asset i and asset j

The contribution of each asset to the portfolio active variance (CAVi) is

$CAVi=(xi−bi)RCip$𝐶𝐴𝑉𝑖=(𝑥𝑖−𝑏𝑖)𝑅𝐶𝑖𝑝12where RCip is the covariance of relative returns between asset i and the portfolio.

If you are assessing risk using a relative risk construct, you can no longer assume that a lower-risk asset reduces active risk or that a higher-risk asset increases it. In fact, depending on the composition of the benchmark, a lower-risk asset could increase active risk whereas a higher-risk asset might reduce it.

Let’s consider a simple example. Assume a benchmark is composed of a 50/50 allocation to two equity indexes. The portfolio is composed of allocations to these two indexes and to a third asset—cash. What happens to the active risk of the portfolio if, instead of a 50/50 allocation to the two indexes, the portfolio allocation is 40/40 and 20% in cash? The benchmark is still 50/50. Let’s look at the contribution of the active weights to the active variance of the portfolio. Exhibit 13 presents the relevant information and the results.

Exhibit 13:

Relative Risk Attribution

					Correlation of Active Returns	Variance of Active Returns Attributed to Each Asset
	Benchmark Weight	Portfolio Weight	Standard Deviation	Active Risk	Index A	Index B	Cash
Index A	50%	40%	16%	5.0%	1.00	−1.00	−0.69	14.3%
Index B	50%	40%	10%	5.0%	−1.00	1.00	0.69	−14.3%
Cash	0%	20%	0.5%	12.0%	−0.69	0.69	1.00	100%
Total	100%	100%		2.4%	−0.69	0.69	1.00	100%

Index A and Index B have absolute volatilities of 16% and 10%, respectively, whereas cash has a very low volatility. The manager is concerned with active risk, however, not portfolio volatility. Both Index A and Index B have an active risk of 5% against the 50/50 benchmark. Cash has higher active risk because it has a low correlation with the equity benchmark.

Exhibit 13 shows that the correlations of active returns between the benchmark and Index A and between the benchmark and Index B are both −1.0. This is not a coincidence; it must be so. Because the benchmark comprises just these two indexes, any outperformance of one index relative to the benchmark must be offset by underperformance of the other index. Similarly, cash has a positive correlation of relative returns with one index and a negative relative correlation with the other.

This example illustrates that this portfolio’s risk (defined here as variance of active returns) can be attributed entirely to the allocation to cash, which is a low-risk asset—in an absolute sense. Hence, in the context of relative measures of risk, what matters is not the volatility of an asset but its relative (active) volatility. Introducing a low-volatility asset within a portfolio benchmarked against a high-volatility index would increase the active risk. Similarly, introducing a high-volatility asset to a portfolio might lower the active risk if the asset has a high covariance with the benchmark. These principles hold whether allocating among countries, sectors, securities, or other factors.

Exhibit 14 is similar to Exhibit 12, but it considers the attribution of active risk rather than absolute risk. It shows how much of the active risk of each product can be attributed to the four factors and how much remains unexplained. The Russell 1000 Index has some active risk (though very low, at 2% annualized). The active risk of the Russell 1000 Value Index and the Value fund are higher, at 6.0% and 11.4%, respectively.29

The Market factor does not explain much of the active risk; the very action of building a portfolio that is structurally different from the market creates the active risk. The two indexes have a significant portion of their active risk explained by the four rewarded factors. More than half of the active risk of the Russell 1000 Index is generated from the larger-cap tilt of the index. About 37% of the active risk remains unexplained. More than half of the active risk of the Russell 1000 Value Index is generated from the value tilt of the index. About 31% of the active risk remains unexplained. Finally, the Value fund has significant active risk (11.4%). Virtually all of this risk can be attributed the Value factor. In this case, though, nearly two-thirds of the active risk remains unexplained. An investor would want to investigate more carefully what is driving the active risk of the value manager.

Exhibit 14:

Active Risk Factor Attribution

	Russell 1000	Russell 1000 Value	Value Fund
Total active risk	2.0%	6.0%	11.4%

Source: Calculations by authors.

Risk Factor Contribution to Active Risk
Market	3.0%	6.0%	1.2%
Size	56.4%	15.4%	0.8%
Value	3.0%	53.9%	38.4%
Momentum	0.5%	−5.4%	−4.1%
Total explained risk	62.8%	69.9%	36.4%
Total unexplained risk	37.2%	31.1%	63.6%

https://study.cfainstitute.org/app/cfa-institute-program-level-iii-for-august-2024#read/study_task/2564233/determining-the-appropriate-level-of-risk-1

DETERMINING THE APPROPRIATE LEVEL OF RISK

DETERMINING THE APPROPRIATE LEVEL OF RISK

Learning Outcomes

• discuss the application of risk budgeting concepts in portfolio construction

• discuss risk measures that are incorporated in equity portfolio construction and describe how limits set on these measures affect portfolio construction

Listed below are representative examples of risk targets for different mandates:

• a market-neutral hedge fund targeting an absolute risk of 10%,

• a long-only equity manager targeting an active risk of something less than 2% (a closet indexer),

• a long-only manager targeting active risk of 6%–10% (benchmark agnostic), and

• a benchmark-agnostic equity manager targeting an absolute risk equal to 85% of the index risk.

Establishing the appropriate level of absolute or relative risk is a subjective exercise, highly sensitive to managers’ investment style and their conviction in their ability to add value using the various levers at their disposal. Managers with similar investment approaches may have very different risk appetites. This has implications for portfolio structure, portfolio turnover, and other facets of portfolio implementation. Managers must clearly communicate to investors their overall risk orientation, and investors must understand the implications of this risk orientation. This does not mean that a strategy can or should be executed at any level of risk. Here are three scenarios that give some insights into practical risk limits:

• portfolios may face implementation constraints that degrade the information ratio if active risk increases beyond a specific level;

• portfolios with high absolute risk targets face limited diversification opportunities, which may lead to a decrease in the Sharpe ratio; and

• there is a level of leverage beyond which volatility reduces expected compounded returns.

Implementation constraints

Consider two managers (A and B), each with a relative risk focus. Irrespective of the targeted level of active risk, the managers seek to use that risk efficiently. They are concerned with the ratio of active return to active risk—the information ratio. Assume that their portfolios have the same information ratio but different levels of active risk. If the investor is willing to tolerate the higher level of active risk, Manager A might proportionately scale up his active risk to match the active risk level of Manager B. He would accomplish this by scaling up his active weights, which would increase Manager A’s excess returns while maintaining the same information ratio. This scenario is illustrated in Exhibit 15.

Exhibit 15:

Active Returns and Active Risk

However, there may be constraints that prevent Manager A from scaling his active weights. For example, if the investment policy does not allow short positions, he may be unable to increase underweights. If the policy does not allow leverage, he may be unable to increase overweights. If some of the security positions have poor liquidity, leveraging these positions may be imprudent and may also have a trading cost impact. If the policy restricts maximum position sizes, Manager A may be unable to proportionately scale his active risk.30

Limited diversification opportunities

Consider a manager with a high absolute risk target. Despite his higher risk tolerance, he still strives to use risk efficiently. We know, though, that twice the absolute risk will not lead to twice the return: The mathematics of the Markowitz efficient investment frontier clearly shows that the relationship between return and risk is concave. Expected returns increase with risk but at a declining pace. Portfolios with higher risk/return targets eventually run out of high-return investment opportunities and lose the ability to diversify efficiently, thereby reducing the Sharpe ratio.

Leverage and its implications for risk

Sharpe demonstrated that if there is a risk-free rate at which investors can borrow or lend, there is a linear relationship between absolute risk and return in a one-period setting. Managers can scale expected returns and absolute risk up or down proportionately and maintain a constant, optimal Sharpe ratio. A manager could choose to leverage her portfolio to extend the implementation limits of a strategy. However, as we show below, leverage eventually leads to a reduction of expected compounded return in a multi-period setting.

We know that the expected compounded/geometric return of an asset (Rg) is approximately related to its expected arithmetic/periodic return (Ra) and its expected volatility (σ):31

$Rg=Ra−σ2/2$𝑅𝑔=𝑅𝑎−𝜎2/213

For example, let’s consider again the performance of the Russell 1000 over a discrete 26-year period. The average monthly compounded return was 0.789%, the monthly arithmetic return was 0.878%, and the volatility, as measured by the standard deviation of return, was 4.199%. Applying Equation 13, we obtain the compounded return as follows:$Rg=0.878$𝑅𝑔=0.878%−4.199%22=0.790%which is very close to the realized compounded return. Now, what happens to the relationship between the arithmetic return and the compounded return when leverage is used? Let’s consider an asset with a 20% standard deviation and a 10% expected arithmetic return. This asset has an expected compounded return of 8%:10% − 20%2/2 = 8%Ignoring the cost of funding, if we leverage the asset by a factor of 2, the expected compounded return increases to 12%:2 × 10% − (2 × 20%)2/2 = 12%If we leverage the asset by a factor of 3, however, there is no additional improvement in return:

3 × 10% − (3 × 20%)2/2 = 12%

If we incorporate the cost of funding leverage, the active return is reduced while the volatility remains proportional to the amount of leverage. The Sharpe ratio will decline even faster. For example, using the same example, we could show that a portfolio with a leverage of 3× would have the same expected return as an unlevered portfolio if the cost of funding leverage were 2%:

(3 × 10% − 2 × 2%) − (3 × 20%)2/2 = 8%

Furthermore, if the realized volatility is significantly greater than expected, such as in crisis time, the combined impact of volatility and leverage on compounded return could be dramatic.

The information ratio and the Sharpe ratio will not always be degraded by a reasonable rise in active or absolute risk, and a reasonable level of leverage can increase expected compounded return. The appropriate tactics must be evaluated by the manager in the context of his investment approach and investors’ expectations.

https://study.cfainstitute.org/app/cfa-institute-program-level-iii-for-august-2024#read/study_task/2564243/allocating-the-risk-budget-2

ALLOCATING THE RISK BUDGET

Learning Outcomes

• discuss the application of risk budgeting concepts in portfolio construction

• discuss risk measures that are incorporated in equity portfolio construction and describe how limits set on these measures affect portfolio construction

We have explained how absolute and relative risk are determined by the position sizing of assets/factors (absolute or relative) and by the covariance of assets/factors with the portfolio (absolute or relative). By understanding both components (position sizing and covariance), a manager can determine the contribution of each position (whether a factor, country, sector, or security) to the portfolio’s variance or active variance.

