Robert Gordon, president of Twenty-First Securities Corp., explains how a recent Treasury Department ruling grants unique tax advantages to listed calls used in collar strategies.

In years past, equity investors could use equity swaps, short-against-the-box and other strategies to deflect burdensome taxation while enjoying upside gains. Unfortunately, the constructive-ownership legislation passed as part of the Taxpayer Relief Act of 1997 served to close down those increasingly popular avenues.

However, a recent private-letter ruling from the Treasury Department (No. 199925044) on the tax implications of collar transactions has opened the door for a new breed of tax-advantaged hedging plays that can be implemented with listed derivatives contracts.

Until recently, it was thought that the Treasury Department would treat a collar effectively as one big straddle consisting of the stock, a put and a call. This latest ruling, however, treats the stock and the put as one straddle, and the stock and the call as another distinct straddle. This seemingly simple change has enormous potential benefits for equity hedgers.

The biggest problem associated with using collars to hedge equity exposure occurs when investors roll over their options position. Many individual investors close their contracts in one expiration period and then immediately reestablish the equivalent contract in a later expiration to keep their hedge going until the ultimate forgiveness of capital gains tax at death.

But the rolling process creates a classic tax whipsaw: All gains on sales that occur as the contracts are rolled over are taxed immediately as capital gains, while losses are deferred. Although these deferred losses cause a real outlay of cash, in many cases these losses are postponed until the forgiveness of capital gains in the taxpayer’s final tax return.

The new ruling does nothing to eliminate the whipsaw associated with the put straddle. But it opens the door to a number of tax-advantaged plays involving option strategies with listed call options.

The reason for this curious inconsistency dates back to the efforts of former Illinois Representative Dan Rostenkowski in 1984, when the straddle rules were modified to treat a stock with an option as a straddle. Because of Rostenkowski’s work (which undoubtedly benefited his Chicago Board Options Exchange constituents), listed calls were excluded from the modified straddle rules, creating “qualified covered calls” with significant tax advantages (see box).

To avoid constructive-sale treatment, only out-of-the-money calls can be used. Instead of being labeled straddles (and taxed accordingly), they are considered “qualified covered calls” as long as they also comply with the requirement of being listed on an exchange. If the qualified covered call is too deep in the money, however, it will be classified as a straddle and taxed accordingly.

Stopping the Whipsaw

Assume a client owns XYZ stock with a zero cost basis, and its yield is 3 percent. In 1998, say, the client entered into a collar when the stock was at $100. The client sold a call with a strike price of $124 for $2, and bought a put with a strike price of $83 for $2. Both options had one-year expirations. Fast forward one year. XYZ’s price has soared to $180. The client’s put expires worthless, and the $2 loss is deferred (the new Treasury Department ruling doesn’t change this). The client buys back the call for $56, creating a $54 loss. To roll over the position, the client sells a new call at a strike price of $223 for $2, and buys a put at a strike price of $144 for $2. According to the new Treasury Department ruling, the differences between listed and OTC calls would be pronounced. If the client had used listed calls, he or she would have needed $56 to buy back the call. The client could simply sell $54 of XYZ, creating a $54 capital gain to offset the loss, because the qualified covered call rule doesn’t make the position a straddle. If the client had used OTC options, however, this would not be possible, and he or she would be whipsawed, since all gains must be taxed while losses are deferred. The result: if the client had used listed products, he or she would have ended up with an additional $2 invested, with only the $2 put loss deferred, since the listed call isn’t considered part of a straddle. If the client had used OTC options, however, he or she would have ended up investing $56 more, with the $2 put loss and the $54 call loss being deferred. If the client had used a listed call, the capital loss would be deductible today rather than being trapped by the straddle rules. The client would have realized a $54 gain that goes against the $54 loss, without any additional tax liability.

Listed options have long offered significant benefits over over-the-counter products: They are guaranteed by the Options Clearing Corp., a triple-A rated entity, and they can be closed out with any market participant rather than via a private renegotiation with a counterparty. Moreover, flex options available combine many of the benefits of OTC products—flexibility being the most important—with the benefits of the listed markets.

Now, thanks to the latest ruling, listed options have one more advantage: They can alleviate the biggest burden in using options to hedge a position over a long time period—the whipsaw.

