HEURISTICS AND OTHER APPROACHES TO ASSET ALLOCATION

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The text outlines various heuristic and other approaches to asset allocation, which serve as simplified strategies for investors to determine how to allocate their investments across different asset classes. These methods range from simple rules of thumb based on age to more complex models emphasizing diversification and risk management. Below, we summarize and evaluate these approaches:

The “120 Minus Your Age” Rule and Variants

• Description: This rule suggests that investors should allocate a percentage of their portfolio to stocks based on the formula "120 minus your age" (or variants like "100 minus your age" or "125 minus your age"). The idea is to decrease equity exposure as one ages, reflecting a decreasing risk tolerance.

• Evaluation: While lacking a theoretical basis, this heuristic aligns with the glide paths of many target-date funds, which automatically adjust the asset mix as investors age, moving from higher risk (stocks) to lower risk (bonds) investments. It offers a simple way for individuals to gauge their equity exposure relative to age, but it might not suit everyone's financial situation or risk tolerance.

The 60/40 Stock/Bond Heuristic

• Description: An allocation of 60% equities and 40% fixed income.

• Evaluation: This traditional mix aims to balance growth (via equities) with risk reduction (via bonds). It reflects a historical average market composition but may not be optimal for all investors, especially given varying market conditions and personal risk tolerances.

The Endowment Model

• Description: Favored by university endowments, this model emphasizes large allocations to non-traditional investments (like private equity) and aims to capture illiquidity premiums.

• Evaluation: This model, requiring access to and expertise in alternative investments, may not be feasible for most individual investors. It's praised for its diversification benefits and long-term performance but critiqued for its complexity and the need for professional management.

Risk Parity

• Description: Aims for equal risk contribution from each asset in the portfolio, often requiring leverage to adjust the overall risk level to meet the investor's risk appetite.

• Evaluation: Risk parity addresses diversification not just by asset allocation but by risk contribution. Critics argue it neglects expected returns, making it potentially unattractive during periods when returns from various asset classes diverge significantly.

The 1/N Rule

• Description: Equally divides investment across N assets, simplifying allocation without making assumptions about future returns.

• Evaluation: Despite its simplicity, the 1/N rule has shown resilience in empirical studies, often performing comparably to more sophisticated strategies. Its effectiveness might be due to its avoidance of estimation errors common in more complex models.

Overall Evaluation: Each approach has its merits and limitations. Heuristic methods like the "120 minus your age" rule offer simplicity and a good starting point for novice investors. The 60/40 split is a traditional approach that has stood the test of time but may not cater to the specific needs of all investors. The Endowment Model and Risk Parity offer more sophisticated strategies that emphasize diversification and risk management but may require more expertise and resources to implement effectively. Finally, the 1/N rule showcases the potential benefits of simplicity in asset allocation, challenging the notion that more complex, optimized strategies always lead to better outcomes. Ultimately, the choice of asset allocation strategy should be guided by the individual's financial situation, investment goals, risk tolerance, and access to various investment opportunities.

Learning Outcome

• describe and evaluate heuristic and other approaches to asset allocation

In addition to the various asset allocation approaches already covered, a variety of heuristics (rules that provide a reasonable but not necessarily optimal solution) and other techniques deserve mention:

The “120 Minus Your Age” Rule

The phrase “120 minus your age” is a heuristic for inferring a hidden, age-driven risk tolerance coefficient that then leads directly to an age-based stock versus fixed income split: 120 − Age = Percentage allocated to stocks. Thus, a 25-year-old man would allocate 95% of his investment portfolio to stocks. Although we are aware of no theoretic basis for this heuristic—or its older and newer cousins, “100 minus your age” and “125 minus your age,” respectively—it results in a linear decrease in equity exposure that seems to fit the general equity glide paths associated with target-date funds, including those that are based on a total balance sheet approach that includes human capital. A number of target-date funds (sometimes called life-cycle or age-based funds) and some target-date index providers report that their glide path (the age-based change in equity exposure) is based on the evolution of an individual’s human capital. For example, one set of indexes35 explicitly targets an investable proxy for the world market portfolio in which the glide path is the result of the evolving relationship of financial capital to human capital.36

Exhibit 41 displays the glide paths of the 60 largest target-date fund families in the United States. The retirement year (typically part of the fund’s name) on the x-axis denotes the year in which the investor is expected to retire, which is almost always assumed to be the year the investor turns 65. Thus, as of 2016, the 2060 allocations correspond to a 21-year-old investor (79% equity, using the heuristic), whereas the 2005 allocation corresponds to a 76-year-old investor (24% equity, using the heuristic).37 One dashed line represents the equity allocation based on the “100 minus your age” heuristic, while another dashed line represents the “120 minus your age” heuristic. The heuristic lines lack some of the nuances of the various glide path lines, but it would appear that an age-based heuristic leads to asset allocations that are broadly similar to those used by target-date funds.

