Asset allocation within a fund of hedge funds Ezra Zask, Azimuth Trust Company, New York
This article continues the discussion on funds of funds in Alternative IQ, by reviewing the major alternative methods for incorporating expected returns and non-normal distributions into the portfolio construction process.
Asset allocation in a hedge fund portfolio receives more lip service than actual implementation. While academic literature is definitive on the fact that asset allocation accounts for a large portion of the returns of any portfolio, it is fair to state that the overwhelming proportion of time and effort in the hedge fund industry is devoted to manager selection. Manager selection is obviously important. The dispersion of returns between managers is wider for hedge funds (and indeed for alternative investments) making manager selection crucial in generating alpha and above-market returns. Nonetheless, asset allocation still receives short shrift compared to manager selection. Arguably, this is one major reason for the uniformity of results in the funds of funds universe, where returns are relatively concentrated around a mean. The search for 30–40 managers capable of generating excess returns (alpha) is extremely difficult. A more likely portfolio consists of some managers with above average performance and some with below average. Even the selection of several managers with outstanding returns is diluted in a diversified portfolio. While hedge funds are not an asset class, we view a number of asset allocation approaches for constructing hedge fund portfolios starting with traditional mean variance optimisation. Following a discussion of the strengths and weaknesses of this approach, we review the major alternative methods for incorporating expected returns and non-normal distributions into the portfolio construction process.
Mean variance optimisation Mean variance optimisation (MVO) is the cornerstone of modern portfolio theory. Intellectually elegant, it has one drawback: it is rarely used in practice for portfolio construction. In practice, portfolios are constructed using qualitative overlays or constraints that, for all intents and purpose, negate the results of the optimisation. The reasons that MVO is seldom used in its pure state are relatively well-known. Aside from issues of the accuracy of the data used in hedge fund analysis, a number of assumptions underlay the MVO methodology that is often not valid. For example, MVO assumes that the asset return data in normally distributed, an assumption that often does not hold in the hedge fund space. In point of fact, the distribution of returns in many financial markets is not normally distributed, partly as a result of recurring financial markets. The chart below shows that financial crises occur more frequently than many people assume, one reason for the non-normal distribution of returns.
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The recurrence of financial crises — market shocks occur more often than commonly perceived
Stock Market Crash, 1987 • DJIA drops 23%; S&P 500 falls 20% on 10/19/87 • Contagion effects befall the Nikkei, FSTE, and Hang Seng Index
Nikkei Crash, 1990 • Nikkei fell 48% over the year • One-week volatility exceeds 120% in September / October • Japan Real Estate Index falls 56%
Mexican Peso Crisis, 1994-1995 • Peso devalued 15% at end of 1994 • The one-week volatility exceeds 150% in December
High Yield Crash, 1990 • Salomon HY composite falls 13% in October • Drexel Burnham Lambert collapses
Brazil Crisis, 1999 • Brazil devalues currency by 8% in January • Bovespa drops 10% in same day • Price volatilities exceed 80%
Latin America Crisis, 1995 From 9/94 – 3/95: • Brazilian Bovespa Stock Index drops 61% • Mexican Bolsa Index drops 49% • Argentine Merval Index drops 58%
9/11 Terror Attacks, 2001
1987
2005 Oil Crisis, 1991 Operation Desert Storm (1st Gulf War)
European Currency Crisis, 1992 • Band breaks on European Rate Mechanism • Rate hikes and devaluations follow
U.S. and Euro Bond Crash, 1994 • Fed Funds short term target rate raised six times during the year (3.0% to 5.5%) Asian Crisis, 1997 • Thai bhat falls 16% in one day • Spreads to other Asian currencies • Extreme volatility levels
Yen Appreciation, 1998 • Pressure on corporate profits, weak final demand
TMT / Nasdaq Crash, 2000 • Technology bubble bursts • U.S. equity market downturn • S&P, Nasdaq peak to trough: -49% and -70% respectively • Corporate Malfeasance
Russian Default, 1998 • Russian ruble falls 41% as government defaults on debt
Source: Capital Market Risk Advisors, Azimuth Trust analysis
Equity market crisis
Macroeconomic crisis
Long Term Capital Management, 1998 • Drastic increase in credit spreads • DJIA price volatilities exceed 70% in August
Emerging market crisis
Relative-value hedge fund crisis
Source: Capital Markets Risk Advisors, Azimuth Trust Analysis
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Iraqi War, 2003
The non-normal distribution of asset returns has generated a whole industry of analyses designed to incorporate non-normal parameters into optimisation programs with varying degrees of success. The problem and a possible solution are laid out below in a proprietary methodology used by Azimuth Trust Company known as FaTCatTM. The method combines a normal distribution of returns, which holds during normal market conditions, with a distribution that is representatives of times of financial market stress. The combined distribution, which is then incorporated into the portfolio construction, clearly gives more weight to downside market movements. As shown in Table 1, the probability of gain or loss under the normal distribution and the combined distributions are significantly different. For example, the probability of incurring a 2% loss is zero under the normal distribution, but 1.35% under the stress distribution. The combined distribution, which assigns a 5% weight to the stress distribution, shows that probability of loss of 0.07%. While seemingly small, this represents a significant change in distributions of the portfolio.
