Table 26.2 shows that hedge funds on average seem to produce positive alphas. Hasanhodzic and Lo more systematically calculate style-adjusted alphas as well as Sharpe ratios for a large sample of funds and find that average performance measures appear considerably
higher than those of a passive index such as the S&P 500. 6 What might be the source of this performance?
One possibility, of course, is the obvious one: these results may reflect a high degree of skill among hedge fund managers. Another possibility is that funds maintain some expo- sure to omitted risk factors that convey a positive risk premium. One likely candidate for such a factor would be liquidity, and we will see shortly that liquidity and liquidity risk are associated with average returns. Moreover, several other factors make hedge fund perfor- mance difficult to evaluate, and these too are worth considering.
Liquidity and Hedge Fund Performance
One explanation for apparently attractive hedge fund performance is liquidity. Recall from Chapter 9 that one of the more important extensions of the CAPM is a version that allows for the possibility of a return premium for investors willing to hold less liquid assets.
Hedge funds tend to hold more illiquid assets than other institutional investors such as mutual funds. They can do so because of restrictions such as the lock-up provisions that commit investors to keep their investment in the fund for some period of time. Therefore, it is important to control for liquidity when evaluating performance. If it is ignored, what may be no more than compensation for illiquidity may appear to be true alpha, that is, risk- adjusted abnormal returns.
Aragon demonstrates that hedge funds with lock-up restrictions do tend to hold less liq- uid portfolios. 7 Moreover, once he controlled for lock-ups or other share restrictions (such as redemption notice periods), the apparently positive average alpha of those funds turned insignificant. Aragon’s work suggests that the typical “alpha” exhibited by hedge funds may be better interpreted as an equilibrium liquidity premium rather than a sign of stock- picking ability, in other words a “fair” reward for providing liquidity to other investors.
One symptom of illiquid assets is serial correlation in returns. Positive serial correla- tion means that positive returns are more likely to be followed by positive than by negative returns. Such a pattern is often taken as an indicator of less liquid markets for the following reason. When prices are not available because an asset is not actively traded, the hedge fund must estimate its value to calculate net asset value and rates of return. But such proce- dures are at best imperfect and, as demonstrated by Getmansky, Lo, and Makarov, tend to result in serial correlation in prices as firms either smooth out their value estimates or only gradually mark prices to true market values. 8 Positive serial correlation is therefore often interpreted as evidence of liquidity problems; in nearly efficient markets with frictionless trading, we would expect serial correlation or other predictable patterns in prices to be minimal. Most mutual funds show almost no evidence of such correlation in their returns, and the serial correlation of the S&P 500 is just about zero.
Hasanhodzic and Lo find that hedge fund returns in fact exhibit significant serial cor- relation. This suggestion of smoothed prices has two important implications. First, it lends further support to the hypothesis that hedge funds are holding less liquid assets and that their apparent alphas may in fact be liquidity premiums. Second, it implies that their performance measures are upward-biased, because any smoothing in the estimates
6 Jasmina Hasanhodzic and Andrew W. Lo, “Can Hedge Fund Returns Be Replicated? The Linear Case,” Journal of Investment Management 5 (2007), pp. 5–45.
7 George O. Aragon, “Share Restrictions and Asset Pricing: Evidence from the Hedge Fund Industry,” Journal of Financial Economics 83 (2007), pp. 33–58.
8 Mila Getmansky, Andrew W. Lo, and Igor Makarov, “An Econometric Model of Serial Correlation and Illiquidity in Hedge Fund Returns,” Journal of Financial Economics 74 (2004), pp. 529–609.
of portfolio value will reduce total volatility (increasing the Sharpe ratio) as well as covariances and therefore betas with systematic factors (increasing risk-adjusted alphas). In fact, Figure 26.2 shows that hedge fund serial correlations are highly associated with their apparent Sharpe ratios.