Exhibit 41:

Target-Date Funds and Age Heuristics (as of January 2016)

The 60/40 Stock/Bond Heuristic

Some investors choose to skip the various optimization techniques and simply adopt an asset allocation consisting of 60% equities and 40% fixed income.

The equity allocation is viewed as supplying a long-term growth foundation, and the fixed-income allocation as supplying risk reduction benefits. If the stock and bond allocations are themselves diversified, an overall diversified portfolio should result.

There is some evidence that the global financial asset market portfolio is close to this prototypical 60/40 split. Exhibit 42 displays the estimated market value of eight major components of the market portfolio from 1990 to 2012. In approximately 7 of the 23 years, equities, private equity, and real estate account for slightly more than 60%, while for the rest of the time, the combined percentage is slightly less.

Exhibit 42:

Global Market Portfolio, 1990 to 2012

Source: Doeswijk, Lam, and Swinkels (2014).

The Endowment Model

An approach to asset allocation that emphasizes large allocations to non-traditional investments, including equity-oriented investments driven by investment manager skill (e.g., private equities), has come to be known as the endowment model or Yale model. The label “Yale model” reflects the fact that the Yale University Investments Office under David Swensen pioneered the approach in the 1990s; the label “endowment model” reflects the influence of this approach among US university endowments. Swensen (2009) stated that most investors should not pursue the Yale model but should instead embrace a simpler asset allocation implemented with low-cost funds. Besides high allocations to non-traditional assets and a commitment to active management, the approach characteristically seeks to earn illiquidity premiums, which endowments with long time horizons are well positioned to capture. Exhibit 43, showing the Yale endowment asset allocation, makes these points. In the exhibit, “absolute return” indicates investment in event-driven and value-driven strategies.

Exhibit 43:

Yale University Endowment Asset Allocation as of June 2014

	Yale University	US Educational Institution Mean
Absolute return	17.4%	23.3%
Domestic equity	3.9	19.3
Fixed income	4.9	9.3
Foreign equity	11.5	22.0
Natural resources	8.2	8.5
Private equity	33.0	10.0
Real estate	17.6	4.2
Cash	3.5	3.5

Source: Yale University (2014, p. 13).

In almost diametrical contrast to the endowment model is the asset allocation approach of Norway’s Government Pension Fund Global (Statens pensjonsfond Utland), often called the Norway model.38 This model’s asset allocation is highly committed to passive investment in publicly traded securities (subject to environmental, social, and governance [ESG] concerns), reflecting a belief in the market’s informational efficiency. Since 2009, the asset allocation has followed an approximate 60/40 stock/bond mix.

Risk Parity

A risk parity asset allocation is based on the notion that each asset (asset class or risk factor) should contribute equally to the total risk of the portfolio for a portfolio to be well diversified. Recall that in Sections 2–9, we identified various criticisms and potential shortcomings of mean–variance optimization, one of which was that, while the resulting asset allocations may appear diversified across assets, the sources of risk may not be diversified. In the section on risk budgeting, Exhibit 16 contained a risk decomposition of a reverse-optimization-based asset allocation from a United Kingdom–based investor. There, we noted that the overall equity/fixed income split was approximately 54% equities and 46% fixed income, yet of the 10% standard deviation, approximately 74% of the risk came from equities while only 26% came from fixed income.

Risk parity is a relatively controversial approach. Although there are several variants, the most common risk parity approach has the following mathematical form:$wi×Cov(ri,rP)=1nσ2P$��×Cov(��,��)=1���23where

wi = the weight of asset i

Cov(ri,rP) = the covariance of asset i with the portfolio

n = the number of assets

$σ2P$��2 = the variance of the portfolio

In general, there is not a closed-form solution to the problem, and it must be solved using some form of optimization (mathematical programming). Prior to Markowitz’s development of mean–variance optimization, which simultaneously considered both risk and return, most asset allocation approaches focused only on return and ignoredrisk (or accounted for it in an ad hoc manner). The primary criticism of risk parity is that it makes the opposite mistake: It ignoresexpected returns. In general, most of the rules-based risk approaches—such as other forms of volatility weighting, minimum volatility, and target volatility—suffer from this shortcoming.