Kevin Dowd, professor of economics at the University of Sheffield, explains how extreme value theory can be used to estimate the probability of extreme events when there are few data to work with.

Researchers and practitioners in finance and risk management have struggled for years with the problem of how to deal with extreme values—those rare, high-impact events that can strike unexpectedly and sometimes with deadly effect. Such events might include stock market or commodity market crashes, sudden devaluations, unusually large movements in the underlying variables in derivatives contracts, and even the financial after-effects of earthquakes.

Finance practitioners have long understood the importance of such events, but until recently no one really knew how to deal with them. The best they could do was to respond in ad hoc ways—they could try to make their stress test capabilities more sophisticated; they could replace assumptions of normally distributed risk factors with alternative distributional assumptions that allowed for fatter tails, so that extreme events were modeled as more likely, and more likely to be big, than under normality; they could worry about their gamma risk exposures and try to cover them; they could look at their exposures to sudden changes in major correlations; and so on. Each of these responses is reasonable in the right circumstances, but none fully addresses the core questions posed by the possibility of future extreme events: What is the probability of a specific extreme event?

And, turning the question around, what is the most extreme event that can occur, at a given level of probability?

The extreme value approach

The answers to these questions are provided by a relative newcomer to the world of finance—extreme value theory (EVT), which is a methodology specifically designed to handle the peculiar issues posed by extreme values. EVT was developed by statisticians and researchers in the applied physical sciences—most particularly, hydrology—to deal with some of the problems that occur in those areas.

To illustrate the basic concepts, suppose we lived next to the sea and were worried about the prospect of a flood. We would not be particularly interested in the more frequent and moderate day-to-day fluctuations of the sea level; we would, however, be concerned about those rare but damaging occurrences when the sea level rises to high levels and we get a flood. We might respond by building a sea wall to protect ourselves, but we would then have to decide how high to build it. It would have to be high enough to give us reasonable protection against a flood. At the same time, we wouldn’t want it to be too high or it would be unnecessarily expensive. We would have to trade off the greater protection of a higher sea wall against the greater cost of constructing it. To do so, we need to strike a balance, taking account of the likelihood of floods, the damage they would probably inflict and the costs of building sea walls of various possible heights. Assessing the damage of floods and the costs of sea walls are fairly standard problems, albeit not necessarily easy ones. But how do we determine the likelihood of a flood?

Fundamentally similar types of problems are common in finance and risk management. How likely is the stock market to fall by at least 10 percent in a single day? How likely is a particular financial institution to become insolvent over the next month? How likely is it that payouts on automobile insurance will be 50 percent more than their previous maximum? How likely is a payout on a catastrophe insurance contract? Each of these questions relates to the likelihood of a rare event, and possibly an event that has never occurred before. Moreover, in these and all other extreme value problems, paucity of data is always a major headache.

Using EVT

From a statistical point of view, extreme value problems in finance are much the same as extreme value problems in hydrology, and can therefore be tackled using the same statistical methods. However, it is only in the last few years that finance practitioners have realized the similarity and begun to apply EVT to the extreme value problems they face.

There are a great many possible applications. In the portfolio management area, EVT helps us to model the probabilities of large rises or falls in market prices or rates, probabilities of sudden insolvency, and so on. These can be useful, among many other reasons, for determining capital requirements for securities firms and banks, and for determining margin requirements in organized exchanges. In the area of insurance, we can use EVT to model large claims, loss-severity distributions, probable maximum losses, probabilities of ruin and the like. These are all useful for pricing insurance contracts, dealing with insurance risks and determining excess loss layers in reinsurance. In the catastrophe derivatives area, EVT enables us to model the probabilities of catastrophes, their expected losses and their associated capital requirements. In the risk management area, EVT gives us a new approach to value-at-risk, and one that is superior to the standard parametric and non-parametric estimation approaches often used.

EVT gives us a new approach to value-at-risk, and one that is superior to the standard parametric and non-parametric estimation approaches often used.

The key to EVT is the extreme value theorem. Subject to certain fairly reasonable conditions, this theorem tells us that the distribution of extreme observations (such as extremely high or low returns) should converge to a particular known form as our sample size increases. The limiting distribution of extreme returns always has this same form, whatever the distribution of returns from which the extreme returns are drawn. The theorem is important because it enables us to estimate the limiting distribution of extreme returns without having to make strong assumptions concerning a parent distribution—the distribution of returns—about which we may have little information anyway.

