AEI - Portfolio Constructions (Practices)
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Last updated
Ayanna Chen is a portfolio manager at Aycrig Fund, where she supervises assistant portfolio manager Mordechai Garcia. Aycrig Fund invests money for high-net-worth and institutional investors. Chen asks Garcia to analyze certain information relating to Aycrig Fund’s three sub-managers, Managers A, B, and C.
Manager A has $250 million in assets under management (AUM), an active risk of 5%, an information coefficient of 0.15, and a transfer coefficient of 0.40. Manager A’s portfolio has a 2.5% expected active return this year.
Chen directs Garcia to determine the maximum position size that Manager A can hold in shares of Pasliant Corporation, which has a market capitalization of $3.0 billion, an index weight of 0.20%, and an average daily trading volume (ADV) of 1% of its market capitalization.
Manager A has the following position size policy constraints:
Allocation: No investment in any security may represent more than 3% of total AUM.
Liquidity: No position size may represent more than 10% of the dollar value of the security’s ADV.
Index weight: The maximum position weight must be less than or equal to 10 times the security’s weight in the index.
Manager B holds a highly diversified portfolio that has balanced exposures to rewarded risk factors, high active share, and a relatively low active risk target.
Selected data on Manager C’s portfolio, which contains three assets, is presented in Exhibit 1.
Exhibit 1:
Selected Data on Manager C’s Portfolio
Chen considers adding a fourth sub-manager and evaluates three managers’ portfolios, Portfolios X, Y, and Z. The managers for Portfolios X, Y, and Z all have similar costs, fees, and alpha skills, and their factor exposures align with both Aycrig’s and investors’ expectations and constraints. The portfolio factor exposures, risk contributions, and risk characteristics are presented in Exhibits 2 and 3.
Exhibit 2:
Portfolio Factor Exposures and Factor Risk Contribution
Exhibit 3:
Portfolio Risk Characteristics
Portfolio X
Portfolio Y
Portfolio Z
Annualized volatility
10.50%
13.15%
15.20%
Annualized active risk
2.90%
8.40%
4.20%
Active share
0.71
0.74
0.63
Chen and Garcia next discuss characteristics of long–short and long-only investing. Garcia makes the following statements about investing with long–short and long-only managers:
Statement 1
A long–short portfolio allows for a gross exposure of 100%.
Statement 2
A long-only portfolio generally allows for greater investment capacity than other approaches, particularly when using strategies that focus on large-cap stocks.
Chen and Garcia then turn their attention to portfolio management approaches. Chen prefers an approach that emphasizes security-specific factors, engages in factor timing, and typically leads to portfolios that are generally more concentrated than those built using a systematic approach.
QuestionQ.
The number of truly independent decisions Manager A would need to make in order to earn her expected active portfolio return this year is closest to:
A.8.
B.11.
C.69.
Solution
Q.
Which of the following position size policy constraints is the most restrictive in setting Manager A’s maximum position size in shares of Pasliant Corporation?
Solution
A is correct. The maximum position size in shares of Pasliant Corporation (PC) is determined by the constraint with the lowest dollar amount. The maximum position size for PC under each constraint is calculated as follows:
Liquidity Constraint
Dollar value of PC traded daily = PC market cap × Average daily trading volume
Dollar value of PC traded daily = $3 billion × 1.0% = $30 million
Liquidity constraint = Dollar value of PC traded daily × Liquidity % threshold
Liquidity constraint = $30 million × 10% = $3 million
Allocation Constraint
Allocation constraint = AUM × Maximum position size threshold
Allocation constraint = $250 million × 3.0% = $7.5 million
Index Weight Constraint
Index weight constraint = AUM × (Index weight × 10)
Index weight constraint = $250 million × (0.20% × 10) = $5.0 million
The liquidity constraint of $3.0 million is less than both the $5.0 million index weight constraint and the $7.5 million allocation constraint. Therefore, the maximum allowable position size that Manager A may take in PC is $3.0 million.
Q.
Manager B’s portfolio is most likely consistent with the characteristics of a:
A.pure indexer.
B.sector rotator.
C.multi-factor manager.