With risk parity, the contribution to risk is highly dependent on the formation of the opportunity set. For example, if the opportunity set consists of seven equity asset classes and three fixed-income asset classes, intuitively, 70% of risk will come from the equities and 30% of risk will come from fixed income. Conversely, if the opportunity set consists of three equity asset classes and seven fixed-income asset classes, intuitively, 70% of risk will come from fixed income and 30% of risk will come from equities. The point is that practitioners of risk parity must be very cognizant of the formation of their opportunity set.

Exhibit 44 gives a US-centric example consisting of five equity asset classes and three fixed-income asset classes. A constrained optimization routine (weights must sum to 100%) was used to determine the weight to each asset class, such that all asset classes contributed the same amount to total risk. In this case, each asset class contributed 0.8%, resulting in an asset allocation with a total standard deviation of 6.41%. In this example, 5/8 of total risk comes from equity asset classes and 3/8 comes from fixed-income asset classes. Earlier, we explained that reverse optimization can be used to infer the expected return of any set of presumed efficient weights. In Exhibit 44, based on a total market risk premium of 2.13% and a risk-free rate of 3%, we inferred the reverse-optimized total returns (final column). In this case, these seem to be relatively reasonable expected returns.

Exhibit 44:

Risk Parity Portfolio Weights and Risk-Budgeting Statistics Based on Reverse-Optimized Returns

Asset Class	Weight	Marginal Contribution to Total Risk (MCTR)	ACTR	Percentage Contribution to Total Standard Deviation	Reverse-Optimized Total Returns
US large-cap equities	7.7%	10.43%	0.80%	12.50%	6.47%
US mid-cap equities	6.1	13.03	0.80	12.50	7.33
US small-cap equities	5.9	13.61	0.80	12.50	7.52
Non-US developed market equities	5.6	14.38	0.80	12.50	7.78
Emerging market equities	4.5	17.74	0.80	12.50	8.89
Non-US bonds	15.5	5.17	0.80	12.50	4.72
US TIPS	23.9	3.36	0.80	12.50	4.12
US bonds	30.8	2.60	0.80	12.50	3.86
Total	100.0%		6.41%	100.00%	5.13%

After deriving a risk parity–based asset allocation, the next step in the process is to borrow (use leverage) or to lend (save a portion of wealth, presumably in cash) so that the overall portfolio corresponds to the investor’s risk appetite. Continuing with our example, the market risk premium is 2.13% (above the assumed risk-free rate of 3%) and the market variance is 0.41% (i.e., 6.41% squared); thus, the implied market trade-off of expected return (in excess of the risk-free rate) for risk is 2.13% divided by 0.41%, which equals approximately 5.2. Investors with a greater appetite for risk than the market as a whole would borrow money to lever up the risk parity portfolios, while investors with a lower appetite for risk would invest a portion of their wealth in cash.

Back tests of levered risk parity portfolios have produced promising results, although critics of these back tests argue that they suffer from look-back bias and are very dependent on the ability to use extremely large amounts of leverage at low borrow rates (which may not have been feasible); see, for example, Anderson, Bianchi, and Goldberg (2012). Proponents of risk parity have suggested that the idea of “leverage aversion” contributes to the success of the strategy. Black (1972) suggested that restrictions on leverage and a general aversion to leverage may cause return-seeking investors to pursue higher-returning assets, such as stocks. All else equal, this behavior would reduce the price of bonds, thus allowing the investor to buy bonds at a small discount, hold them to maturity, and realize the full value of the bond. Asness, Frazzini, and Pedersen (2012) have offered this idea as a potential explanation for why a levered (bond-centric) asset allocation might outperform an equity-centric asset allocation with equivalent or similar risk.

The 1/N Rule

One of the simplest asset allocation heuristics involves equally weighting allocations to assets. DeMiguel, Garlappi, and Uppal (2009) define an approach in which 1/N of wealth is allocated to each of N assets available for investment at each rebalancing date. Calendar rebalancing to equal weighting at quarterly intervals is one common rebalancing discipline used. By treating all assets as indistinguishable in terms of mean returns, volatility, and correlations, in principle, 1/N rule portfolios should be dominated by methods that optimize asset class weights to exploit differences in investment characteristics. In empirical studies comparing approaches, however, the 1/N rule has been found to perform considerably better, based on Sharpe ratios and certainty equivalents, than theory might suggest. One possible explanation is that the 1/N rule sidesteps problems caused by optimizing when there is estimation error in inputs.