This distribution has three parameters—a mean, a standard deviation and a third parameter, the tail index, which gives an indication of the “fatness” of the tails of our distribution. The first two parameters occur almost everywhere in statistics and are quite familiar, but the tail index is a parameter specific to extreme value problems and is much less well-known. To apply EVT, we must first estimate these parameters—EVT gives us a variety of ways to do so—and then apply standard formulas to give concrete answers to particular problems.

These answers may be estimates of the probabilities of specific extreme events (such as the probability of a greater than 20 percent fall in a particular market price). Alternatively, they may be estimates of the extreme “quantiles” (that is, the quantity-terms on the horizontal axes of probability functions) associated with specific probabilities. Thus, for example, we may want to estimate a VAR at the 99.9 percent confidence level or the capital needed to reduce the probability of insolvency to negligible levels. We can therefore use EVT to derive probability estimates from specified quantiles or, conversely, we can derive quantile estimates from specified probabilities.

EVT also gives us confidence intervals for each probability or quantile estimate, so we can be 95 percent confident, say, that the true (unknown) probability or quantile lies within a certain range. These confidence intervals can be quite useful for gauging the precision of our estimates, so we can take an informed view on how much we should rely on them.

Points to watch for

As in other areas of practical statistics, the successful implementation of EVT depends more on good judgment than on the mechanical application of particular formulas. One issue on which such judgment is essential is where to place the dividing line between extreme and non-extreme observations. This dividing line separates the tail of the distribution function, which includes the extreme observations, from the rest of the distribution, which covers the more central observations. This is a tricky issue because our results depend of the choice of tail size and yet theory gives us little guidance on how large the tail should be. Perhaps the best response is to try out various tail sizes, assess their effects on estimates of the tail index, and then use our judgment to determine where to draw the line.

There is a second issue requiring considerable care on the part of the EVT user—how to handle observations that are correlated with each other over time. Basic EVT assumes that our observations are independently distributed over time, although most financial series exhibit some form of temporal dependence (that is, most financial returns exhibit volatility clustering, with periods of alternating high and low volatility), which can make our estimates unreliable. The simplest response to this problem is to apply EVT to per-period “maxima” (or “mimina”) instead of raw returns. We exploit the point that these block maxima are usually less clustered than the underlying data from which they are drawn, and become even less clustered as the periods of time from which they are drawn get longer. If we adopt this approach, however, we still have to make a judgment about how big these blocks of time should be. Alternatively, we could model the temporal dependency explicitly by working with a conditional distribution rather than an unconditional one (that is, we might fit a GARCH model to a set of returns data to capture the temporal dependency, and then work with the tail of the GARCH residuals rather than the tail of the return data). Finally, we could adopt an “extremal” index approach—we can estimate an extremal index, which gives us a measure of the degree of clustering, and then rely on statistical theory that tells us how to modify our estimators to take account of clustering.

EVT vs. the alternatives

How does EVT compare to alternative parametric and non-parametric estimation approaches?

EVT is tailor-made for handling extreme values, and only EVT makes the best possible use of both the available statistical theory and the limited data we have when dealing with extreme value problems.

Traditional parametric estimation approaches assume that returns follow a normal distribution, a “t” distribution or some alternative arbitrary distribution. These approaches try to accommodate the whole empirical distribution of returns, however, and since the central observations are the most numerous, they tend to fit those observations best. As a result, extreme observations are often left appearing as awkward outliers.

More to the point, EVT improves over traditional parametric approaches because it imposes the correct distribution and they do not. In imposing inappropriate distributions on the data, traditional parametric approaches effectively flout the statistical theory that actually tells us what the distribution should be.

EVT improves on traditional non-parametric approaches (such as the historical simulation approach to VAR) because it is more efficient and generates estimates of quantiles (and associated probabilities) that are beyond our sample range—estimates that non-parametric approaches cannot deliver.