Let’s consider a benchmark-agnostic US sector rotator. Although he himself is benchmark agnostic, his client is going to evaluate his performance relative to some benchmark—one that represents the universe of securities he typically draws from. The nature of his strategy indicates that he will likely exhibit a high level of active risk. In assessing whether he has effectively used this risk budget, the client will look to decompose the sources of realized risk: How much is attributable to market risk and other risk factors? How much is attributable to other decisions, such as sector and security allocation? If the manager runs a concentrated portfolio, we should expect sector and security allocation to be the main source of active risk. Although all these aspects may not be explicit elements of his portfolio construction process, because his effectiveness will be evaluated using these metrics, he would be well served to understand their contributions to his risk and return.

A fund’s style and strategy will also dictate much of the structure of its risk budget. We explore this further with an examination of the three US equity managers presented in Exhibit 16. All managers draw their securities from a universe of large-cap and mid-cap securities defined by the Russell 1000 index, which has a weighted average market capitalization of approximately $446.1 billion as of January 31, 2021. The first two managers believe their skill is their ability to create balanced exposures to rewarded risk factors. The third specializes in sector timing, but he also makes significant use of cash positions. The first two managers have many securities in their portfolios, which suggests that their active risk is unlikely to be driven by idiosyncratic risks related to security concentration. Their low level of security concentration is consistent with their respective investment style.

The third manager runs a highly concentrated portfolio. As a sector rotator, he is exposed to significant unrewarded risk related to his sector views and to idiosyncratic risk related to his security views. A sector rotator could choose to run either a diversified portfolio or a highly concentrated portfolio within sectors. Manager C chose the latter. A greater concentration of risk implicitly leads to a greater sensitivity to unrewarded factors and idiosyncratic risks.

Exhibit 16:

Comparative Sources of Risk, Drivers of Return

	Manager A	Manager B	Manager C
Investment Approach:	Factor Diversified	Factor Diversified	Sector Rotator
Number of securities	251	835	21
Weight of top 5 securities	6.54%	3.7%	25.1%
Cash and bond position	0.8%	0.0%	21.3%
Weighted average capitalization ($ billions)	33.7	21.3	164.0
Market beta	0.90	0.97	1.28
Absolute risk	10.89%	10.87%	11.69%
Active risk	3.4%	3.6%%	4.5%
Active Share	0.76	0.63	0.87
Average sector deviation	3.6%	3.9%	5.6%
Source of risk: Market	98.0%	99.2%	69.2%
Source of risk: Sectors	−0.8%	−3.8%	11.6%
Source of risk: Styles	1.8%	4.2%	9.7%
Unexplained	1.0%	0.4%	9.5%

Note: Manager C owns 49 positions, but several of these positions are cash and bond related.

Source: Bloomberg.

None of the managers is tightly tracking the benchmark; active risk exceeds 3% for all three. Somewhat surprisingly, the active risk of the sector rotator (4.5%) is only slightly greater than that for the other managers, especially given that the rotator has 25.1% of his portfolio invested in the top five positions and holds 21.3% in cash and bonds.32 The large position in cash and bonds may also explain why the absolute volatility is not higher. We can see, however, that the sector rotator is taking less of a size bet: The weighted average capitalization of his portfolio is close to that of the index, whereas the weighted average capitalization of the two factor managers is quite low. This smaller size bet is likely what has constrained the active risk of the sector rotator.

Although managers may view their investment process and evaluation of securities as benchmark agnostic, the outcomes may, in fact, be similar to the benchmark along critical dimensions, such as active risk. The portfolio construction process of multi-factor managers often leads to a balanced exposure to risk factors, constraining active risk. The sector rotator has a higher level of active risk, but not dramatically so. The returns of the sector rotator are more driven by concentrated sector and style exposures than are the returns of the multi-factor managers. These differences are likely to influence returns over shorter horizons. Two strategies with similar active risk may have very different patterns of realized returns. When evaluating an investment manager, the asset owner needs to understand the drivers of active risk that can lead to differences in realized portfolio returns over time.

The strategy and portfolio structure of Manager C is also revealed by the sources of absolute risk. The risk attribution in Exhibit 16 not only considers the Market factor but also adds a sector factor and a style factor.

The exposures of Managers A and B are dominated by the Market factor. Manager B’s active risk, however, can be explained in part by the sector and style factors: The sector exposure reduces risk by 3.8%, and the style exposure increases it by 4.2%.

Let’s look more closely at the risk profile of Manager C in Exhibit 17.

Exhibit 17

	Manager C
Investment Approach:	Sector Rotator	Risk Positioning Relative to Managers A and B
Number of securities	21	Very concentrated; high levels of security-specific risk
Weight of top 5 securities	25.1%
Cash and bond position	21.3%	Large cash position dampens overall portfolio volatility
Weighted average capitalization ($ billions)	164.0	Much closer to the capitalization of the index
Market beta	1.28	Significantly higher, consistent with the absolute risk measures
Absolute risk	11.69%	Absolute risk only slightly higher, likely dampened by the large cash position
Active risk	4.5%	Higher
Active Share	0.87	High, consistent with the level of security concentration
Average sector deviation	5.6%	Higher, consistent with willingness to take sector bets
Source of risk: Market	69.2%	Significantly less exposure to the Market factor, consistent with a concentrated, high-Active-Share manager
Source of risk: Sectors	11.6%	Significantly more Sector risk
Source of risk: Styles	9.7%	Significantly more Style risk
Unexplained	9.5%	Significantly higher proportion of risk is unexplained

Taken together, these measures indicate a benchmark-agnostic strategy with significant and concentrated security, sector, and style exposures.

EXAMPLE 5

Application of Risk Budgeting Concepts

1. Using the information in Exhibit 16, discuss key differences in the risk profiles of Manager A and Manager C.

   Solution to 1:

   Manager C holds significantly fewer positions than Manager A, and the weight of his top five securities is nearly four times that of Manager B. This indicates a willingness to assume a much higher level of idiosyncratic risk. This observation is reinforced by Manager C’s higher Active Share and higher proportion of unexplained risk. The Market beta of Manager C is significantly greater, and the risk decomposition indicates that Manager C appears more willing to make sector and style bets. Finally, the absolute risk of Manager’s C portfolio is higher, even though it appears that he makes greater use of lower-risk bond and cash positions.

2. The table below presents the risk factor coefficients of a four-factor model and the factor variance–covariance matrix of a manager running a low-risk strategy. All data are monthly. The monthly standard deviation of the manager’s return is 3.07%. What portion of the total portfolio risk is explained by the Market factor?

   		Variance/Covariance of Returns
   Coefficients	Market	Size	Value	Momentum
   Market	0.733	0.00178	0.00042	0.00066	−0.00062
   Size	−0.328	0.00042	0.00048	0.00033	−0.00035
   Value	0.045	0.00066	0.00033	0.00127	−0.00140
   Momentum	0.042	−0.00062	−0.00035	−0.00140	0.00214

   Solution to 2:

   91% of total portfolio risk is explained by the Market factor. From Equation 8b (repeated below), the contribution of an asset to total portfolio variance is equal to the product of the weight of the asset and its covariance with the entire portfolio. To calculate the variance attributed to the Market factor,

   $CVi=∑j=1nxixjCij=xiCip$𝐶𝑉𝑖=∑𝑗=1𝑛𝑥𝑖𝑥𝑗𝐶𝑖𝑗=𝑥𝑖𝐶𝑖𝑝14where

   xj = the asset’s weight in the portfolio

   Cij = the covariance of returns between asset i and asset j

   Cip = the covariance of returns between asset i and the portfolio

   Therefore, the variance attributed to the Market factor is

   (0.733 × 0.00178 × 0.733) + (0.733 × 0.00042 × −0.328) + (0.733 × 0.00066 × 0.045) + (0.733 × −0.00062 × 0.042) = 0.000858

   Divide this result by the portfolio variance of returns:

   0.000858/3.07%2 = 0.000858/0.000942 = 91% of total portfolio variance is explained by the Market factor.

3. If a manager benchmarked against the FTSE 100 makes a significant allocation to cash, how will that allocation affect the portfolio’s absolute risk and active risk?

   Solution to 3:

   Cash has a low volatility and a low correlation of returns with any asset. Therefore, it will contribute to a reduction in absolute risk. However, because cash has a low correlation with other assets, it will contribute to an increase in active risk.

4. Manager A has been running a successful strategy achieving a high information ratio with a relatively low active risk of 3.4%. The manager is considering offering a product with twice the active risk. What are the obstacles that may make it difficult for the manager to maintain the same information ratio?

   Solution to 4:

   If the manager is running a long-only portfolio without leverage, she is likely able to increase her exposure to securities she wants to overweight, but she may be limited in her ability to reduce exposure to securities she wishes to avoid or underweight. Increased exposure to the most desirable securities (in her view) will lead to increased security concentration and may substantially increase active risk. The manager risks a degradation of her information ratio if there is not a corresponding increase in her active return. If the manager can short, she will be able to increase underweighting when desired (assuming the securities can be easily borrowed). Although leverage can increase total exposure and reduce concentration issues, its impact on volatility may be substantial, and the additional return enabled by leverage may be eroded by the impact of the increased volatility on compounded returns and the other associated costs.

https://study.cfainstitute.org/app/cfa-institute-program-level-iii-for-august-2024#read/study_task/2564253/additional-risk-measures-1

ADDITIONAL RISK MEASURES

Learning Outcomes

• discuss the application of risk budgeting concepts in portfolio construction

• discuss risk measures that are incorporated in equity portfolio construction and describe how limits set on these measures affect portfolio construction

Risk constraints imposed as part of the portfolio construction process may be either formal or heuristic. Heuristic constraints appear as controls imposed on the permissible portfolio composition through some exogenous classification structure. Such constraints are often based on experience or practice, rather than empirical evidence of their effectiveness. These risk controls may be used to limit

• exposure concentrations by security, sector, industry, or geography;

• net exposures to risk factors, such as beta, size, value, and momentum;

• net exposures to currencies;

• degree of leverage;

• degree of illiquidity;

• turnover/trading-related costs;

• exposures to reputational and environmental risks, such as actual or potential carbon emissions; and

• other attributes related to an investor’s core concerns.