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Table 1— Probability of achieving gain/loss Fund gain/loss (%)
Normal distribution
Crisis distribution
Combined distribution
-4%
0.00%
0.00%
0.00%
-3%
0.00%
0.11%
0.01%
-2%
0.00%
1.35%
0.07%
-1%
0.00%
6.05%
0.31%
0
0.11%
9.97%
0.60%
1%
1.35%
6.05%
1.58%
2%
6.05%
1.35%
5.81%
3%
9.97%
0.11%
9.48%
4%
6.05%
0.00%
5.75%
5%
0.79%
0.00%
0.75%
6%
0.05%
0.00%
0.05%
Another major problem with MVO portfolios is the dominance of one or two assets in the overall allocation. The mathematics of the MVO dictates that assets that have higher risk-adjusted returns squeeze out those that are even marginally lower. As a result, the results of MVO are notoriously unstable, with major shifts in allocation caused by relatively minor shifts of asset returns or volatility. The results opposite indicate this in a dramatic fashion. A popular software optimiser using hedge fund-style data from 1995-2004, allocates the overwhelming majority of the portfolio to event driven and global macro strategies.
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Optimal allocation Convertible Arbitrage Index
0.00
Dedicated Short Bias Index
0.00
Emerging Markets Index
0.00
Equity Market Neutral Index
8.23%
Event Driven Index Fixed Income Arbitrage Index Global Macro Index
45.57% 0.00 46.20%
Long/Short Equity Index
0.00
Managed Futures Index
0.00
TASS Fund of Funds Universe Average
0.00
Summary statistics Expected return
1.00
Standard deviation
1.96
Sharpe Ratio
0.51
So where does that leave us? One commonly used approach to modify the MVO process is to place minimum and/or maximum constraints on the amount that may be allocated to any given hedge fund and/or hedge fund strategy. The problem with this approach is that it tends to drive the allocation to the maximum and minimum. In the above example, event driven and global macro strategies will certainly reach the maximum, no matter where it is placed, while most other strategies will reach the minimum. In effect, constraints negate the MVO results. A second commonly used approach attempts to forecast the returns and standard deviations of hedge fund strategies using a combination of quantitative (usually factor) analysis and qualitative (or judgmental) The table over the page shows one attempt to decompose the returns of hedge fund strategies since 1998 into their market betas and alpha. In some cases, the explanatory power is relatively high. This means that by accurately forecasting the direction of market movement, one can forecast the returns of the hedge fund strategies. This approach is usually supplemented by qualitative analysis of each strategy, including such factors as market supply and demand, overbought and oversold, and volatility measurements.
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Since February 1998 Compound annual return (%) Convertible arbitrage
Annual alpha (%)
Betas Stocks Bonds Cash RSQ
7.4%
0.3%
-0.03
0.05 0.05
0.17
Emerging markets
11.6%
12.6%
0.33
0.16 0.17
0.29
Event driven
10.8%
3.9%
0.14
0.05 0.05
0.61
Fixed income arbitrage
7.2%
6.3%
-0.07
0.06 0.06
0.13
Statistical arbitrage
5.7%
2.0%
0.04
0.06 0.06
0.06
Directional trading
8.2%
7.6%
-0.13
0.13 0.13
0.07
Specialist credit
10.6%
10.8%
0.09
0.07 0.07
0.41
Security selection
11.8%
-1.4%
0.23
0.09 0.10
0.39
Short bias
4.9%
2.2%
-0.78
0.19 0.20
0.55
Relative value
7.3%
1.5%
-0.01
0.04 0.04
0.24
Multi process
9.8%
-0.8%
0.06
0.05 0.06
0.46
Composite Index
9.4%
1.6%
0.08
0.06 0.06
0.33
A final approach to this issue seeks to place the asset returns on a different footing than the historical analysis used in MVO. For example, this may take the form of forecasting future returns of each asset. A more theoretically satisfying approach is the Black Litterman model that begins with the assumption that historical returns are not the correct measure of future returns. The approach is also wary of forecasted returns, which vary widely from one forecaster to another. The Black Litterman approach essentially posits that the starting place for asset allocation is the implied returns of the existing asset allocation in the marketplace. Thus, the ‘equilibrium’ portfolio weights among hedge fund strategies, using the MSCI hedge fund indices, are as shown in the first column of the table below. The second column calculates the returns (over the risk-free rate) that are implied by the market allocation between strategies. Finally, the next several columns show the required returns for each strategy suggested by overweighing or underweighting these strategies. Thus, in order to overweigh global macro by 50% in the portfolio (compared to the equilibrium weights), the portfolio manager must feel confident that the global macro strategy will return 11.6% over the risk free rate of return.
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Required excess return
Initial weights
Equilibirum Underweight excess return by 25%
Underweight by 50%
Overweight Overweight by 25% by 50%
Global macro
19.90%
6.3%
2.5%
-1.8%
9.3%
11.6%
L/S equity
38.86%
8.1%
5.5%
0.8%
9.1%
9.1%
Credit
15.64%
4.6%
1.8%
-1.1%
7.1%
9.3%
Fixed inc arbitrage
9.29%
5.6%
4.6%
3.6%
6.7%
7.7%
Conv & vol arbitrage
5.92%
7.3%
5.7%
4.1%
8.9%
10.4%
Statistical arbitrage
3.22%
2.4%
2.2%
2.1%
2.5%
2.6%
Event driven
9.17%
6.0%
5.4%
4.9%
6.5%
7.0%
Which approach to asset allocation works best? While we feel that a model that incorporates the non-normal distribution of returns and the concept of an equilibrium allocation that serves as the market’s benchmark or bogie is the most theoretically meaningful, it is fair to say that the majority of our industry uses some version of the qualitative forecast approach with arbitrary minimum and maximum allocations to provide diversification. The issue is important because asset allocation is as important, if not more important, than manager selection in hedge fund returns, but receives disproportionately less attention from practitioners. The result is fund of funds portfolios whose returns are overly concentrated around the industry mean. Ezra Zask Azimuth Trust Company, New York Tel: 212 366 8720 ezra.zask@azimuthtrust.com
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