EVT offers practitioners an attractive solution to a difficult problem—how to estimate extreme quantiles and extreme probabilities where we have little data to work with. It does so by making the best possible use of the insights into extreme values that statistical theory has to offer. The EVT approach is intuitive and elegant, yet the theory itself is powerful and the answers it provides do not attempt to disguise the high levels of uncertainty inevitable in extreme value problems. But perhaps most important of all, EVT offers an extremely useful practical tool.

George Martin, research director at the Center for International Securities and Derivatives Markets, explains what matters and what doesn’t in looking at hedge fund returns.

While the past year has seen a lot of attention focused on a few notable hedge fund failures, little effort has been made to consider the sources of returns for hedge funds in general. Consideration needs to be devoted to the economic determinants of hedge fund returns during periods of relative market tranquility as well as during periods of profound market turbulence, such as August 1998.

Based on my research, I argue that hedge fund returns at the index level can be explained by economics. But this is only somewhat helpful in understanding the returns of individual funds. Furthermore, the difficulties in systematically determining and representing the sources of individual fund returns cannot be readily compensated for through the superior selection of hedge fund managers. This is therefore justification for the creation of index-based products designed to deliver efficiently the returns to particular hedge fund styles. The research also provides a rationale for the development of models for the dynamic allocation of capital across hedge fund styles.

Any analysis of hedge fund returns must begin with a system for classifying individual funds into groups that represent particular investment styles or strategies; these classifications typically rely on an assessment of the underlying assets traded and the types of return patterns exploited by the fund. The problem is that these classifications have shortcomings, as became clear most dramatically in the case of market-neutral hedge funds such as Long-Term Capital Management. A different and perhaps more satisfying approach is to rely on actual hedge fund performance to determine classifications.

Although there are many statistical techniques that can be used to do this, the technique most directly applicable is cluster analysis. Cluster analysis attempts to group data to minimize intragroup variation while maximizing intergroup variation. For example, suppose we have a sample of hedge fund returns on two dates, and those returns are represented graphically in an X–Y scatterplot. If we observe two distinct clouds of data—one in the northwest quadrant and the other in the northeast quadrant, for instance—then cluster analysis would identify the hedge funds associated with each of the clouds as coming from distinct groups.

Table 1
Statistics for Cluster Groups
Without August 1998
	Managed Futures	Market Arb	Event-Driven	Global Est.	Emerging Markets: Asia	Emerging Markets: Latin Am.	Long Equity	Short
funds	33	168	96	184	26	20	53	24
mean	0.0115	0.0122	0.0136	0.0188	0.0078	0.0040	0.0206	0.0014
st. dev.	0.0266	0.0090	0.0248	0.0372	0.0583	0.0936	0.0362	0.0518
skew	0.7890	-2.8736	-0.7462	-1.3755	0.0730	-1.6244	-1.5467	0.9067
kurtosis	2.2705	13.4128	2.8829	3.4108	2.2304	6.3640	5.0030	2.7511
With August 1998
	Managed Futures	Market Arb	Event-Driven	Global Est.	Emerging Markets: Asia	Emerging Markets: Latin Am.	Long Equity	Short
funds	42	115	87	209	22	47	54	28
mean	0.0118	0.0119	0.0123	0.0185	0.0075	0.0090	0.0210	0.0031
st. dev.	0.0247	0.0063	0.0144	0.0362	0.0543	0.0655	0.0392	0.0477
skew	0.7491	-1.3000	-3.0488	-1.4238	0.4154	-1.9570	-1.7810	0.9980
kurtosis	1.3806	3.3797	15.9687	3.8063	2.3830	7.7163	5.9191	3.3109

Table 2
Stability of Classifications
	Managed Futures	Market Arb	Event-Driven	Global Est.	Emerging Markets: Asia	Emerging Markets: Latin Am.	Long Equity	Short
managed futures	93.94%	3.03%	0.00%	0.00%	0.00%	3.03%	0.00%	0.00%
market arb.	0.00	63.69	28.57	2.38	0.00	2.38	0.00	2.98
event-driven	7.29	6.25	27.08	35.42	2.08	19.79	2.08	0.00
global est.	0.54	0.00	6.52	92.39	0.00	0.00	0.54	0.00
emerging markets: Asia	0.00	0.00	0.00	3.85	76.92	11.54	7.69	0.00
emerging markets: Latin Am.	0.00	0.00	0.00	0.00	0.00	100.00	0.00	0.00
long equity	5.66	0.00	1.89	0.00	0.00	0.00	92.45	0.00
short	0.00	4.17	0.00	0.00	0.00	0.00	0.00	95.83

For the analysis presented here, I used hedge fund data from the MAR Hedge and Hedge Fund Research databases. I collected all hedge funds with complete monthly data from January 1995 through June 1999, conscious of the survivorship biases induced by this sampling. I added a number of indices, as well as a small sample of large commodity trading advisers from MAR, totaling 583 funds and 21 indices. Clustering was done via a robust mediod method on scaled return data. Experimentation led to the conclusion that having eight separate clusters generated the most useful results.