A major concern of any portfolio manager is a risk that is unknown or unexpected. Risk constraints are one way that managers try to limit the portfolio losses from unexpected events. Listed below are sample heuristic constraints that may be used by a portfolio manager:

• Any single position is limited to the lesser of

  • five times the weight of the security in the benchmark or

  • 2%.

• The portfolio must have a weighted average capitalization of no less than 75% of that of the index.

• The portfolio may not size any position such that it exceeds two times the average daily trading volume of the past three months.

• The portfolio’s carbon footprint must be limited to no more than 75% of the benchmark’s exposure.

Such heuristic constraints as these may limit active managers’ ability to fully exploit their insights into expected returns, but they might also be viewed as safeguarding against overconfidence and hubris.

Managing risk through portfolio characteristics is a “bottom-up” risk management process. Managers that rely on such an approach express their risk objectives through the heuristic characteristics of their portfolios. The resulting statistical risk measures of such portfolios do not drive the portfolio construction process but are an outcome of those heuristic characteristics. For example, if a manager imposes maximum sector deviations of ±3% and limits security concentration to no more than the index weight + 1% or twice the weight of any security in the index, then we could expect the active risk of that portfolio to be small even if no constraint on active risk is explicitly imposed. The portfolio construction process ensures that the desired heuristic risk is achieved. Continuous monitoring is necessary to determine whether the evolution of market prices causes a heuristic constraint to be breached or nearly breached.

Managers will often impose constraints on the heuristic characteristics of their portfolios even if they also use more formal statistical measures of risk. The investment policy of most equity products, for example, will usually specify constraints on allocations to individual securities and to sectors or, for international mandates, regions. Some may also have constraints related to liquidity and capitalization. Even managers with a low-volatility mandate will have security and sector constraints to avoid unbalanced and concentrated portfolio solutions that may have significant idiosyncratic risk or allocations that are unduly influenced by estimation error.

Formal Constraints

Formal risk measures are distinct from these heuristic controls. They are often statistical in nature and directly linked to the distribution of returns for the portfolio.

Formal measures of risk include the following:

• Volatility

• Active risk

• Skewness

• Drawdowns

• Value at risk (VaR)

• Conditional Value at risk (CVaR)

• Incremental Value at risk (IVaR)

• Marginal Value at risk (MVaR)

A major difference between formal and heuristic risk measures is that formal measures require a manager to estimate or predict risk. For example, a formal risk measure might be that predicted active risk be no more than, say, 5%. With the benefit of hindsight, one can always calculate the historical active risk, but in portfolio construction, the forward-looking view of risk and active risk is what matters: Portfolio decisions are based on these forward-looking estimates. If predicted risk deviates substantially from realized risk, it is likely that portfolio performance will be quite different than expected. In times of crisis or financial stress, predicted and realized risks could diverge very significantly.

Exhibit 18 presents five different risk measures for the same three products discussed in Exhibit 15. Four one-day VaR measures are presented: VaR and CVaR at two different levels of probability (1% and 5%).

Exhibit 18:

Risk Measures

	Manager A	Manager B	Manager C
Risk Measure	Factor Diversified	Factor Diversified	Sector Rotator
Absolute risk	10.89%	10.87%	11.69%
Active risk	3.4%	3.6%%	4.5%
VaR (5%)	1.08%	1.11%	1.20%
VaR (1%)	1.77%	1.77%	1.87%
CVaR (5%)	1.50%	1.53%	1.65%
CVaR (1%)	2.21%	2.24%	2.41%

Source: Bloomberg.

In this example, Manager A has a 5% probability of realizing a one-day loss greater than 1.08% and a 1% probability of a loss greater than 1.77%. If we look at the distribution of losses beyond the 5% and 1% probability levels, the averages of the tail losses (CVaR) are 1.50% and 2.21%, respectively. Despite the high security concentration, the loss estimates of Manager C are not much higher than those of Managers A and B, most likely because of the large position in cash and bonds.

Risk Measures

• Volatility is the standard deviation of portfolio returns.

• Active risk is the standard deviation of the differences between a portfolio’s returns and its benchmark’s returns. It is also called tracking error or tracking risk.

• Skewness is a measure of the degree to which return expectations are non-normally distributed. If a distribution is positively skewed, the mean of the distribution is greater than its median (more than half of the deviations from the mean are negative and less than half are positive) and the average magnitude of positive deviations is larger than the average magnitude of negative deviations. Negative skew indicates that the mean of the distribution lies below its median and the average magnitude of negative deviations is larger than the average magnitude of positive deviations.

• Drawdown measures the portfolio loss from its high point until it begins to recover.

• VaR is the minimum loss that would be expected a certain percentage of the time over a specific period of time (e.g., a day, a week, a month) given the modeled market conditions. It is typically expressed as the minimum loss that can be expected to occur 5% of the time.

• CVaR is the average loss that would be incurred if the VaR cutoff is exceeded. It is also sometimes referred to as the expected tail loss or expected shortfall. It is not technically a VaR measure.

• IVaR is the change in portfolio VaR when adding a new position to a portfolio, thereby reducing the position size of current positions.

• MVaR reflects the effect of a very small change in the position size. In a diversified portfolio, marginal VaR may be used to determine the contribution of each asset to the overall VaR.

Formal risk constraints may be applied as part of a portfolio optimization process (as is common with systematic strategies) or using an iterative feedback mechanism to determine whether the portfolio would remain within the risk tolerance limits given the proposed change (an approach more common among discretionary managers).

All risk measures, whether formal or heuristic, can be expressed on an absolute basis or relative to a benchmark. For example, a benchmark-aware long-only equity manager may limit sector deviations to 5%, whereas a long/short hedge fund manager concerned with the overall diversification of his portfolio may limit any given sector exposure to no more than 30% of his gross exposure. Similarly, a long-only equity manager may limit active risk to 5%, whereas a long/short equity manager may limit overall portfolio volatility to 10%. In many cases, the investment policy imposes both formal and heuristic constraints on a portfolio. Exhibit 19 illustrates a product for which the investment policy statement considers constraints on both types of risk measures.

Exhibit 19: Sample Investment Policy Risk Constraint

The MSCI Diversified Multi-Factor Index

This index uses an optimization process to maximize the exposure score to several risk factors. The index seeks to achieve this objective while controlling for several portfolio and risk characteristics, such as the following:

• Weight of index constituents: maximum of weight in the parent (capitalization-weighted) index + 2% or 10 times weight in the parent index

• Sector weights: restricted to a 5% deviation against the parent index

• Exposure to style factors, such as growth and liquidity: restricted to a 0.25 standard deviation from the parent index

• Limit on volatility: restricted to a 0.25 standard deviation from the parent index

The Risks of Being Wrong

The consequences of being wrong about risk expectations can be significant but even more so when a strategy is leveraged. In 2008, for example, a hedge fund owned a two-times levered portfolio of highly rated mortgage-related securities. Although the specific securities were not materially exposed to subprime mortgages, concerns about the economy and poor market liquidity led to a steep decline in the prices of these securities. Prices quickly recovered, but the presence of the 2× leverage combined with an unprecedented price decline led to a forced liquidation of the assets just a few days before prices recovered. The manager and his investors lost all capital.

Similarly, a pension fund created an indexed equity position by combining an investment of short-term highly rated (AAA) commercial paper with an equivalent notional position in equity derivatives (a receiver swap on a large-cap equity index), creating a synthetic indexed equity position. In principle, this pension fund believed it owned the equivalent of an index equity position. However, as the liquidity crisis worsened in 2008 and early 2009, the pension fund was faced with a substantial decline in equity markets and a simultaneous spike in the perceived riskiness of the short-term commercial paper. The equity derivatives position and the commercial paper each lost 50% of their value, creating a paper loss equivalent to 100% of the invested capital. Although both components eventually recovered, such unexpected losses can lead to a forced liquidation of all or part of the portfolio in an unfavorable market environment, crystalizing the losses.

Exhibit 20 illustrates the time-varying volatility of the S&P 500 from 1995-2020. Although volatility remains in a range of 10%–20% most of the time, periods of much higher volatility are observed: in 2000–2002 when technology stocks collapsed, in the 2008-2009 the Global Financial Crisis, and in 2020 during the COVID-19 pandemic.. Effective risk management requires the manager to account for the fact that unexpected volatility can derail the investment strategy. Furthermore, spikes in volatility can also be sector specific—the technology sector in the early 2000s and the energy sector in 2014 and 2015. Therefore, what may seem to be an acceptable sector deviation limit in normal times may be the source of significant active losses in a different environment. Some managers may tighten risk constraints in more volatile periods to protect the portfolio against excessive variability.

Despite these “tail events,” risk can usually be managed efficiently. The dotted line in Exhibit 2033 shows the realized volatility of a portfolio dynamically allocated between the S&P 500 Index and short-term bonds. The portfolio targets a 10% annualized volatility.34 The realized volatility stayed very close to the target.

Exhibit 20:

Volatility of the S&P 500, 1995–2020

The statistical risk measures used in equity portfolio construction often depend on the style of management. A benchmark-agnostic manager with an absolute return philosophy is less likely to be concerned with active risk but is much more likely to be concerned with drawdowns. A long/short equity manager who neutralizes market risk but is exposed to other risk premiums is likely to target a volatility within a specific range.

Portfolios with a very limited number of securities may be more difficult to manage using formal risk measures because estimation errors in portfolio risk parameters are likely to be higher: The dispersion in possible outcomes may be wide, and the distributions may not easily conform to standard assumptions underlying many of the formal risk measures.

This does not mean, however, that these measures cannot be used on an ex ante basis. It merely suggests that they should be used with an understanding of their limitations. For example, VaR is particularly useful to a pension plan sponsor that has a multi-asset-class portfolio and needs to measure its exposure to a variety of risk factors (Simons, 2000). However, this information may be less useful to an equity manager holding only 40 equity positions. Measures of risk and their efficacy must be appropriate to the nature and objective of the portfolio mandate.