Whereas Aragon focuses on the average level of liquidity, Sadka addresses the liquidity risk of hedge funds. 9 He shows that exposure to unexpected declines in market liquidity is an impor- tant determinant of average hedge fund returns, and that the spread in average returns across the funds with the highest and lowest liquid- ity exposure may be as much as 6% annually. Hedge fund perfor- mance may therefore reflect sig- nificant compensation for liquidity risk. Figure 26.3 , constructed from data reported in his study, is a scatter diagram relating average return for the hedge funds in each style group of Table 26.2 to the liquidity-risk beta for that group.
Average return clearly rises with exposure to changes in market liquidity.
Returns can be even more dif- ficult to interpret if a hedge fund takes advantage of illiquid markets to manipulate returns by purposely misvaluing illiquid assets. In this regard, it is worth noting a Santa effect: hedge funds report average returns in December that are substantially greater than their average returns in other months. 10 The pattern is stronger for funds that are near or beyond the threshold return at which performance incentive fees kick in and suggests that illiquid assets are more generously valued in December, when annual performance relative to benchmarks is being calculated. In fact, it seems that the December spike in returns is stronger for lower-liquidity funds. If funds take advantage of illiquid markets to manage returns, then accurate performance measurement becomes almost impossible.
9 Ronnie Sadka, “Liquidity Risk and the Cross-Section of Hedge-Fund Returns,” Journal of Financial Economics, forthcoming.
10 Vikas Agarwal, Naveen D. Daniel, and Narayan Y. Naik, “Why Is Santa So Kind to Hedge Funds? The December Return Puzzle!” March 29, 2007, http://ssrn.com/abstract 5 891169.
Figure 26.2 Hedge funds with higher serial correlation in returns, an indicator of illiquid portfolio holdings, exhibit higher Sharpe ratios.
Source: Plotted from data in Hasanhodzic and Lo, “Can Hedge Funds Be Replicated?”
3.0 2.5 2.0 1.5 1.0 0.5 0.0
Sharpe Ratio
0.0 0.1 0.2
Serial Correlation
0.3 0.4 0.5
Figure 26.3 Average hedge fund returns as a function of liquidity risk
Source: Plotted from data in Sadka, “Liquidity Risk and the Cross-Section of Hedge-Fund Returns.”
0 0.5
Liquidity Beta
1 1.5
0.1 0.2 0.3 0.4 0.5
Average Excess Return (%/month)
−0.5
0.6
0
Hedge Fund Performance and Survivorship Bias
We already know that survivorship bias (when only successful funds are included in a database) can affect the estimated performance of a sample of mutual funds. The same problems, as well as related ones, apply to hedge funds. Backfill bias arises because hedge funds report returns to database publishers only if they choose to. Funds started with seed capital will open to the public and therefore enter standard databases only if their past performance is deemed sufficiently successful to attract clients. Therefore, the prior per- formance of funds that are eventually included in the sample may not be representative of typical performance. Survivorship bias arises when unsuccessful funds that cease opera- tion stop reporting returns and leave a database, leaving behind only the successful funds.
Malkiel and Saha find that attrition rates for hedge funds are far higher than for mutual funds—in fact, commonly more than double the attrition rate of mutual funds—making this an important issue to address. 11 Estimates of survivorship bias in various studies are typically substantial, in the range of 2–4%. 12
Hedge Fund Performance and Changing Factor Loadings
In Chapter 24, we pointed out that an important assumption underlying conventional per- formance evaluation is that the portfolio manager maintains a reasonably stable risk profile over time. But hedge funds are designed to be opportunistic and have considerable flex- ibility to change that profile. This too can make performance evaluation tricky. If risk is not constant, then estimated alphas will be biased if we use a standard, linear index model.
And if the risk profile changes in systematic manner with the expected return on the mar- ket, performance evaluation is even more difficult.
To see why, look at Figure 26.4 , which illustrates the characteristic line of a perfect market timer (see Chapter 24, Section 24.4) who engages in no security selection but moves funds from T-bills into the market portfolio only when the market will outperform bills. The characteristic line is nonlinear, with a slope of 0 when the market’s excess return is negative, and a slope of 1 when it is positive. But a nạve attempt to estimate a regression equation from this pattern would result in a fitted line with a slope between 0 and 1, and a positive alpha. Neither statistic accurately describes the fund.