Solution
C is correct. Most multi-factor products are diversified across factors and securities and typically have high active share but have reasonably low active risk (tracking error), often in the range of 3%. Most multi-factor products have a low concentration among securities in order to achieve a balanced exposure to risk factors and minimize idiosyncratic risks. Manager B holds a highly diversified portfolio that has balanced exposures to rewarded risk factors, a high active share, and a relatively low target active risk—consistent with the characteristics of a multi-factor manager.
Selected data on Manager C’s portfolio, which contains three assets, is presented in Exhibit 1.
Exhibit 1:
Selected Data on Manager C’s Portfolio
Solution
B is correct. The contribution of an asset to total portfolio variance equals the summation of the multiplication between the weight of the asset whose contribution is being measured, the weight of each asset (xj), and the covariance between the asset being measured and each asset (Cij), as follows:
The contribution of Asset 2 to portfolio variance is computed as the sum of the following products:
Weight of Asset 2 × Weight of Asset 2 × Covariance of Asset 2 with Asset 2, plus
0.45 × 0.45 × 0.01960
Weight of Asset 2 × Weight of Asset 3 × Covariance of Asset 2 with Asset 3
0.45 × 0.25 × 0.00224
= Asset 2’s contribution to total portfolio variance
0.005639
Imagine you have three ingredients (assets) in a recipe (portfolio). Each ingredient's amount (weight) and how it mixes with the main ingredient (covariance with Asset 2) affect the overall flavor (risk). By considering both the amount and how well it mixes, we get the total impact on the flavor.
Q.
Based on Exhibits 2 and 3, which portfolio best exhibits the risk characteristics of a well-constructed portfolio?
A.Portfolio X
B.Portfolio Y
C.Portfolio Z
Solution
A is correct. Well-constructed portfolios should have low idiosyncratic (unexplained) risk relative to total risk. Portfolio Y exhibits extremely high unexplained risk relative to total risk, and Portfolios X and Z have low unexplained risk relative to total risk. Therefore, Portfolio Y may be eliminated.
Portfolios X and Z have comparable factor exposures. In comparing portfolios with comparable factor exposures, the portfolio with lower absolute volatility and lower active risk will likely be preferred, assuming similar costs. Portfolio X has lower absolute volatility and lower active risk than Portfolio Z, although both have similar costs.
Finally, for managers with similar costs, fees, and alpha skills, if two products have similar active and absolute risks, the portfolio having a higher active share is preferred. Portfolio X has lower absolute volatility, lower active risk, and higher active share than Portfolio Z. As a result, Portfolio X best exhibits the risk characteristics of a well-constructed portfolio.
Q.
Which of Garcia’s statements regarding investing with long–short and long-only managers is correct?
A.Only Statement 1
B.Only Statement 2
C.Both Statement 1 and Statement 2
Solution
C is correct. Both Statement 1 and Statement 2 are correct.
Statement 1 is correct because, similar to a long-only portfolio, a long–short portfolio can be structured to have a gross exposure of 100%. Gross exposure of the portfolio is calculated as the sum of the long positions and the absolute value of the short positions, expressed as percentages of the portfolio’s capital.
Gross exposure = Long positions + |Short positions|
Gross exposure long-only portfolio = 100% (Long positions) + 0% (Short positions) = 100%
Gross exposure long–short portfolio = 50% (Long positions) + |−50%| (Short positions) = 100%
Statement 2 is correct because long-only investing generally offers greater investment capacity than other approaches, particularly when using strategies that focus on large-cap stocks. 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 investing.
Q.
Chen’s preferred portfolio management approach would be best described as:
A.top down.
B.systematic.
C.discretionary.
Solution
C is correct. Chen prefers an approach that emphasizes security-specific factors, engages in factor timing, and typically leads to portfolios that are generally more concentrated than those built using a systematic approach. These characteristics reflect a discretionary bottom-up portfolio management approach.
Monongahela Ap is an equity fund analyst. His manager asks him to evaluate three actively managed equity funds from a single sponsor, Chiyodasenko Investment Corp. Ap’s assessments of the funds based on assets under management (AUM), the three main building blocks of portfolio construction, and the funds’ approaches to portfolio management are presented in Exhibit 1. Selected data for Fund 1 is presented in Exhibit 2.
Exhibit 1:
Ap’s Assessments of Funds 1, 2, and 3
Fund
Fund Category
Fund Size (AUM)
Number of Securities
Description
1
Small-cap stocks
Large
Small
Fund 1 focuses on skillfully timing exposures to factors, both rewarded and unrewarded, and to other asset classes. The fund’s managers use timing skills to opportunistically shift their portfolio to capture returns from factors such as country, asset class, and sector. Fund 1 prefers to make large trades.