Formal, statistical measures of risk are often not outlined in investment policy statements even if the manager is actively tracking such risks and using such measures to adjust security weights. One reason may be the difficulty in measuring and forecasting such measures as volatility and value at risk. The resultant answers are likely to be different depending on what methodology is used. Even if the historical measures were in alignment with one another, what happened in the past will not necessarily be indicative of what is to come. When formal, statistical measures of risk are used by managers, they are typically expressed as a soft target, such as, “We are targeting a 10%–12% annualized volatility.”

Calibrating risk is as much an art as it is a science. If an active manager imposes restrictions that are too tightly anchored to her investment benchmark (or perhaps these restrictions are imposed by the investor), the resulting portfolio may have performance that too closely mirrors that of the benchmark.

EXAMPLE 6

Risk Measures in Portfolio Construction

Matthew Rice runs a discretionary equity strategy benchmarked on the Russell 1000 Index. His fund contains approximately 80 securities and has recently passed $2 billion in assets. His strategy emphasizes quality companies that are attractively priced within their sector. This determination is based on careful analyses of the balance sheet, free cash flows, and quality of management of the companies they invest in. Rice is not benchmark agnostic, but his strategy does require the ability to tolerate some sector deviations because attractive positions are sometimes concentrated in three or four sectors. Rice is supported by a team of six analysts but makes all final allocation decisions. Historically, no single position or bet has dominated the performance of the fund. However, Rice believes there is no point in holding a position so small that it will barely affect excess returns even if it is successful. Rice does not believe in taking aggressive views. His investors do not expect him to have the active risk of a sector rotator. The portfolio has lower turnover than that of most of his peers. Single positions can easily remain in the portfolio for two or three years.

1. What heuristic constraints could be appropriate for such a fund?

   Solution to 1:

   Because no single position or bet has dominated historical returns, a heuristic constraint on maximum position size is a logical one. Given that his portfolio is built around a relatively small number of positions (80), single positions might be constrained to no more than 3%. Given his view on small position sizes, a minimum position size of 0.5% might also be appropriate.

   Rice’s strategy requires some active risk, but he could not tolerate the sector deviations taken by a sector rotator. A sector constraint in the range of ±5%–7.5% relative to the index is appropriate for his strategy.

   The fund’s benchmark incorporates many mid-cap securities. With $2 billion in assets, a single position can be as small as $10 million (0.5%) but as high as perhaps $60 million (3%). Positions on the higher end of this range could represent a large portion of the average daily trading of some mid-cap securities, which range in size from $2 billion to $10 billion. The fund’s long investment horizon means that trading into and out of a position can be stretched over days or even weeks. Nevertheless, it could make sense to consider a constraint that accounts for the size (capitalization) of individual securities and their trading volume, such as not owning more than five times the capitalization weight in the index of any security.

2. What role might such statistical measures as VaR or active risk play in the management of Rice’s fund?

   Solution to 2:

   Discretionary managers usually do not use statistical measures as hard constraints, but they can be used as guidelines in the portfolio management process. A fund that contains only 80 positions out of a universe of 1,000 possible securities and takes views across capitalization and sectors is likely to see significant variability in its active risk or VaR over time. Although Rice is not very sensitive to what happens in the short run (he is a long-term investor), statistical measures can be used to monitor changes in the risks within his portfolio. If these risk exposures deviate from his typical risk exposures, it might signal a need to investigate the sources of such changes and initiate some portfolio changes if those exposures are unwanted.

https://study.cfainstitute.org/app/cfa-institute-program-level-iii-for-august-2024#read/study_task/2564263/implicit-cost-related-considerations-1

IMPLICIT COST-RELATED CONSIDERATIONS

Learning Outcome

• discuss how assets under management, position size, market liquidity, and portfolio turnover affect equity portfolio construction decisions

There are numerous costs that can affect the net performance of an investment product. The same investment strategy can easily cost twice as much to manage if a manager is not careful with her implementation approach. Assets under management (AUM) will affect position size. Position size and the liquidity of the securities in the portfolio will affect the level of turnover that can be sustained at an acceptable level of costs.35 Although smaller-AUM funds may pay more in explicit costs (such as broker commissions), these funds may incur lower implicit costs (such as delay and market impact) than large-AUM funds. Overall, smaller funds may be able to sustain greater turnover and still deliver superior performance. A manager needs to carefully weigh both explicit and implicit costs in his implementation approach.

Thoughtful portfolio management requires a manager to balance the potential benefits of turnover against the costs of turnover. When considering a rebalancing or restructuring of the portfolio, the benefits of the post-trade risk/return position must justify the costs of getting there.

This section concerns the implicit costs of implementing an active strategy and implementation issues related to asset under management, position sizing, turnover, and market liquidity. Explicit costs, such as broker commissions, financial transaction taxes, custody/safekeeping fees, and transaction processing, are covered in other parts of the CFA Program curriculum.

Implicit Costs—Market Impact and the Relevance of Position Size, Assets under Management, and Turnover

The price movement (or market impact) resulting from a manager’s purchase or sale of a security can materially erode a manager’s alpha. Market impact is a function of the liquidity and trade size of the security. A manager’s investment approach and style will influence the extent to which he is exposed to market impact costs. A manager whose strategy demands immediacy in execution or requires a higher portfolio turnover is likely to incur higher market impact costs relative to a manager who patiently trades into a position. A manager who believes her investment insights will be rewarded over a longer-term investment horizon may be able to mitigate market impact costs by slowly building up positions as liquidity becomes available. A manager whose trades contain “information” is more vulnerable to market impact costs. A trade contains information when the manager’s decision to buy or sell the security signals to the market that something has changed. If a discretionary manager with sizable assets under management begins to buy a stock, the trade signals to other market participants that there is likely to be upward pressure on the stock price as the manager builds the position. Some market participants may try to “front-run” the manager, buying up known supply to sell it to the manager at a higher price. If that same manager begins to sell his position following a company “event,” it signals to the market that the manager’s view on the stock has changed and he is likely to be selling off his position, putting downward pressure on the price. Assets under management, portfolio turnover, and the liquidity of the underlying assets all affect the potential market impact costs.

Consider the relationship between the size of a security, as measured by its capitalization, and a manager’s ability to trade in this security, as measured by its average daily trading volume. Exhibit 21 presents the capitalization and average daily trading volume of the Russell 1000 companies in declining order of their capitalization. The figure is built using a moving average of the capitalization of groups of 20 companies. The first point on the graph shows the average capitalization and trading volume of the largest 20 companies by capitalization. The next point on the graph presents the same information for the averages of the companies ranking 2nd to 21st in terms of capitalization, and so on.

Exhibit 21:

Capitalization and Trading Volume (in $) of the Russell 1000 Companies in Declining Order of Capitalization

Source: Data from Bloomberg.

Two observations are warranted. First, the distribution of market cap is skewed: The average capitalization declines quickly. The combined capitalization of the top 500 companies is more than seven times that of the bottom 500 companies. Second, smaller-capitalization companies have lower daily trading volume (in dollars). However, smaller-cap companies trade a greater percentage of their capitalization. The smallest 900 companies within the index trade nearly two times more volume—as a percentage of their market capitalization—than the 100 largest companies (e.g., the 900 smallest companies on average trade 1% of their market cap daily, whereas the 100 largest companies trade 0.5% of their market cap daily). Nevertheless, the lower absolute level of average trading volume of the smaller securities can be a significant implementation hurdle for a manager running a strategy with significant assets under management and significant positive active weights on smaller companies.

For example, let’s assume the smallest company within an index has a capitalization of $2 billion and that 1% of its capitalization trades each day on average—about $20 million. Let’s also assume that a manager has a policy not to own a position that constitutes more than 10% of the average trading volume of a security and that no position in the portfolio can be larger than 2% of total assets. If this manager has $200 million under management, the allocation constraint indicates that he could own as much as $4 million of that security ($200 million × 2% = $4 million), but the liquidity constraint limits the position to $2 million ($20 million × 10%). Thus, the position size is limited to about 1.0% of the fund’s assets. A $1 billion fund with similar constraints would be limited to the same $2 million position, a much smaller position size relative to his total portfolio.

A $100 million fund can typically implement its strategy with very few obstacles arising from trading volume and position size constraints. However, the manager of a $5 billion fund could not effectively operate with the same constraints. A 2% position in a $5 billion fund is $100 million, yet only approximately 35% of the securities in the Russell 1000 have an average daily trading volume greater than $100 million. The trading volume constraint significantly limits the manager’s opportunity set. A large-AUM fund can address this issue in several ways:

• It may establish position limits on individual securities that consider their respective market-cap weights on both an absolute and relative basis. For example, it may limit the allocation to the lesser of market-cap weight + 1% (100 bps) or 10 times the market-cap weight allocation of the security within the index. In other words, the position limit would be related to the market cap of each security.

• It may establish position limits based on the average daily trading volume of a security. For example, it may limit the position size to, say, no more than 10 days of average trading volume.

• It may build a rebalancing strategy into the investment process that anticipates a longer rebalancing period or that gradually and consistently rebalances over time, assuming the performance of the strategy is not affected by the implementation delay.

The challenges are even greater for small-cap funds. The weighted average capitalization of the Russell 2000 Index is only $2.2 billion, and nearly 60% of the companies in the index have a market capitalization below $1 billion (as of March 2017). The average market cap of companies over this $1 billion market-cap threshold is only $1.2 billion. The average daily volume of these “larger” companies is approximately 2% of their market capitalization—less than $25 million. Approximately 75% of securities within the index have a lower average daily trading volume.

A small-cap manager with the same limits on position size relative to trading volume as the manager above would have an average position size of no more than $2.5 million, based on average daily trading volume. A strategy rooted in a smaller number of securities—say, 40—may find it difficult to run a $100 million fund and may have to concentrate its allocation among the 25% largest securities in the index or accept a lower turnover. Although a strategy with a larger number of securities—say, 200—would be able to support a substantially higher level of AUM, it may still be constrained to concentrate its exposure among the larger and more liquid securities. Small-cap funds with capacities of $1 billion or greater may very well need to hold 400 securities or more.