As we noted in Chapter 24, and as is evident from Figure 26.4 , an ability to conduct per- fect market timing is much like obtaining a call option on the underlying portfolio without having to pay for it. Similar nonlinearities would arise if the fund actually buys or writes options. Figure 26.5 A illustrates the case of a fund that holds a stock portfolio and writes put options on it, and panel B illustrates the case of a fund that holds a stock portfolio and writes call options. In both cases, the characteristic line is steeper when portfolio returns are poor—in other words, the fund has greater sensitivity to the market when it is falling than when it is rising. This is the opposite profile that would arise from timing ability, which is much like acquiring rather than writing options, and therefore would give the fund greater sensitivity to market advances. 13
11 Burton G. Malkiel and Atanu Saha, “Hedge Funds: Risk and Return,” Financial Analysts Journal 61 (2005), pp. 80–88.
12 For example, Malkiel and Saha estimate the bias at 4.4%; G. Amin and H. Kat, “Stocks, Bonds and Hedge Funds: Not a Free Lunch!” Journal of Portfolio Management 29 (Summer 2003), pp. 113–20, find a bias of about 2%; and William Fung and David Hsieh, “Performance Characteristics of Hedge Funds and CTA Funds: Natural versus Spurious Biases,” Journal of Financial and Quantitative Analysis 35 (2000), pp. 291–307, find a bias of about 3.6%.
13 But the fund that writes options would at least receive fair compensation for the unattractive shape of its char- acteristic line in the form of the premium received when it writes the options.
Figure 26.6 presents evidence on these sorts of nonlinearities. A nonlinear regres- sion line is fitted to the scatter diagram of returns on hedge funds plotted against returns on the S&P 500. The fitted lines in each panel suggest that these funds have higher down-market betas (higher slopes) than up-market betas. 14
This is precisely what investors presum- ably do not want: higher market sensitivity when the market is weak. This is evidence that funds may be writing options, either explicitly or implicitly through dynamic trad- ing strategies (see Chapter 21, Section 21.5, for a discussion of such dynamic strategies).
Tail Events and Hedge Fund Performance
Imagine a hedge fund whose entire invest- ment strategy is to hold an S&P 500 index fund and write deep out-of-the-money put options on the index. Clearly the fund man- ager brings no skill to his job. But if you knew only his investment results over lim- ited periods, and not his underlying strategy, you might be fooled into thinking that he is extremely talented. For if the put options are written sufficiently out-of-the-money, they will only rarely end up imposing a loss, and such a strategy can appear over long periods—even over many years—to be con- sistently profitable. In most periods, the strat- egy brings in a modest premium from the written puts and therefore outperforms the S&P 500, yielding the impression of consis- tently superior performance. The huge loss that might be incurred in an extreme market decline might not be experienced even over periods as long as years. Every so often, such as in the market crash of October 1987, the strategy may lose multiples of its entire gain over the last decade. But if you are lucky enough to avoid these rare but extreme tail events (so named because they fall in the far- left tail of the probability distribution), the strategy might appear to be gilded.
14 Not all the hedge fund categories exhibited this sort of pattern. Many showed effectively symmetric up- and down-market betas. However, Figure 26.6 A shows that the asymmetry affects hedge funds taken as group. Panels B and C are for the two sectors with the most prominent asymmetries.
Figure 26.4 Characteristic line of a perfect market timer.
The true characteristic line is kinked, with a shape like that of a call option. Fitting a straight line to the relationship will result in misestimated slope and intercept.
Return to Perfect Market Timer
Fitted Regression Line Portfolio Return
Market Return rf
Figure 26.5 Characteristic lines of stock portfolio with written options. Panel A, Buy stock, write put. Here, the fund writes fewer puts than the number of shares it holds.
Panel B, Buy stock, write calls. Here, the fund writes fewer calls than the number of shares it holds.