2
Large- cap stocks
Large
Large
Fund 2 holds a diversified portfolio and is concentrated in terms of factors. It targets individual securities that reflect the manager’s view that growth firms will outperform value firms. Fund 2 builds up its positions slowly, using unlit venues when possible.
3
Small- cap stocks
Small
Large
Fund 3 holds a highly diversified portfolio. The fund’s managers start by evaluating the risk and return characteristics of individual securities and then build their portfolio based on their stock-specific forecasts. Fund 3 prefers to make large trades.
Exhibit 2:
Selected Data for Fund 1
Factor
Market
Size
Value
Momentum
Coefficient
1.080
0.098
−0.401
0.034
Variance of the market factor return and covariances with the market factor return
0.00109
0.00053
0.00022
−0.00025
Portfolio’s monthly standard deviation of returns
3.74%
Ap learns that Chiyodasenko has initiated a new equity fund. It is similar to Fund 1 but scales up active risk by doubling all of the active weights relative to Fund 1. The new fund aims to scale active return linearly with active risk, but implementation is problematic. Because of the cost and difficulty of borrowing some securities, the new fund cannot scale up its short positions to the same extent that it can scale up its long positions.
Ap reviews quarterly holdings reports for Fund 3. In comparing the two most recent quarterly reports, he notices differences in holdings that indicate that Fund 3 executed two trades, with each trade involving pairs of stocks. Initially, Fund 3 held active positions in two automobile stocks—one was overweight by 1 percentage point (pp), and the other was underweight by 1pp. Fund 3 traded back to benchmark weights on those two stocks. In the second trade, Fund 3 selected two different stocks that were held at benchmark weights, one energy stock and one financial stock. Fund 3 overweighted the energy stock by 1pp and underweighted the financial stock by 1pp.
In Fund 3’s latest quarterly report, Ap reads that Fund 3 implemented a new formal risk control for its forecasting model that constrains the predicted return distribution so that no more than 60% of the deviations from the mean are negative.
QuestionQ.
Based on Exhibit 1, the main building block of portfolio construction on which Fund 1 focuses is most likely:
Solution
A is correct. The three main building blocks of portfolio construction are alpha skills, position sizing, and rewarded factor weightings. Fund 1 generates active returns by skillfully timing exposures to factors, both rewarded and unrewarded, and to other asset classes, which constitute a manager’s alpha skills.
Q.
Which fund in Exhibit 1 most likely follows a bottom-up approach?
Solution
C is correct. Bottom-up managers evaluate the risk and return characteristics of individual securities and build portfolios based on stock-specific forecasts; Fund 3 follows this exact approach. Example views of bottom-up managers include expecting one auto company to outperform another, expecting a pharmaceutical company to outperform an auto company, and expecting a technology company to outperform a pharmaceutical company. Both bottom-up and top-down managers can be either diversified or concentrated in terms of securities.
Q.
Which fund in Exhibit 1 most likely has the greatest implicit costs to implement its strategy?
Solution
A is correct. Because Fund 1 has a large AUM but focuses on small-cap stocks, holds a relatively small number of securities in its portfolio, and prefers to make large trades, Fund 1 likely has the highest implicit costs. Each of these characteristics serves to increase the market impact of its trades. Market impact is a function of the security’s liquidity and trade size. The larger a trade size relative to a stock’s average daily volume, the more likely it is that the trade will affect prices. The relatively low level of trading volume of small-cap stocks 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.
Q.
Based on Exhibit 2, the portion of total portfolio risk that is explained by the market factor in Fund 1’s existing portfolio is closest to:
A.3%.
B.81%.
C.87%.
Q.
Relative to Fund 1, Chiyodasenko’s new equity fund will most likely exhibit a lower:
A.information ratio.
B.idiosyncratic risk.
C.collateral requirement.