The strategy of the manager must be consistent with the feasibility of implementing it. A high-turnover strategy with a significant allocation to smaller securities will at some point reach a level of AUM at which the strategy becomes difficult to implement successfully. The level of idiosyncratic risk inherent in the strategy will also play a role in the suitable level of AUM. A manager targeting low levels of idiosyncratic risk in his portfolio is likely to have more securities and smaller position sizes and could, therefore, conceivably support a higher level of AUM.

Estimating the Cost of Slippage

Slippage is often measured as the difference between the execution price and the midpoint of the bid and ask quotes at the time the trade was first entered.36 It incorporates both the effect of volatility/trend costs and market impact. (Volatility/trend costs are the costs associated with buying in a rising market and selling in a declining market.) This measure provides an estimate of the cost to execute a transaction when the order is executed in a single trade.

When a larger trade is executed in increments over multiple days, the estimate of market impact costs for later trades does not account for the impact of earlier trades on subsequent execution prices. Depending on the size of the trade, the manager’s own sell (buy) orders may put downward (upward) pressure on the security’s price, thereby increasing the effective cost of implementation. Large institutional investors today will often try to camouflage the potential size of their trade by breaking a trade into many smaller trades or by trading in “unlit” venues. Unlit venues allow buyers and sellers to trade anonymously with one another. Dark pools and crossing networks are examples of unlit venues.37

Studies have shown that small-cap stocks have consistently had higher effective trading costs than large-cap stocks and that illiquidity can be very cyclical, increasing prior to the beginning of a recession and decreasing prior to the end of a recession.38 It is difficult to quantify this cost, but we know intuitively that a given trading volume causes a larger price move for a less liquid asset.39 The larger a trade size relative to a stock’s average daily volume is, the more likely it is that the trade will affect prices. Thus, a fund with a focus on large-cap stocks can support a higher level of AUM than can a similar-strategy fund focused on small-cap stocks. A fund focused on small-cap stocks must either limit its AUM, hold a more diversified portfolio, limit turnover, or devise a trading strategy to mitigate market impact costs.

Exhibit 22 provides estimates of the average slippage for several markets in 2020. There are three conclusions we can draw:

• Slippage costs are usually more important than commission costs.

• Slippage costs are greater for smaller-cap securities than for large-cap securities.

• Slippage costs can vary substantially over time, especially when market volatility is higher.

Exhibit 22:

Average Slippage by Cap Size and Country

Source: ITG, “Global Cost Review Q4/2016” (2017).

Slippage cost can be managed with a strategic approach to implementation. Smaller-AUM managers have an advantage in this respect. For example, two hypothetical $100 million trades were sent to an execution platform that provides estimates of trading costs. The first trade mirrored the Russell 1000. The second trade bought just 250 securities in the same Russell 1000 universe, but the weighted average capitalization was only $26 billion (versus $133 billion for the index). Assuming the trading was accomplished in the course of a single day, the first trade had an estimated implementation cost of just 1 bp, whereas the second trade incurred implementation costs of 3%.

For some strategies, the true cost of slippage may be the opportunity cost of not being able to implement the strategy as assets grow. Investors choose a given fund based on the manager’s stated strategy and implementation approach. If this approach is modified as the manager’s level of AUM grows, it may have unanticipated consequences for expected risks and returns to investors. In these situations, the manager must either inform investors of changes being made to the strategy and its implementation or they must limit the size of the fund assets—that is, close the fund to new investors or new contributions from existing investors. Managers need to very carefully think about capacity as a new product is launched; although historical results based on a lower level of AUM may attract attention and clients, if the strategy cannot be scaled for the larger AUM, the product delivered to clients may be different from the strategy they thought they were investing in.

A study by AQR Capital Management “Factor Momentum Everywhere”, 2019 documents robust persistence in the returns of equity factor portfolios. This persistence is exploitable with a time-series momentum trading strategy that scales factor exposures up and down in proportion to their recent performance. Factor timing in this manner produces economically and statistically large excess performance relative to untimed factors. Taken alongside the evidence of time series momentum in commodity, bond, and currency factors, the findings of momentum among equity factors—in the time series, in the cross section, and around the world—support the conclusion that factor momentum is a pervasive phenomenon in financial markets.40

EXAMPLE 7

Issues of Scale

1. Stephen Lo has been the sole portfolio manager of the Top Asia Fund since its inception 20 years ago. He is supported by a group of analysts. The fund has been highly successful as it grew from assets of less than $30 million in his first year to more than $7 billion. As a potential investor in the Top Asia Fund, you have been asked to determine how Lo has been able to generate his performance and whether his style has evolved over the years. You prepared the following analysis of the return and risk characteristics of the fund for its first five years and last five years of existence.

   Discuss the evolution of the fund’s characteristics and its implications for Lo’s success as a manager.

   Top Asia Fund Characteristics	First Five Years	Last Five Years
   Average assets ($ millions)	200	5,000
   Average number of positions	80	300
   Market Beta	0.90	0.91
   Size coefficient	0.30	−0.10
   Value coefficient	0.25	0.24
   Momentum coefficient	0.20	0.10
   Portfolio turnover	100%	30%
   Alpha (gross of fees)	2.5%	0.40%

   Solution to 1:

   AUM grew rapidly over the past 20 years. The number of positions in the portfolio nearly quadrupled while assets grew by a factor of 25. Still, there are aspects of his style that have not changed: He is still very much a value manager investing in lower-beta securities. However, the portfolio no longer has a small-cap tilt, and the exposure to the momentum factor has also declined. It is likely that these are both byproducts of the increase in AUM; for example, a large fund has greater difficulty executing in small-cap securities. This last point is supported by the decline in portfolio turnover. The decline in alpha indicates that the growth in AUM has altered the implementation of the investment approach.

2. Andrew Isaac runs a $100 million diversified equity portfolio (about 200 positions) using the the Russell 1000 as his investable universe. The total capitalization of the index is approximately $20 trillion. Isaac’s strategy is very much size agnostic. He consistently owns securities along the entire size spectrum of permissible securities. The strategy was designed with the following constraints:

   • No investment in any security whose index weight is less than 0.015% (approximately 15% of the securities in the index)

   • Maximum position size equal to the lesser of 10× the index weight or the index weight plus 150 bps

   • No position size that represents more than 5% of the security’s average daily trading volume (ADV) over the trailing three months

   The smaller securities in Isaac’s permissible universe trade about 1% of shares outstanding daily. At what level of AUM is Isaac’s strategy likely to be affected by the liquidity and concentration constraints?

   Solution to 2:

   Based on the index capitalization of $20 trillion, the size constraint indicates that the smallest stocks in his portfolio will have a minimum market cap of about $3 billion (0.015% × $20 trillion). The ADV of the stocks at the lower end of his capitalization constraint would be about $30 million (1% × $3 billion). Because Isaac does not want to represent more than 5% of any security’s ADV, the maximum position size for these smaller-cap stocks is about $1.5 million (5% × $30 million). It appears that Isaac’s strategy will not be constrained until the portfolio reaches about $1 billion in size ($1.5 million ÷ 0.15% = $1 billion). If the level of AUM exceeds $1 billion, his position size constraints will require the portfolio to hold a larger number of smaller-cap positions. There is room to grow this strategy.

https://study.cfainstitute.org/app/cfa-institute-program-level-iii-for-august-2024#read/study_task/2564273/the-well-constructed-portfolio-1

THE WELL-CONSTRUCTED PORTFOLIO

Learning Outcome

• evaluate the efficiency of a portfolio structure given its investment mandate

A well-constructed portfolio should deliver results consistent with investors’ risk and return expectations. It will not guarantee excess return relative to the appropriate benchmark, especially over a shorter horizon, but it will be designed to deliver the risk characteristics desired by the manager and promised to investors. The well-constructed portfolio possesses

• a clear investment philosophy and a consistent investment process,

• risk and structural characteristics as promised to investors,

• a risk-efficient delivery methodology, and

• reasonably low operating costs given the strategy.

Investors and managers may have different requirements with respect to the characteristics they seek in a well-structured portfolio. For some managers, substantial diversification is required, whereas others seek a high-conviction, less diversified strategy. Some investors require formal and heuristic risk metrics that are tightly constrained, and others tolerate more permissive risk limits. A well-structured portfolio must, at the very least, deliver the promised characteristics in a cost- and risk-efficient way.

Consider the following large-cap US equity products, Product A and Product B. Between January 1999 and September 2016, the two products had similar annualized absolute volatility, 15.1% and 15.2%, and similar active risk, 4.9% and 4.8%. However, they differ on other dimensions. Exhibit 23 presents the factor exposure of each product using a six-factor model. The factors are Market, Size, Value, Momentum, Betting against Beta (BAB), and Quality. The exhibit also shows the volatility of each factor. Exhibit 24 illustrates the contribution to the total variance of each product originating from these factors, as well as the portion of total variance that remains unexplained. Other characteristics are also presented.41

Exhibit 23:

Factor Exposure, January 1999–September 2016

Factor	Product A	Product B	Factor Volatility
Market	0.92	1.08	15.8%
Size	−0.29	0.04	9.7%
Value	0.33	0.06	14.7%
Momentum	0.04	0.06	19.2%
BAB	0.02	0.09	14.4%
Quality	0.03	0.23	11.4%

Sources: Data are from Bloomberg and AQR.

Exhibit 24:

Risk Characteristics

Factor	Factor Risk Contribution
Product A	Product B
Market	87.4%	105.9%
Size	−2.3%	0.6%
Value	14.0%	1.2%
Momentum	−2.7%	−2.0%
BAB	−0.4%	−2.0%
Quality	−1.6%	−10.5%
Unexplained	5.5%	6.8%
Total	100%	100%

	Other Characteristics
Number of securities	≈320	≈120
Annualized active risk	4.9%	4.8%
Active Share	0.43	0.80
Annualized volatility	15.1%	15.2%
Maximum drawdown	54.6%	51.8%

Since the two products have similar volatility and active risk, what opinion can we form about the risk efficiency of each product?