Stock Alone
Stock Alone A
B
Exercise Price
Stock Value
Exercise Price
Stock Value Stock with Written Put
Stock with Written Call
5%
−5% 0%
−10%
−15%
5%
−5%
0%
Return on Broad Hedge Fund Index
S&P 500 Return
−10%
−20% 10%
A
B
5%
−5% 0%
−10%
−15%
−5%
0%
Return on Fixed-Income Arbitrage Funds
S&P 500 Return
−10%
−15%
−20% 10%
5%
C
5%
−5% 0%
−10%
−15%
5%
−5%
−10%
0%
Return on Event-Driven Funds
S&P 500 Return 10%
−15%
−20% 10%
Figure 26.6 Monthly return on hedge fund indexes versus return on the S&P 500, 1993–2009. Panel A, hedge fund index. Panel B, fixed-income arbitrage funds. Panel C, event-driven funds.
Source: Constructed from data downloaded from www.hedgeindex.com and finance.yahoo.com.
The evidence in Figure 26.6 indicating that hedge funds are at least implicitly option writers should make us nervous about taking their measured performance at face value. The problem in interpreting strategies with exposure to extreme tail events (such as short options positions) is that these events by definition occur very infrequently, so decades of results may be needed to fully appreciate their true risk and reward attributes. In two influential books, Nassim Taleb, who is a hedge fund operator himself, makes the case that many hedge funds are analogous to our hypothetical manager, racking up fame and fortune through strat- egies that make money most of the time but expose investors to rare but extreme losses. 15
Taleb uses the metaphor of the black swan to discuss the importance of highly improb- able, but highly impactful, events. Until the discovery of Australia, Europeans believed that all swans were white: they had never encountered swans that were not white. In their experi- ence, the black swan was outside the realm of reasonable possibility, in statistical jargon, an extreme outlier relative to their sample of observations. Taleb argues that the world is filled with black swans, deeply important developments that simply could not have been predicted from the range of accumulated experience to date. While we can’t predict which black swans to expect, we nevertheless know that some black swan may be making an appearance at any moment. The October 1987 crash, when the market fell by more than 20% in 1 day, might be viewed as a black swan—an event that had never taken place before, one that most market observers would have dismissed as impossible and certainly not worth modeling, but with high impact. These sorts of events seemingly come out of the blue, and they caution us to show great humility when we use past experience to evaluate the future risk of our actions. With this in mind, consider again the example of Long Term Capital Management.
15 Nassim N. Taleb, Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets (New York:
TEXERE (Thomson), 2004); Nassim N. Taleb, The Black Swan: The Impact of the Highly Improbable (New York: Random House, 2007).
Example 26.3 Tail Events and Long-Term Capital Management In the late 1990s, Long Term Capital Management was widely viewed as the most suc- cessful hedge fund in history. It had consistently provided double-digit returns to its inves- tors, and it had earned hundreds of millions of dollars in incentive fees for its managers.
The firm used sophisticated computer models to estimate correlations across assets and believed that its capital was almost 10 times the annual standard deviation of its portfolio returns, presumably enough to withstand any “possible” shock to capital (at least, assum- ing normal distributions!). But in the summer of 1998, things went badly. On August 17, 1998, Russia defaulted on its sovereign debt and threw capital markets into chaos. LTCM’s 1-day loss on August 21 was $550 million (approximately nine times its estimated monthly standard deviation). Total losses in August were about $1.3 billion, despite the fact that LTCM believed that the great majority of its positions were market-neutral relative-value trades. Losses accrued on virtually all of its positions, flying in the face of the presumed diversification of the overall portfolio.
How did this happen? The answer lies in the massive flight to quality and, even more so, to liquidity that was set off by the Russian default. LTCM was typically a seller of liquid- ity (holding less liquid assets, selling more liquid assets with lower yields, and earning the yield spread) and suffered huge losses. This was a different type of shock from those that appeared in its historical sample/modeling period. In the liquidity crisis that engulfed asset markets, the unexpected commonality of liquidity risk across ostensibly uncorrelated asset classes became obvious. Losses that seemed statistically impossible on past experience had in fact come to pass; LTCM fell victim to a black swan.