Solution
A is correct. As the new fund scales up active risk by doubling active weights, it will face implementation constraints that will prevent it from increasing the weights of many of its short positions. The information ratio (IR) is defined as the ratio of active return to active risk. If there were no constraints preventing the new fund from scaling up active weights, it could scale up active risk by scaling up active weights, proportionally increase active return, and keep the IR unchanged. Implementation constraints experienced by the new fund, however, such as the cost and difficulty in borrowing securities to support the scaled-up short positions, will prevent the active return from proportionally increasing with the active risk. Therefore, the IR would most likely be lower for the new fund than for Fund 1. As the following chart illustrates, as active risk is scaled up, implementation constraints create diminishing returns to scale for active returns, thereby degrading the IR.
Q.
As a result of Fund 3’s two trades, the portfolio’s active risk most likely:
A.decreased.
B.remained unchanged.
C.increased.
Solution
C is correct. Active risk is affected by the degree of cross-correlation. The correlation of two stocks in different sectors is most likely lower than the correlation of two stocks in the same sector. Therefore, the correlation of the energy/financial pair is most likely lower than that of the automobile/automobile pair. Because both positions were implemented as an overweight and underweight, the lower correlation of the two stocks in the new position should contribute more to active risk than the two-stock position that it replaced.
Q.
What was the effect of Fund 3’s two trades on its active share? Fund 3’s active share:
Solution
B is correct. Active share changes only if the total of the absolute values of the portfolio’s active weights changes. For the two trades in Fund 3, both the initial position and the new position involved two stocks such that one was 1pp underweighted and the other was 1pp overweighted. Although the active weights of particular securities did change between the initial position and the new position, the total absolute active weights did not change. Therefore, the portfolio’s active share did not change.
Which risk measure does Fund 3’s new risk control explicitly constrain?
Solution
B is correct. Skewness measures 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 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. Fund 3’s new risk control constrains its model’s predicted return distribution so that no more than 60% of the deviations from the mean are negative. This is an explicit constraint on skewness.
Lisette Langham Case Scenario
Exhibit 1
Rewarded Factor Results
Factor Sources of Performance over 15 years
Market
Russell 1000 Value (Benchmark)
MFC Value Fund
Market
0.71%
0.59%
0.50%
Size
0.0%
–0.04%
0.02%
Value
0.0%
0.08%
0.11%
Momentum
0.0%
0.08%
0.05%
Alpha (non-factor related)
0.0%
–0.05%
–0.05%
Total monthly performance
0.71%
0.66%
0.63%
On viewing Exhibit 1, Shaw makes the following comments about the MFC Value Fund:
The small-cap tilt helped.
Value funds were out of favor, as shown by the Value factor results.
Of course, the MFC Value Fund must have a lower alpha because its performance was 0.03 percentage point worse than its benchmark.
Shaw has particular interest in MFC’s popular Soar Fund (Soar), which relies on returns from factor exposures. The description of the fund states that it emphasizes security-specific factors, maintains low security concentration to keep idiosyncratic risk down, and embraces quality and value styles. Soar occasionally considers the economic and geopolitical environment, especially during unusual economic conditions. Langham tells Shaw how she classifies Soar’s portfolio construction approach.
Noting that MFC has two managers who use the same index as their benchmark, Shaw observes that Fund A and Fund B have similar Active Share and a similar number of positions, but Fund A’s realized active risk of 7% is almost three times greater than that of Fund B. Shaw makes the following comments:
I think Fund B makes a lot of sector bets.
Fund A likely has higher fees than Fund B
Fund A should have a greater dispersion of returns about the benchmark.
Shaw next asks Langham to show how risk targets and constraints might differ between fund managers depending on their respective skills. Langham has Shaw consider three fund managers, each of whom use the MSCI World Index benchmark. For each fund, risk targets have been assigned that allow the portfolio managers some flexibility to exercise their perceived skillsets. Skills include stock picking, factor exposure, and sector rotation. Based on only the data shown in Exhibit 2, Langham identifies the skill applied by each manager.
Exhibit 2:
Risk Targets and Constraints
Manager constraints
Fund X
Fund Y
Fund Z
Target active risk
8%
7%
4%
Max. sector deviations
1%
15%
10%
Max. risk contribution, single security
4%
2%
1%
Another of Langham’s clients, Marianne Quint, sits on the investment committee of the Amity Island Endowment. The $2 billion equity portion of the Amity fund is invested using a global equity index approach. Quint has been charged with identifying an active equity fund to replace 20% of the indexed portfolio. Three candidate funds with similar performance histories, benchmarks, and fees have been identified. Based on the characteristics shown in Exhibit 3, Quint asks Langham to recommend the fund that has demonstrated the best risk-efficient delivery of results.