Product A exhibits the following relevant characteristics:

• A Market β slightly less than 1

• A large-cap bias (a negative coefficient on the Size factor)

• A very large exposure to the Value factor

• Greater security-level diversification than Product B

• Market risk representing only 87.4% of the total portfolio risk

• A significant portion of the absolute risk attributed to the Value factor

The relevant characteristics for Product B are:

• A Market β slightly more than 1

• A more balanced exposure to all factors

• A large exposure to the Quality factor (although the factor itself has a relatively low volatility)

• Active Share nearly double that of Product A

• Modestly lower drawdowns

• More than 100% of its absolute risk attributed to the Market factor

Thus, Product B’s emphasis on quality companies having a high return on equity, a low debt-to-equity ratio, and a low earnings variability is a likely explanation for absolute and relative risk measures that are not significantly different from those of Manager A. That Product B can achieve this level of risk efficiency with less than half the number of securities held by Product A indicates that risk management is an important component of the portfolio construction process of Product B. Although there is no guarantee that a more efficiently risk-structured portfolio will outperform, Product B outperformed Product A by more than 3.1% annually over the period.

In a well-constructed portfolio, we would be looking for risk exposures that are aligned with investor expectations and constraints and low idiosyncratic risk (unexplained) relative to total risk. If two products have comparable factor exposures, the product with a lower absolute volatility and lower active risk will likely be preferred (assuming similar costs). If two products have similar active and absolute risks, the portfolios have similar costs, and the alpha skills of the managers are similar, the product having a higher Active Share is preferable, because it leverages the alpha skills of the manager and will have higher expected returns.

Finally, the “risk efficiency” of any given portfolio approach should be judged in the context of the investor’s total portfolio. The active risk of a concentrated stock picker should be higher than that of a diversified factor investor, and the concentrated stock picker may have a lower information ratio. Yet both managers could be building a well-structured portfolio relative to their mandate. It is important to consider the diversification effect of a manager’s portfolio on the total portfolio of the investor to arrive at an appropriate solution.

EXAMPLE 8

The Well-Structured Portfolio

David Larrabee is CIO of a pension fund with $5 billion in assets. The fund has 60% of its assets invested in equities with more than 10 managers. Larrabee is considering creating a core equity position that would represent 65% of all equity assets. The remaining 35% would then be allocated to approximately five active satellite (non-core) managers. The core position would be invested in a customized passive portfolio designed specifically for the pension fund using a well-documented construction and rebalancing process. The portfolio would be implemented by a known counterparty at a low cost (less than 10 bps). The main specifications for the custom portfolio were the following:

• Investable universe composed of securities within the MSCI World Index

• Low volatility achieved through an optimization process

• High payout yield (dividend and share repurchase)

• No fewer than 250 securities

• No position greater than 2%

• Average portfolio turnover less than 50% annually

Larrabee understands that a low-volatility objective usually leads to portfolios with large-cap, Value, and Quality biases.

Exhibit 25 and Exhibit 26 present the results of a pro forma analysis of the custom portfolio. The portfolio was simulated over a period of 12 years. Exhibit 25 presents some key risk and structural characteristics, as well as the average active sector exposure. Exhibit 26 presents the results of factor analyses for both the MSCI World and the custom portfolio.

Exhibit 25

	MSCI World	Custom Portfolio
Return annualized	7.0%	8.45%
Volatility annualized	11.3%	9.0%
Active risk	—	6.0%
Number of securities	1,700	325
Turnover	2.4%	35%
Dividend yield	2.6%	3.6%
Average Active Sector Exposure
Energy	—	−2.00%
Materials	—	−1.50%
Industrials	—	−1.50%
Consumer discretionary	—	3.00%
Consumer staples	—	4.20%
Health care	—	2.40%
Financials	—	−1.00%
Information technology	—	−10.00%
Telecommunication services	—	3.20%
Utilities	—	3.20%

Exhibit 26

	Factor Exposure		Factor Relative Risk Attribution
MSCI World	Custom Portfolio		MSCI World	Custom Portfolio
Alpha (annualized)	−1.0%	−3.1%		—	—
Market	1.00	0.84		103%	105%
Size	−0.13	−0.26		−1%	−1%
Value	0.06	0.30		2%	10%
Momentum	0.02	0.02		−1%	−3%
BAB	0.01	0.32		0%	2%
Quality	0.10	0.54		−4%	−22%
Unexplained	—	—		1%	9%

Larrabee has hired you to advise him on the proposed core product. Considering the information provided,

1. Does the pro forma custom portfolio meet the specifications of a well-structured portfolio, and are there any characteristics of this product that concern you?

   Solution to 1:

   The proposed solution is aligned with many of the characteristics of a well-constructed portfolio. It is based on a consistent investment process, and it appears to meet the requirements of the investor: It has significantly lower volatility than the MSCI World and a significantly higher dividend yield (although we do not have the information on the payout yield), the portfolio has a low security concentration, and the estimated turnover is lower than the required limit. It can also be implemented at a low cost. The factor analysis also confirms what we could expect from a high-payout/low-volatility portfolio. The Market beta is significantly below 1, the negative Size coefficient indicates a larger-capitalization bias, and finally, the portfolio has a Value and Quality bias. The risk attribution analysis indicates that the exposure to Quality companies is largely responsible for reducing the total risk of the portfolio.

   However, there are some aspects of the portfolio that create some concerns. Although the custom portfolio meets all of Larrabee’s specified objectives, the portfolio construction process leads to a high tracking error (active risk). Given the size of this allocation relative to the total equity portfolio, this poses a problem. Some of this tracking error may be attributed to a significant under-allocation to the information technology sector. Finally, although the portfolio would have generated an excess return on average over the past 12 years, the alpha is negative. Understanding the source of this negative alpha is essential. In this instance, the excess return was achieved largely through a very high and intentional exposure to rewarded factors, such as Value, BAB, and Quality, which may not have been rewarded over the simulated period.

2. If the custom portfolio were implemented, what recommendations would you make to Larrabee in terms of the style of the satellite managers or in general?

   Solution to 2:

   The first recommendation would be to investigate further the source of the significant negative alpha. Because the excess performance is so strongly explained by exposure to specific factors, we should be concerned about how the portfolio would perform if factor returns were to decline. Is there a systemic reason that can explain this observation? Secondly, if tracking error is a concern, it is important to identify satellite managers whose active returns have a low correlation with the core mandate, perhaps even a lower active risk. Finally, considering the importance of the information technology sector, it could be prudent to hire a manager that has a strong technology orientation. The objective is not necessarily to maintain a technology exposure equal to that of the MSCI World Index but perhaps to lower the consistent underexposure to a more reasonable level. At the very least, these structural biases should be continuously monitored.

https://study.cfainstitute.org/app/cfa-institute-program-level-iii-for-august-2024#read/study_task/2564283/longshort-long-extension-and-market-neutral-portfolio-construction-1

LONG/SHORT, LONG EXTENSION, AND MARKET-NEUTRAL PORTFOLIO CONSTRUCTION

Learning Outcome

• discuss the long-only, long extension, long/short, and equitized market-neutral approaches to equity portfolio construction, including their risks, costs, and effects on potential alphas

Long/short, long extension, and market-neutral portfolio approaches are all variations on a theme: Each is predicated on the belief that research insights can be exploited not only in the pursuit of stocks that are expected to perform well but also to profit from the negative insights gathered during the research process. “Long/short” is the most encompassing term and can include long extension and market-neutral products. Most commonly, the term “long/short” refers to strategies that are relatively unconstrained in the extent to which they can lever both positive and negative insights.

Long extension strategies are constrained long/short strategies. The capital committed by the client is invested similarly to a manager’s long-only strategy but levered to some extent to exploit the manager’s insights on projected losers as well as winners. A typical long-extension strategy is constrained to have a net exposure of 100%; for example, 130% of the capital is invested long and 30% of the capital is invested short, for a net exposure of 100%—the same as it would be in a long-only portfolio. There may or may not be a relationship between the long and the short portfolios.

Market-neutral strategies are long/short portfolios constructed in a manner to ensure that the portfolio’s exposures to a wide variety of risk factors is zero. In addition, these portfolios may be neutralized against a wide variety of other risk factors.

The Merits of Long-Only Investing

An investor’s choice of whether to pursue a long-only strategy or some variation of a long/short strategy is likely to be influenced by several considerations:

• Long-term risk premiums

• Capacity and scale (the ability to invest assets)

• Limited legal liability and risk appetite

• Regulatory constraints

• Transactional complexity

• Management costs

• Personal ideology

Long-term risk premiums

A major motivation for investors to be long only is the generally accepted belief that there is a positive long-run premium to be earned from bearing market risk. Investors may also believe that risk premiums can be earned from other sources of risk, such as Size, Value, or Momentum. To capture these risk premiums, investors must over time own (go net “long”) the underlying securities that are exposed to these risks. Although risk premiums have been shown to earn a return in the long run, realized risk premium returns can be negative in the short run; the market can and does experience returns less than the risk-free rate, and recall the earlier discussion regarding the cyclicality of the Size, Value, and Momentum factors. For investors with shorter-term investment horizons, the potential benefits of a positive expected risk premium over the long run may not offset the potential risk of market declines or other reversals. These investors may pursue an approach other than strictly long-only investing and may prefer to short-sell some securities.

Capacity and scalability

Long-only investing, particularly strategies that focus on large-cap stocks, generally offers greater investment capacity than other approaches. For example, the MSCI ACWI has a total market cap of nearly $65.8 trillion, and the 10 largest companies are worth $10.4 trillion as of September 30, 2021.42 For large institutional investors, such as pension plans, there are no effective capacity constraints in terms of the total market cap available for long-only large-cap investing. Long-only strategies may face capacity constraints, however, if they focus on smaller and illiquid stocks or employ a strategy reliant on a high level of portfolio turnover. Unlike long-only strategies, the capacity of short-selling strategies is limited by the availability of securities to borrow.

Limited legal liability

Common stocks are limited liability financial instruments. The lowest a stock price can fall to is zero, so the maximum amount that a long-only investor in a common stock can lose is the amount of money that she invested in the stock. Thus, long-only investing puts a firm floor on how much an investor can lose. In contrast, a short-seller’s potential losses are unlimited in principle. The short-seller loses money as the stock price rises, and there is no ceiling limiting the price increase. This type of “naked” short-selling is quite risky. To offset this risk, investors often combine a short-selling strategy with a long-only strategy. Indeed, long/short strategies are often less risky than long-only or short-only strategies.