To examine the effects of the events of August 1998 on the clustering algorithm, I initially excluded that data from the clustering routine, although the index returns are computed from all data.

Table 1 presents summary statistics for the clusters, computed from the equal-weighted returns of individual funds. We can see that the first two moments of cluster characteristics, with perhaps the exception of “emerging markets: Latin America,” are relatively stable. Higher-order moments are, as expected, less stable. A clear indication of the stability or lack of stability in a cluster is given in Table 2 by a markov transition matrix of funds from classifications established without August 1998 data to classifications with that data.

Based on Tables 1 and 2, we can see that the most robust classifications are managed futures, long equity and short, followed by global-established, emerging markets, and market arbitrage. Event-driven is the least-stable classification, behaving akin to global-established or emerging-market funds. This suggests that investors seeking to include event-driven funds in their portfolios should be concerned about whether candidate funds’ previous performance characteristics are likely to persist in the future, especially during times of market stress. Figure 1 provides a graphical representation of the cumulative returns of each cluster, based off clusters determined with data that include August 1998. As expected, each cumulative return path appears to be rather different.

Table 3
The Sensitivity of Indices to a Range of Economic Factors
	managed futures	market arb.	event-driven	global est.	emerging markets: Asia	emerging markets: Latin Am.	long equity	short
intercept	0.32	2.84	1.64	-0.05	-1.30	0.43	-0.45	1.30
sp2yrs	0.03	2.57	2.92	-2.50	-5.35	-1.19	0.11	0.47
sp10yr	-4.00	1.06	-0.18	4.26	3.96	0.03	-0.05	-2.12
sp2chg	9.74	28.69	19.49	-25.22	-23.74	38.14	6.92	17.16
sp10ch	-41.92	-15.31	-64.57	-32.88	10.52	6.26	14.83	60.34
sp500r	15.77	-64.64	84.12	183.83	105.10	7.93	430.40	- 218.30
msci	-1.07	2.12	2.16	-1.02	10.59	4.38	-0.18	-1.24
uscur	-2.93	18.77	5.07	-0.91	0.22	13.52	1.26	-2.02
eurobond	-5.77	7.25	6.42	2.18	2.41	9.53	1.05	1.88
elmi	-23.39	-43.38	-27.00	-53.49	-35.75	6.30	9.70	-0.12
jpmus	-4.81	-20.56	-13.15	4.88	0.01	-6.13	-1.82	-1.22
mlconvert	7.84	2.42	8.75	20.78	0.00	1.07	3.77	-15.25
sp500corr	-5.67	3.79	3.21	2.53	-4.24	-0.58	0.25	-2.16
vix	0.04	-0.16	-0.06	-0.04	0.02	0.00	0.01	0.02
avesp500vol	7.39	-2.69	-5.38	-2.23	5.70	-1.04	-1.78	-0.25

We can examine the sensitivity of each of these indices to a range of economic factors that reflect the returns on underlying assets, the costs of financing those assets, and the risk-related return patterns (for example, volatilities and correlations) that underlie the trading strategies pursued by hedge funds. In particular, Table 3 reports OLS regression results of the standardized indices for two- and 10-year swap spreads and changes in swap spreads (sp2yrs, sp10yr, sp2ch, sp10ch); a broad index of U.S. government bonds (jpmus); Standard & Poor’s 500 returns (sp500r), the average volatility of stocks in the S&P 500 (avesp500vol); the average interstock correlation in the S&P 500 (sp500corr); the MSCI ex-US (msci); emerging-market eurobond rates (eurobond); emerging-market local currency money-market instrument returns (elmi); the implied volatility on the S&P 100 (vix); an index of the returns to holding convertible bonds (mlconvert); and an index of U.S. dollar returns (uscur).