Exhibit 3
Characteristics of Candidates for Amity Equity Portfolio
Fund Name
Blue
Ash
March
Sharpe ratio
1.11
0.90
0.92
Annualized active risk
5.5%
6.0%
3.2%
Active Share
0.41
0.48
0.75
Number of securities
340
290
140
Annualized portfolio volatility
11.5%
14.7%
14.9%
Covariance with Amity Fund
Low
High
Low
Langham also identifies the fund that could minimize the active risk of the total $2 billion Amity equity portfolio after replacement is complete.
Question
Which of Shaw’s comments about the MFC Value Fund in Exhibit 1 is most accurate? The comment concerning:
A.
alpha.
B.
small-cap tilt.
C.
value being out of favor.
Solution
B is correct. Shaw’s comment about a small-cap tilt is correct. Additional exposure to smaller firms resulted in a positive performance of 0.02% for the Size factor.
A is incorrect. Alpha is defined here to include performance unexplained by the factors and matches that of the benchmark.
C is incorrect. Although the value style does appear to be out of favor as shown by the lower return than that of the market (0.66% versus 0.71%), the Value factor has a positive contribution to the return (0.08%).
Active Equity Portfolio Construction Learning Outcome
Describe elements of a manager’s investment philosophy that influence the portfolio construction process
From the description of the Soar Fund, the most appropriate classification of its portfolio construction process is:
Solution
B is correct. The Soar Fund has characteristics most consistent with those of a bottom-up systematic manager. Emphasizing security-specific factors is a bottom-up method. Targeting low idiosyncratic risk along with low concentrations indicates a systematic approach, not a discretionary approach. Although the Soar Fund does sometimes consider macro data and events, this is not its primary top-down driver of portfolio construction.
A is incorrect. Although Soar does sometimes consider macro data and events, this is not its primary top-down driver of portfolio construction.
C is incorrect. Targeting low idiosyncratic risk along with low concentrations indicates a systematic approach, not a discretionary approach.
Active Equity Portfolio Construction Learning Outcome
Discuss approaches for constructing actively managed equity portfolios
In regard to Shaw’s comments about Fund A and Fund B, the one that is most accurate concerns:
A.
Fund A’s fees.
B.
Fund A’s dispersion.
C.
Fund B’s sector bets.
Solution
B is correct. Shaw’s comment about Fund A’s dispersion is correct. With a higher active risk (tracking error), Fund A has a greater likelihood of having results dispersed more broadly (both positive and negative) around benchmark results than Fund B has. Investors are more likely to be willing to pay higher fees for higher Active Share as an indicator of greater active management, but Active Share is identical for Fund A and Fund B. Sector bets are likely to affect active risk; therefore, Fund A is more likely to be using sector bets, not Fund B.
A is incorrect. Investors are more likely to be willing to pay higher fees for higher Active Share as an indicator of greater active management, but Active Share is identical for Fund A and Fund B.
C is incorrect. Sector bets are likely to affect active risk; therefore, it is Fund A that is more likely to be using sector bets, not Fund B.
Active Equity Portfolio Construction Learning Outcome
Contrast Active Share with active risk and discuss how each measure relates to a manager’s investment strategy
Among the funds shown in Exhibit 2, which one is most likely managed using a diversified multi-factor investor approach?
A. Fund X
B. Fund Y
C. Fund Z
Solution
C is correct. The risk targets for Fund Z are most likely those of a manager using a diversified multi-factor approach. Low single-security risk of 1% and modest overall portfolio risk of 4%, combined with flexibility on sector risk, demonstrate a highly diversified portfolio that primarily emphasizes factor exposures. Fund X has risk targets consistent with an emphasis on stock picking—namely, high active risk, high exposure to risk from a single security, and low sector deviations. Fund Y has risk targets consistent with an emphasis on sector rotation—namely, high active risk and a high tolerance for sector deviations.
A is incorrect. Fund X has risk targets consistent with an emphasis on stock picking—namely, high active risk, high exposure to risk from a single security, and low sector deviations.
B is incorrect. Fund Y has risk targets consistent with an emphasis on sector rotation—namely, high active risk and a high tolerance for sector deviations.