Regulatory

Some countries ban short-selling activities. Others have temporarily restricted or banned short-selling. For example, on 18 September 2008, the UK Financial Services Authority (FSA) temporarily prohibited the short-selling of financial companies to protect the integrity of the financial system. The US Securities and Exchange Commission (SEC) followed suit the next day. Additionally, many countries that allow short-selling prohibit or restrict naked short-selling, a practice consisting of short-selling a tradable asset without first borrowing the security or ensuring that it can be borrowed.

Transactional complexity

The mechanics of long-only investing are relatively simple and easy to understand. The investment manager instructs a broker (or uses an electronic platform) to buy stock XYZ. The broker executes the trade on the client’s behalf and arranges for the security to be delivered to the client’s account. Typically, a custodial bank sits between the investment adviser and the client. In this case, the custodian would deliver the cash for the stock and take possession of the shares of XYZ stock. If the shares are held in a custodial bank, the adviser can liquidate the position at any time (a caveat is that to exercise this flexibility completely, the custodian must be instructed not to lend out the shares). In long-only investing, buying and selling stocks are straightforward, intuitive transactions.

A short-selling transaction is more complex. The investor first needs to find shares of stock to borrow. Although many stocks are easy to borrow, others may be hard to locate, and the cost to borrow these shares can be much higher. Investors must also provide collateral to ensure that they can repay the borrowed stock if the price moves up. Borrowed stock may also be recalled at an inopportune time for the short-seller.

In many regions, regulated investment entities must use a custodian for all the transactions. When a custodian is involved, complicated three-party agreements (between the fund, prime broker, and custodian) are required. The agreements govern the buying and selling of securities as well as the management of collateral. An investor who does not use a custodian is exposed to counterparty risk—the collateral is often held in a general operating account of a prime broker. If the prime broker goes bankrupt, the collateral can vanish (which happened to many investors in the Lehman Brothers bankruptcy). Operational risk is significantly greater with long/short investing.

Management costs

Long-only investing is less expensive, both in terms of management fees and from an operational perspective. Managers of long/short products often charge fees that are a multiple of what long-only managers typically charge. Three categories of long/short products are active extension, market neutral, and directional.43 As of 2021, long/short hedge funds typically charge hedge fund fixed fees of about 2% and performance fees of about 20%. It follows, then, that the investor in a long/short product must have a high degree of confidence in the manager’s ability to extract premiums or generate alpha relative to lower-fee, long-only managers.

Personal ideology

Some investors may express a preference for long-only investment for ideological reasons. They may feel that directly gaining from the losses of others is morally wrong, as might be the case in short-selling. Some investors may believe that short-selling requires significantly greater expertise than long-only investing and that such expertise is not reliably available or consistent. And some might argue that short-selling requires significant leverage to achieve the targeted long-term expected return, and they may be unwilling to assume this risk. In short, some investors may “just say no” to anything other than long-only investing.

Long/Short Portfolio Construction

Investors may be interested in long/short strategies for a variety of reasons. For example, the conviction of negative views can be more strongly expressed when short-selling is permitted than in a long-only approach. In addition, short-selling can help reduce exposures to sectors, regions, or general market movements and allow managers to focus on their unique skill set. Finally, the full extraction of the benefits of risk factors requires a long/short approach (i.e., short large cap and long small cap, short growth and long value, short poor price momentum and long high price momentum, etc.). Long-only investors can profit from only part of the opportunity set.

There are many different styles of long/short strategies, each driven by its own investment thesis. Exhibit 27 presents a range of possible options to structure a long/short portfolio. Implementation of long/short strategies varies with their intended purpose. In a long-only portfolio construction process, the weights assigned to every asset must be greater than or equal to 0 and the weights must sum to 1. In the long/short approach, position weights can be negative and the weights are not necessarily constrained to sum to 1. Some long/short portfolios may even have aggregate exposure of less than 1. The absolute value of the longs minus the absolute value of the shorts is called the portfolio’s net exposure. The sum of the longs plus the absolute value of the shorts is called the portfolio’s gross exposure.

A comprehensive use of long/short strategies can also be found in the design of equal-risk-premium products. Such products seek to extract return premiums from rewarded factors, often across asset classes. To do so, the manager must create long/short sub-portfolios extracting these premiums (such as Size, Value, Momentum, and Low Beta) and combine these sub-portfolios using weightings that ensure each component will contribute the same amount of risk to the overall portfolio. The combination may be levered across all sub-portfolios to achieve a specific volatility level. In other words, the manager is using long and short positions as well as leverage (or deleveraging) to achieve the most efficient combination of rewarded factors.

Exhibit 27:

Illustrative Long/Short Portfolio Structures (as a percentage of capital)

	Long Positions	Short Positions	Cash	Gross Exposure	Net Exposure
Long only	100	0	0	100	100
130/30 long extension	130	30	0	160	100
Market neutral − low risk	50	50	100	100	0
Market neutral − higher risk	100	100	100	200	0
Directional − low risk	80	40	60	120	40
Net short	40	100	160	140	−60

Long/short managers typically define their exposure constraints as part of the portfolio construction process. For example, many equity hedge funds have a strategy of targeting a gross exposure (long plus short) of 150%–200% while targeting a net exposure (long minus short) of 0%–60%. A net exposure greater than zero implies some positive exposure to the Market factor. Regardless of the investment approach, all long/short strategies must establish parameters regarding the desired level of gross and net exposure, and these parameters will provide the investor with meaningful information about the manager’s strategy and its expected risk profile.

Long Extension Portfolio Construction

Long extension strategies are a hybrid of long-only and long/short strategies. They are often called “enhanced active equity” strategies. A particular enhanced active equity strategy called “130/30” was popular until the market decline during the global financial crisis.44 This strategy is making inroads again as investors better understand the potential pitfalls of shorting and are seeking more return in a low interest rate environment. A 130/30 strategy builds a portfolio of long positions worth 130% of the wealth invested in the strategy—that is, 1.3 times the amount of capital. At the same time, the portfolio holds short positions worth 30% of capital. The long and short positions combined equal 100% of capital. In essence, the short positions are funding the excess long positions, and the resulting gross leverage (160% = 130% + 30%) potentially allows for greater alpha and a more efficient exposure to rewarded factors. Unlike leverage incurred via cash borrowing in a long-only portfolio, which can be used only to exploit long insights, the long/short approach allows the portfolio to benefit not only from insights on companies that are forecasted to perform well (the long positions) but also from insights on companies forecasted to perform poorly (the short positions). In theory, this strategy offers the opportunity to magnify total returns. Of course, the long/short approach could also lead to greater losses if the manager is simultaneously wrong on both his long and short picks.

Another benefit of the 130/30 strategy is that long-only managers are limited in their ability to underallocate to securities that have a small initial allocation in the benchmark. For example, if Security X has a 0.25% allocation within the benchmark, a long-only manager can express a negative view on the stock only to the extent of its 0.25% benchmark weight by omitting the security from the portfolio. A 130/30 strategy affords the possibility of sizing the underweight in line with the manager’s expectations for the stock. This ability allows the strength of the positive and negative views to be expressed more symmetrically.

Market-Neutral Portfolio Construction

Market-neutral portfolio construction is a specialized form of long/short portfolio construction. At a very simple, naive level, one might think that in this strategy, the dollars invested in long securities are identical to the dollars associated with short-selling—that is, a portfolio with zero net investment, often called “dollar neutral.” But dollar neutral is not the same thing as market neutral, because the economic drivers of returns for the long side may not be the same as the economic drivers for the short side.

True market-neutral strategies hedge out most market risk. They are often employed when the investor wants to remove the effects of general market movements from returns to explicitly focus on the manager’s skill in forecasting returns of stocks, sectors, factors, or geographic regions. In essence, the investor wants to remove the “noise” that market movements can create to better focus on the creation of positive abnormal returns. In isolation, this strategy could be considered risky. For example, if stock prices appreciate rapidly (and historically, stock prices do rise), then the investor would miss out on this appreciation. However, some investors might add this type of strategy to their overall portfolio to increase diversification and at least partially offset losses in other parts of the portfolio when stock prices decline.

Market-neutral portfolio construction attempts to exactly match and offset the systematic risks of the long positions with those of the short positions. For example, if one uses beta as the measure of systematic risk, then a market-neutral portfolio, using longs and shorts, would have a Market beta of zero. A simple example of zero-beta investment would be a fund that is long $100 of assets with a Market beta of 1 and short $80 of assets with a Market beta of 1.25. This concept can be extended to include other systematic factors that influence returns, such as Size, Value, and Momentum. In other words, the market-neutral concept can be implemented for a variety of risk factors. The main constraint is that in aggregate, the targeted beta(s) of the portfolio be zero.

A market-neutral strategy is still expected to generate a positive information ratio. Although market neutral may seek to eliminate market risk and perhaps some other risks on an ex ante basis, the manager cannot eliminate all risks. If she could—and did—the expected return would likely be equal to the risk-free rate minus the manager’s fees. The objective is to neutralize the risks for which the manager believes she has no comparative forecasting advantage, thus allowing the manager to concentrate on her very specific skills.

Given that market-neutral strategies seek to remove major sources of systematic risk from a portfolio, these strategies are usually less volatile than long-only strategies. They are often considered absolute return strategies because their benchmarks might be fixed-income instruments. Even if a market-neutral strategy is not fully successful in its implementation, the correlation of market-neutral strategies with other types of strategies is typically quite low. Thus, some market-neutral strategies may serve more of a diversification role in a portfolio, rather than a high-return-seeking role.

A specific form of market-neutral strategy is pairs trading, where an investor will go long one security in an industry and short another security in the same industry, trying to exploit what the investor perceives as “mispricing.” A more quantitatively oriented form of pairs trading called statistical arbitrage (“stat arb”) uses statistical techniques to identify two securities that are historically highly correlated with each other. When the price correlation of these two securities deviates from its long-term average (and if the manager believes that the deviation is temporary), the manager will go long the underperforming stock and simultaneously short the outperforming stock. If the prices do converge to the long-term average as forecasted, the manager will close the trade and realize a profit.