Because the cluster index returns are standardized, we can compare regression quantities across hedge fund strategies. One result we see is that hedge fund returns exhibit different sensitivities to swap spread variables at different maturities. Market arbitrage funds, for example, tend to be positively affected by spread levels and widenings at the two-year horizon, but negatively affected by expansions in 10-year swap rates. There are also more obvious results, such as the fact that long equity is the classification most sensitive to S&P 500 returns.

While these results are interesting, hedge fund investors and structurers are rarely faced with having to evaluate returns to large groups of hedge funds. Evaluations are usually made on individual funds or small collections of funds. We can redo the same regressions for all funds in the data set to determine whether or not inferences drawn from index-level data are applicable to individual funds.

Table 4
Individual Fund Regression Medians
	managed futures	market arb.	event-driven	global est.	emerging markets: Asia	emerging markets: Latin Am.	long equity	short
intercept	0.67	0.91	0.70	-0.13	-0.76	-0.68	-0.49	0.93
sp2yrs	1.54	0.79	-0.45	-1.89	-3.45	-2.46	0.45	1.16
sp10yrs	3.61	1.48	0.30	3.15	3.06	1.03	-0.71	-1.72
sp2chg	34.57	39.56	19.72	-11.57	-23.75	68.80	-0.82	12.09
sp10ch	-59.62	-19.93	-27.44	-20.04	-7.22	51.62	9.20	29.08
sp500r	38.92	20.91	80.23	168.14	54.42	-7.02	383.07	-162.99
msci	3.35	-0.54	2.58	-1.06	8.04	3.81	-1.13	0.11
uscur	-1.92	3.19	8.90	-2.46	1.72	14.72	0.71	0.20
eurobond	-2.86	2.65	2.36	0.73	3.69	10.93	0.37	0.81
elmi	34.14	-44.85	-39.74	-48.14	-7.17	1.09	9.94	13.71
jpmus	-9.92	-3.83	-6.78	6.51	-2.28	8.10	-0.98	-2.70
mlconvert	2.23	2.93	8.45	16.76	1.26	-4.57	4.21	-13.91
sp500corr	3.69	2.02	-0.34	1.81	-2.45	-2.12	-0.22	-2.46
vix	0.04	-0.06	-0.02	-0.02	0.02	0.02	0.01	0.02
avesp500vol	-0.37	-0.66	-0.45	-1.23	2.48	0.69	-1.21	0.22
Standard Deviation of Regression Coefficient Estimates
	managed futures	market arb.	event-driven	global est.	emerging markets: Asia	emerging markets: Latin Am.	long equity	short
intercept	0.67	1.22	0.74	0.75	0.89	0.68	1.03	0.92
sp2yrs	2.30	3.94	2.91	3.20	2.85	2.09	2.59	3.08
sp10yrs	3.08	4.11	2.98	3.51	3.31	2.65	3.18	3.43
sp2chg	63.61	94.80	73.64	73.19	68.39	49.22	64.57	59.22
sp10ch	52.93	68.98	66.20	67.95	55.58	48.84	49.42	57.01
sp500r	121.95	180.86	137.89	157.40	140.27	97.32	184.25	104.75
msci	5.76	6.39	6.80	6.63	7.88	4.47	7.69	4.28
uscur	11.73	10.96	10.11	9.11	9.52	6.20	8.91	11.39
eurobond	3.23	5.00	4.80	4.71	2.89	5.88	3.17	3.84
elmi	33.06	61.44	54.05	45.74	36.33	23.21	43.24	51.00
jpmus	11.83	15.12	12.26	13.26	9.07	8.21	9.89	13.67
mlconvert	6.80	9.81	9.07	7.47	5.25	10.27	6.81	7.57
sp500corr	3.41	3.21	2.69	2.36	2.41	1.79	2.69	2.78
vix	0.04	0.07	0.05	0.05	0.06	0.04	0.04	0.04
avesp500vol	4.23	5.88	5.28	5.03	4.55	4.99	5.12	5.72

The results in Table 4 show the median regression results sorted by classification. We can see that the general results are consistent with the index-level results. However, the standard deviation of regression estimates is generally quite large relative to the median coefficient estimate. This suggests that, despite membership in a specific cluster, the sensitivity of individual funds to the economic variables indicated is quite varied. Only in a few instances is the standard deviation of returns smaller in magnitude than the actual median regression coefficient. Two conclusions can be drawn from this: the first is that reliance on index-level sensitivity analysis may not be particularly informative about the sensitivities of individual funds, and the second is that simple regression-based techniques for classifying hedge funds are likely to generate few useful results. Nonetheless, this does not preclude the usage of the distribution of regression coefficients in the determination of individual fund exposures, which may increase the efficiency of estimates of individual fund sensitivities.