Active Equity Portfolio Construction Learning Outcome
Discuss approaches for constructing actively managed equity portfolios
The fund in Exhibit 3 that is most consistent with Quint’s requirements is:
A. Ash.
B. Blue.
C. March.
Solution
C is correct. The March Fund is the fund that is most consistent with Quint’s requirements for the best risk-efficient delivery of results. It delivers the lowest active risk (3.2%) using far fewer securities (140), indicating an efficient approach. The higher Active Share (0.75) for the similar level of fees also supports this decision.
A is incorrect. Ash has the highest active risk, which indicates active return contributions of a greater dispersion than the benchmark and the competing funds. More securities and lower Active Share are not supportive of this fund choice.
B is incorrect. Blue has the highest number of securities and a relatively low Active Share. Although the overall portfolio volatility is the lowest of the three (producing a higher Sharpe ratio), the more relevant risk is that attributable to active management. Greater active risk despite more securities is not the most efficient method.
Active Equity Portfolio Construction Learning Outcome
Evaluate the efficiency of a portfolio structure given its investment mandate
From Exhibit 3, the replacement candidate fund that, if included, will most likely minimize the active risk of the final Amity equity fund is:
A. Ash.
B. Blue.
C. March.
Solution
A is correct. Active risk is a measure of the volatility of portfolio returns relative to the volatility of benchmark returns. The Ash fund will most likely minimize the active risk when combined in the final Amity equity portfolio because of its high covariance with the present fund. The low-covariance funds may reduce overall portfolio volatility but not active risk.
B is incorrect. The low covariance with the Amity portfolio will lower the overall volatility of the fund but not the active risk, because active risk measures the volatility of portfolio returns relative to that of the benchmark: This will be achieved through the substitution of a high-covariance fund.
C is incorrect. The low covariance with the Amity portfolio will lower the overall volatility of the fund but not the active risk, because active risk measures the volatility of portfolio returns relative to that of the benchmark: This will be achieved through the substitution of a high covariance fund.
Active Equity Portfolio Construction Learning Outcome
Discuss risk measures that are incorporated in equity portfolio construction and describe how limits set on these measures affect portfolio construction
The Epsilon Institute Case Scenario
The Epsilon Institute of Theoretical Physics is a non-profit corporation initially funded from government and private sources. Mitch Lazare is the chairman of the Investment Committee, which oversees the institute’s endowment fund, of which about $750 million is currently under active management. He is currently tasked with finding two additional investment managers to manage a portion of the actively managed funds and, along with his assistant, Brian Warrack, is reviewing the presentations made by several applicants.
John Fraser’s performance is the first that Lazare and Warrack review. Fraser’s fund is constructed with a discretionary approach using the four Fama–French factors; he uses the Russell 1000 Value Index as his benchmark. The most recent 10 years of performance data for both the fund and the benchmark are shown in Exhibit 1.
Exhibit 1
Fraser Fund and Benchmark Average Monthly Performance over the Past 10 years
Russell 1000 Value Index
The Fraser Fund
Factor Performance
Monthly performance in excess of the risk-free rate
0.72%
0.55%
β to specified factor
Market
0.90
0.91
0.61%
Size
–0.27
0.15
0.17%
Value
0.38
0.60
0.18%
Momentum
0.15
0.08
0.72%
Average monthly risk-free rate
0.33%
As part of his evaluation of the applicants, Warrack compiles a record of the Active Share and active risk of the funds that they manage. He observes that the Mattley Fund has relatively high Active Share but relatively low active risk.
Lazare and Warrack make the following comments about Active Share and active risk in the context of a single-factor model:
The level of active risk will rise with an increase in idiosyncratic volatility.
The active risk attributed to Active Share will be smaller in more diversified portfolios.
If the factor exposure is fully neutralized, the Active Share will be entirely attributed to the active risk.
The manager of the Western Fund focuses on smaller companies in the Russell 1000 Value Index and uses the following constraints:
Size: The capitalization of the average company is $1.8 billion. On average, companies of this size trade 0.90% of their capitalization every day.
Liquidity: Positions can be no larger than 7% of average daily trading volume.
Allocation: Positions can be no larger than 1.75% of total assets under management.
Diversification: The portfolio must contain at least 60 securities.
If the manager of the Western Fund is hired by Epsilon, she will have $100 million of Epsilon’s funds to manage.