In other variations of market-neutral investing, one might find portfolios constructed with hundreds of securities identified using systematic multi-factor models that evaluate all securities in the investable universe. The manager will buy the most favorably ranked securities and short the least favorably ranked ones. The manager may impose constraints on exposures of the longs and the shorts to keep gross and net exposures at the desired levels.

Market-neutral strategies have two inherent limitations:

1. Practically speaking, it is no easy task to maintain a beta of zero. Not all risks can be efficiently hedged, and correlations between exposures are continually shifting.

2. Market-neutral strategies have a limited upside in a bull market unless they are “equitized.” Some investors, therefore, choose to index their equity exposure and overlay long/short strategies. In this case, the investor is not abandoning equity-like returns and is using the market-neutral portfolio as an overlay.

Benefits and Drawbacks of Long/Short Strategies

Long/short strategies offer the following benefits:

• Ability to more fully express short ideas than under a long-only strategy

• Efficient use of leverage and of the benefits of diversification

• Greater ability to calibrate/control exposure to factors (such as Market and other rewarded factors), sectors, geography, or any undesired exposure (such as, perhaps, sensitivity to the price of oil)

We’ve explored the first two benefits of long/short portfolio construction listed above. Let’s look more closely at the last one.

A fully invested long-only strategy will be exposed to market risk. To reduce the level of market risk, the manager must either concentrate holdings in low-beta stocks or hold a portion of the assets in cash, an asset that produces minimal return. Conversely, to increase the level of market risk, the long-only manager must own high-beta stocks or use financial leverage; the cost of leverage will reduce future returns. Practically speaking, the portfolio beta of a long-only manager is likely constrained within a range of, say, 0.8–1.2. In contrast, a long/short manager has much more flexibility in adjusting his level of market exposure to reflect his view on the current opportunities.

In long-only portfolios, total portfolio risk is dominated by the Market factor, and the Market factor is a long-only factor. However, all other factor returns can be thought of as long/short portfolios: Size is long small cap and short large cap, Value is long value and short growth, Momentum is long positive momentum and short less positive or negative momentum, and so on. Just like with beta, the ability to tilt a portfolio in favor of these other factors or diversify efficiently across factors is structurally restricted in a long-only portfolio. Because the average of cross correlations among rewarded factors is close to zero or even negative, efficiently allocating across factors could bring significant diversification benefits. But the ability to reduce overall risk and to distribute sources of risk more evenly cannot be optimally achieved without short-selling.

Strategies that short securities contain the following inherent risks, which must be understood:

1. Unlike a long position, a short position will move against the manager if the price of the security increases.

2. Long/short strategies sometimes require significant leverage. Leverage must be used wisely.

3. The cost of borrowing a security can become prohibitive, particularly if the security is hard to borrow.

4. Collateral requirements will increase if a short position moves against the manager. In extreme cases, the manager may be forced to liquidate some favorably ranked long positions (and short positions that might eventually reverse) if too much leverage has been used. The manager may also fall victim to a short squeeze. A short squeeze is a situation in which the price of the stock that has been shorted has risen so much and so quickly that many short investors may be unable to maintain their positions in the short run in light of the increased collateral requirements. The “squeeze” is worsened as short-sellers liquidate their short position, buying back the security and possibly pushing the price even higher.

As previously indicated, to short-sell securities, investors typically rely on a prime broker who can help them locate the securities they wish to borrow. But the prime broker will require collateral from the short-sellers to assure the lenders of these securities that their contracts will be honored. The higher the relative amount of short-selling in a portfolio, the greater the amount of collateral required. A portfolio with 20% of capital invested short may be required to put up collateral equal to 40% of the short positions, whereas a portfolio with 100% of capital invested short could be required to put up collateral equal to 200% of the short positions. In addition, different types of assets are weighed differently in the calculation of collateral value. For example, a US Treasury bill may be viewed as very safe collateral and accorded 100% of its value toward the required collateral. In contrast, a high-yield bond or some other asset with restricted liquidity would have only a portion of its market value counted toward the collateral requirement.

These collateral requirements are designed to protect the lender in the event of adverse price movements. When stock prices are rising rapidly, the lender may recall all the borrowed shares, fearing that the borrower’s collateral will be wiped out. If this were to happen, the leveraged long/short manager would be forced to close out his short positions at an inopportune time, leaving significant profits on the table. In the end, long/short investing is a compromise between return impacts, sources of risk, and costs, as illustrated in the table below.

Benefits	Costs
Short positions can reduce market risk. Shorting potentially expands benefits from other risk premiums and alpha. The combination of long and short positions allows for a greater diversification potential.	Short positions might reduce the market return premium. Shorting may amplify the active risk (but please note that it does note have to do so). There are higher implementation costs and greater complexity associated with shorting and leverage relative to a long-only approach.

EXAMPLE 9

Creating a 130/30 Strategy

Alpha Prime has been managing long-only equity portfolios for more than 15 years. The firm has a systematic investment process built around assessing security valuation and price momentum. Each company is attributed a standardized score (Fk) that is based on a combination of quantitative and fundamental metrics. Positions are selected from among those securities with a positive standardized score and are weighted based on the strength of that score. The security weightings within sectors can be significantly different from those of the benchmark, but the portfolio’s sector weightings adhere closely to the benchmark weights. Investment decisions are made by the portfolio management team and are re-evaluated monthly. A constrained optimization process is used to guide investment decision making. Listed below are the objective function and the primary constraints used by the firm.

• Objective function: Maximize the portfolio factor score

• Total exposure constraint: Sum of portfolio weights must = 1

• Individual security constraint: Minimum weight of 0% and maximum weight of 3%

• Sector constraint: Benchmark weight ±5%

• Constraint on active risk (TE): Active risk less than 5%

The managers at Alpha Prime have realized that their investment process can also generate a negative signal, indicating that a security is likely to underperform. However, the signal is not quite as reliable or stable when it is used for this purpose. There is much more noise around the performance of the expected losers than there is around the performance of the winners. Still, the signal has value.

1. You are asked to draft guidelines for the creation of a 130/30 strategy. What changes to the objective function and to each of the constraints would you recommend?

   Solution to 1:

   • Objective function: The objective function would remain the same. Securities with a positive standardized score would be eligible for positive weights, and securities with a negative standardized factor score would receive negative weights (the fund would short these securities).

   • Total exposure constraint: The portfolio now needs a constraint for gross exposure and one for net exposure. The net exposure constraint in a 130/30 product is constrained to 100%. (The notional value of the longs minus the absolute value of the shorts must be equal to 1.) The portfolio’s gross exposure constraint is implicit in the nature of the 130/30 product. (The notional value of the longs plus the absolute value of the shorts cannot exceed 160%.)

   • Individual security constraint: To take advantage of the negative signals from the model, the portfolio must allow shorting. The minimum weight constraint must be relaxed. Given the issues associated with short-selling, the firm’s relative inexperience in this area, and the lower reliability of the short signal, the maximum short position size should be smaller than the maximum long position size. One might recommend that the initial short constraint be set at 1%. Position limits on the long side could stay the same, but that would likely lead to more long positions, given the increase in long exposure to 130%. The manager must assess whether to expand the number of securities held in the portfolio or to raise the maximum position size limit.

   • Sector constraint: There is no need to change the aggregate sector constraint. The manager now has the ability to offset any overweight on the long side with a short position that would bring the portfolio’s exposure to that sector back within the current constraint.

   • Tracking error target: Sector deviations have a greater bearing on active risk than do security-level differences. Alpha Prime’s sector bets are very limited; thus, no change in the tracking error constraint is necessary. The ability to short gives them greater opportunity to exploit investment ideas without changing the firm’s approach to sector weightings.

2. Discuss the potential challenges of incorporating short positions into the portfolio strategy.

   Solution to 2:

   Shorting adds complexity to both the operational and the risk aspects of portfolio management. Operationally, the firm must establish relationships with one or more prime brokers and ensure that adequate collateral for the short positions remains available. Some securities can be difficult to borrow, and the cost of borrowing some stocks can be prohibitive. This may inhibit Alpha Prime’s ability to implement its short ideas and will raise the operational costs of running the portfolio. In addition, shorting introduces a new type of risk: A short transaction has no loss limit. If the stock moves against the manager in the short run, the manager may have to close the position before he is proven right.

EXAMPLE 10

Long Only vs. Long/Short

Marc Salter has been running a long-only unlevered factor-based strategy in the US market for more than five years. He has delivered a product that has all the expected exposure to rewarded risk factors promised to investors. Salter just met with a pension fund investor looking at a multi-factor based approach. However, the pension fund manager indicates they are also considering investing with a competitor that runs a leveraged long/short factor-based strategy. It appears the competitor’s product has a significantly higher information ratio. The product of the competitor neutralizes market risk and concentrates on exposure to other rewarded factors.

1. Why would the competitor’s long/short product have a higher information ratio?

   Solution to 1:

   Factor returns are usually built from a long portfolio having the desired factor characteristic against a short portfolio that does not. A long-only factor investor is limited in his ability to short (relative to the benchmark) positions that do not have the desired characteristics. Adding the ability to leverage negative as well as positive research insights should improve the transfer coefficient and increase the potential to generate better excess returns.

   In addition, in a long-only strategy, the Market factor dominates all other risks. Adding the ability to short could facilitate a more balanced distribution of risk. Given the similar volatilities and low cross correlations among factors, the more balanced distribution of risk can be expected to reduce the tracking error of the strategy, thereby improving the information ratio.

2. What are its drawbacks?

   Solution to 2:

   Multi-factor products often contain several hundred securities, some of which may be difficult to borrow. The complexity of shorting across this large number of names combined with higher management fees and implementation costs may necessitate more implementation constraints on the short side.

   Removing the risk associated with the Market factor implies that the long/short product would most likely be used as an overlay on long-only mandates. The mandate may also be leveraged (more than 1× long and 1× short) to maximize the potential return per dollar of capital. For example, equal-risk-premium products (that remove the effect of the Market factor) often need three units of leverage long and short to achieve a 10% absolute risk target. Some investors may be uncomfortable with such leverage.