While the data suggest that in general we cannot draw much reliable information about individual funds from the index-level data, we can still use the index-level data as the basis for the evaluation of the returns to manager selection at the individual fund level—since it may be the case that we could merely pick “good” managers rather than take on the specific types of exposures that we think are advantageous.

Table 5
Returns to Manager Selection
cluster/quantile	5%	10%	15%	20%	25%	75%	80%	85%	90%	95%
managed futures	-0.92	-0.73	-0.51	-0.33	-0.28	0.39	0.44	0.52	0.63	0.91
market arb.	-0.57	-0.51	-0.43	-0.36	-0.32	0.16	0.26	0.48	0.62	1.29
event-driven	-0.70	-0.49	-0.34	-0.30	-0.26	0.18	0.35	0.53	0.64	0.88
global est.	-0.99	-0.87	-0.80	-0.62	-0.51	0.42	0.60	0.82	1.00	1.15
emerging markets: Asia	-1.00	-0.83	-0.78	-0.70	-0.58	0.31	0.35	0.49	0.54	0.69
emerging markets: Lat. Am.	-1.71	-0.80	-0.64	-0.60	-0.43	0.50	0.62	0.89	1.51	1.61
long equity	-0.94	-0.89	-0.85	-0.58	-0.50	0.16	0.23	0.37	0.51	0.94
short	-3.09	-1.50	-1.09	-0.85	-0.67	0.77	0.81	1.64	2.06	2.10

To that end, we can calculate the monthly excess returns of each fund relative to its benchmark index, and then compute the associated empirical distribution functions of individual hedge funds. (The benchmark returns and excess returns are not risk-adjusted.) In Table 5, we can see that the returns from manager selection are quite limited, unless the selector is extremely accurate in his or her ability to pick top-quantile managers. In order to earn an additional 50 basis points per month over the period studied, the fund selector must have been able to pick—depending on the hedge fund style—managers in the 80–90 percentile. The stated return penalty for picking a bad manager is relatively small, but these numbers are upward-biased by the survivorship bias produced by the sampling requirement that the funds considered have continuous returns over the four and a half years considered. It should be noted that another way of interpreting this data is that those investors or intermediaries who can repeatedly pick good managers with economically meaningful performance advantages have accomplished an extremely difficult task.

One consequence of this is that it appears that the benefits of proper style selection outweigh the returns to manager selection, at least for those investors and intermediaries with a less-than-perfect ability to select managers who will outperform their peers. The cluster-based methodology produces indices that are maximally diversified, and thus provide the proper basis for efficient dynamic-style allocation. More important, efficient-style allocation need not take the form of sequential allocation between particular sectors, but can be determined by allocating capital between portfolios of style indices whose weights are primarily determined by the eigenvectors of the forecast covariance between style indices. Using the historical covariances between indices over the period under study, allocation in and out of one portfolio of indices would have accomplished the equivalent of 56 percent of optimal allocation across all style indices.

This analysis indicates that hedge fund returns at the index level can be explained by economic factors that relate to the prices of the underlying assets, the costs of financing those positions and the risk-related patterns that exist in the returns across assets. However, the analysis also shows that there is significant variety in individual fund returns and their sensitivities, so conclusions derived from group data are likely to be only weakly applicable to individual funds. Furthermore, the returns from selecting good managers, rather than specific economic risk exposures through individual funds, are generally quite limited. Significant value lies instead in the dynamic allocation of funds across styles through broad style indices. Although there have been some less-than-successful attempts, actual products designed to deliver these returns efficiently via hedge-fund-style indices have yet to be fully developed.

Figure 1  

George Martin can be reached at semimartingale@usa.net.

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