Lazare and Warrack turn their attention to the manager of the Herrick Fund, which is the only fund that involves substantial international exposure. Lazare believes that current political events in Country A may result in greater risk exposure than might be appropriate and wishes to investigate further.
The Herrick Fund manager provides them with the information in Exhibit 2, which they use to carry out a risk attribution analysis.
Exhibit 2
The Herrick Fund—Risk Analysis
Correlation
Country
Country Weight (%)
Standard Deviation (%)
Country A
Country B
Country C
A
30
25
1.0
0.4
0.3
B
50
15
0.4
1.0
0.2
C
20
9
0.3
0.2
1.0
Portfolio
100
13.2
Covariance
Country A
Country B
Country C
Country A
0.062500
0.015000
0.006750
Country B
0.015000
0.022500
0.002700
Country C
0.006750
0.002700
0.008100
Portfolio
0.0276
0.01629
0.004995
Question
The investment process indicated for the Fraser Fund is most likely designed around which of the following?
Solution
C is correct. The discretionary investment process searches for active returns from firm-specific factors, such as pricing power and the competitive landscape. This process results in more concentrated portfolios reflecting the depth of the manager’s insights on firm characteristics and the competitive landscape. A systematic investment approach is likely to be designed around extracting premiums from a balanced exposure to known, rewarded factors and typically incorporates research-based rules across a broad universe of securities.
A is incorrect. A systematic investment approach is likely to be designed around extracting premiums from a balanced exposure to known, rewarded factors, whereas a discretionary approach usually searches for active return from firm-specific factors.
B is incorrect. A systematic investment approach is likely to be designed around research-based rules across a broad universe of securities, whereas a discretionary approach will involve managerial judgments on a smaller subset of securities.
Active Equity Portfolio Construction Learning Outcome
Discuss approaches for constructing actively managed equity portfolios
Using Exhibit 1, the average monthly return of the Fraser Fund that is unexplained by rewarded factors is closest to:
Solution
A is correct. Return from unrewarded factors = Actual monthly performance – Return from rewarded factors.“Alpha” = RA – ∑βpkFkwhere
RA = Actual portfolio performance
βpk = The sensitivity of the portfolio (p) to each rewarded factor (k)
Fk = The return for each rewarded factor
Return from rewarded factors = (0.91 × 0.61%) + (0.15 × 0.17%) + (0.60 × 0.18%) + (0.08 × 0.72%) = 0.75%.
“Alpha” = Return from unrewarded factors = 0.55% – 0.75% = –0.20%.
B is incorrect. This is the “active return”: Actual – Benchmark = 0.55% – 0.72% = –0.17%.
C is incorrect. This adds the risk-free return back to the rewarded factor return = 0.33% – 0.20% = 0.13%.
Active Equity Portfolio Construction Learning Outcome
Describe elements of a manager’s investment philosophy that influence the portfolio construction process
The Mattley Fund manager is most likely following which investment style?
Solution
C is correct. The Mattley Fund exhibited relatively high Active Share but relatively low active risk. High Active Share indicates that a manager’s holdings differ substantially from the benchmark, and low active risk indicates low idiosyncratic risk resulting from diversification: This combination indicates that the manager most likely follows a diversified stock picking strategy. A sector rotator typically has high active risk and could have either high or low Active Share, depending on whether a concentrated or diversified portfolio approach was followed. A closet index would exhibit both low Active Share and low active risk, because such funds make few active bets.
A is incorrect. A sector rotator typically has high active risk and could have either high or low Active Share, depending on whether a concentrated or diversified portfolio approach was followed.
B is incorrect. A closet index would exhibit both low Active Share and low active risk, because such funds make few active bets.
Active Equity Portfolio Construction Learning Outcome
Distinguish between Active Share and active risk and discuss how each measure relates to a manager’s investment strategy
Lazare and Warrack make the following comments about Active Share and active risk in the context of a single-factor model:
The level of active risk will rise with an increase in idiosyncratic volatility.
The active risk attributed to Active Share will be smaller in more diversified portfolios.
If the factor exposure is fully neutralized, the Active Share will be entirely attributed to the active risk.
In Lazare and Warrack’s comments about Active Share and active risk, the comment that is least accurate is the one concerning:
Solution
B is correct. The comment concerning neutralizing factor exposure is incorrect: In a single-factor model, if the factor exposure is neutralized, the active risk will be entirely attributable to the Active Share—a consequence of the manager deviating from benchmark weights. The active risk attributed to Active Share will be smaller for more diversified portfolios with lower idiosyncratic risk. Active risk does rise with an increase in factor and idiosyncratic volatility.
A is incorrect. The active risk attributed to Active Share will be smaller for more diversified portfolios with lower idiosyncratic risk.
C is incorrect. Active risk does rise with an increase in factor and idiosyncratic volatility.
Active Equity Portfolio Construction Learning Outcome
Distinguish between Active Share and active risk and discuss how each measure relates to a manager’s investment strategy
The manager of the Western Fund focuses on smaller companies in the Russell 1000 Value Index and uses the following constraints:
Size: The capitalization of the average company is $1.8 billion. On average, companies of this size trade 0.90% of their capitalization every day.
Liquidity: Positions can be no larger than 7% of average daily trading volume.
Allocation: Positions can be no larger than 1.75% of total assets under management.
Diversification: The portfolio must contain at least 60 securities.
If the manager of the Western Fund is hired by Epsilon, she will have $100 million of Epsilon’s funds to manage.
If the Western Fund manager is hired, which constraint is most restrictive with respect to average position size? The constraint related to:
A.
liquidity.
B.
diversification.
C.
asset allocation.
Solution
A is correct. The most restrictive constraint on position size for the Western Fund manager is the liquidity constraint. It arises from the restriction on average daily trading volume: The average position size cannot exceed $1.13 million.
Average daily trading for the representative company size: 0.90% × $1.8 billion = $16.2 million. ✅
Restriction on trading volume (Liquidity): 7% × Average daily trading = 7% × $16.2 million = $1.13 million. ✅ => 89 securities
Restriction on allocation: 1.75% × $100 million = $1.75 million. ✅
Restriction on diversification: $100 million/60 securities = $1.67 million. ✅ => 60 securities
Position size is restricted by trading volume, and the fund could hold up to $100 million/$1.13 million = 89 securities. ✅
B is incorrect. With a requirement of at least 60 securities, an investment of up to $100 million/60 = $1.67 million is allowed in any security. The restriction on daily trading ($1.13 million) prevents that much from being acquired.
C is incorrect. The allocation restriction is 1.75% of funds under management = 1.75% × $100 million = $1.75 million. However, the restriction on daily trading ($1.13 million) prevents this amount from being acquired.
Active Equity Portfolio Construction Learning Outcome
Discuss how assets under management, position size, market liquidity, and portfolio turnover affect equity portfolio construction decisions
The proportion of the Herrick Fund’s portfolio variance contributed by Country A is closest to:
Solution
B is correct. The covariance of returns between Country A and the portfolio is provided in Exhibit 2 as 0.0276.
The contribution of Country A to total portfolio variance is calculated as follows:
Weight A × Weight A × cov(A,A) = 0.30 × 0.30 × 0.06250 = 0.005625
Weight A × Weight B × cov(A,B) = 0.03 × 0.50 × 0.15000 = 0.002250
Weight A × Weight C × cov(A,C) = 0.30 × 0.20 × 0.00675 = 0.000405
Country A’s contribution to total portfolio variance = 0.00828
The portfolio variance = (Std. dev.)2 = (0.132)2 = 0.01742.
The proportion of total portfolio variance contributed by Country A is 0.00828 ÷ 0.01742 = 47.5%.
Alternatively, Country A’s contribution to total portfolio variance
= Weight A × cov(A,Pf) = 0.30 × 0.0276 = 0.00828.
A is incorrect. It uses cov(A,Pf) but expresses it as a percentage of std(Pf): 0.0276/0.132 × 100 = 20.9%. The cov(A,Pf) of 0.0276 is calculated above in an alternative presentation.
C is incorrect. It takes Weight A × std(A)/std(Pf) = 0.30 × 25/13.2 × 100 = 56.8%.
Active Equity Portfolio Construction Learning Outcome
Discuss the application of risk budgeting concepts in portfolio construction
C is correct. The breadth (number of truly independent decisions made each year by the manager) required to earn the expected portfolio active return of 2.5% per year is approximately 69 decisions, calculated as follows:
(Incorrect)
(Wrong but corrected, good)
(wrong)
(wrong)
(Wrong)
(Absolutely Correct)
(Perfect)
(Absolutely Correct)
(Absolutely Correct)
