STOCKS, BONDS AND HEDGE FUNDS:

NOT A FREE LUNCH!

 
Gaurav S. Amin*
Harry M. Kat**
Working Paper
This version: April 29, 2002

 
Please address all correspondence to:

Harry M. Kat
ISMA Centre
The University of Reading
Whiteknights Park
Reading RG6 6BA
United Kingdom
Tel. +44-118-9316428
E-mail: h.kat@ismacentre.rdg.ac.uk

*Ph.D student, ISMA Centre, University of Reading, #Associate Professor of Finance, ISMA Centre, University of Reading. The authors like to thank Hans de Ruiter and ABP Investments for generous support and Tremont TASS (Europe) Limited for supplying the hedge fund data. The first part of this paper was circulated earlier under the title 'Who Should Buy Hedge Funds?'.

 

STOCKS, BONDS AND HEDGE FUNDS:

NOT A FREE LUNCH!

ABSTRACT

We study the diversification effects from introducing hedge funds into a traditional portfolio of stocks and bonds. Our results make it clear that in terms of skewness and kurtosis equity and hedge funds do not combine very well. Although the inclusion of hedge funds may significantly improve a portfolio's mean-variance characteristics, it can also be expected to lead to significantly lower skewness as well as higher kurtosis. This means that the case for hedge funds includes a definite trade-off between profit and loss potential. Our results also emphasize that to have at least some impact on the overall portfolio, investors will have to make an allocation to hedge funds which by far exceeds the typical 1-5% that many institutions are currently considering.

I. INTRODUCTION

Hedge funds are often said to provide investors with the best of both worlds: an expected return similar to equity with a risk similar to that of bonds. When risk is defined, as is traditionally the case, as the standard deviation of the fund return, this is indeed true. Recently, however, several studies have shown that the risk characteristics of hedge funds are substantially more complex than those of stocks and bonds. This means that when hedge funds are involved it is no longer appropriate to use the standard deviation as the sole measure of risk. Investors will have to give weight to the return distribution's higher moments, in the form of its (co-)skewness and (co-)kurtosis, as well. When doing so, it becomes evident that hedge funds are not necessarily a free lunch: hedge funds' attractive mean-variance characteristics may be accompanied by significantly less attractive skewness and kurtosis properties.

Amin and Kat (2002) investigated the performance of randomly selected baskets of hedge funds ranging in size from 1 to 20 funds. Their analysis showed that increasing the number of funds can be expected to lead not only to a lower standard deviation but also, and less attractive, to lower skewness and increased correlation with the stock market. Mean, kurtosis and correlation with bonds tended to be largely unaffected by the number of funds. In the same paper it was also shown that individual hedge funds show extremely high variation in performance. When combined into portfolios the degree of variation drops strongly, although at a decreasing rate. For portfolios containing more than 15 funds the further decline in variation is only small.

Most investors tend to hold hedge funds as part of a balanced portfolio containing stocks, bonds and possibly real estate and private equity as well. In this paper we therefore extend the analysis of Amin and Kat (2002) to investigate the diversification effects that occur when combining hedge funds with stocks and bonds. We not only look at the means and standard deviations of the resulting portfolios' return distributions, but also at their skewness and kurtosis. Our results make it clear that hedge funds do not mix too well with equity. Although including hedge funds in a traditional investment portfolio may significantly improve that portfolio's mean variance characteristics, it can also be expected to lead to significantly lower skewness as well as higher kurtosis. This means that the case for hedge funds is less straightforward than often suggested and requires investors to make a trade-off between profit and loss potential. Our results also emphasize that as long as investors do not invest a substantial portion of their wealth in hedge funds, hedge funds will have little or no impact on the overall portfolio characteristics. This is an important observation given that most institutional investors that are currently considering to invest in hedge funds do not appear to be planning to allocate more than 1-5% to hedge funds.¹

II. THE DATA

The hedge fund data used in this study were obtained from Tremont TASS, which is one of the largest hedge fund databases currently available. After eliminating funds with incomplete and ambiguous data as well as funds of funds, per May 2001 the database at our disposal contains monthly net of fee returns on 1195 live and 526 dead funds. As shown in Amin and Kat (2001b), concentrating on live funds only will on average overestimate the mean return on individual funds by around 2% as well as introduce a significant downward bias in estimates of the standard deviation, an upward bias in the skewness and a downward bias in the kurtosis estimates of individual fund returns. To correct for this in our analysis we decided not to work with the raw return series of the 264 funds that survived the period 1994-2001. Instead we created 455 7-year monthly return series by, starting off with the 455 funds that were alive in June 1994, replacing every fund that closed down during the sample period by a fund randomly selected from the set of funds alive at the time of closure, following the same type of strategy and of similar age and size. For simplicity, we will still refer to the data series thus obtained as 'fund returns.'

Implicitly we assume that in case of a fund closure investors are able to roll from one fund into the other at the reported end-of-month net asset values and at zero additional costs. This will underestimate the true costs of fund closure to the investor for two reasons. First, when a fund closes shop its investors will have to look for a replacement. This search takes time and is not without costs. Second, investors may get out of the old and into the new fund at values that are less favourable than the end of-month net asset values contained in the database. Unfortunately, it is impossible to incorporate this into the analysis in a satisfactory way without further detailed information.

To represent stocks we use the S&P 500 index, while bonds are represented by the (10- year) Salomon Brothers Government Bond index. Over the sample period monthly S&P returns have a mean of 1.46%, a standard deviation of 4.39%, a skewness of -0.80 and a kurtosis of 3.92. Monthly bond index returns have a mean of 0.43%, a standard deviation of 1.77%, a skewness of 0.56 and a kurtosis of 4.29.

III. DIVERSIFICATION WITH HEDGE FUNDS

One reason why investors allocate to hedge funds is to reduce risk without loss of expected return. Based on monthly return data over the period 1994-2001, a portfolio of 50% stocks and 50% bonds has an expected return of almost 1% per month. The same is true for a diversified hedge fund portfolio. With hedge funds only loosely correlated with stocks and bonds, this means that by replacing stocks and bonds with hedge funds investors can reduce the standard deviation of the portfolio return while maintaining the expected return at around 1%. To study this diversification process in more detail, we created 500 different portfolios containing 20 hedge funds each by random sampling without replacement from the above 455 funds. Subsequently, we combined every one of these hedge fund portfolios with stocks and bonds in proportions ranging from 0% to 100% invested in hedge funds. Doing so, it was assumed that the proportions of wealth invested in stocks and bonds are always equal. This gives rise to portfolios like 40% stocks, 40% bonds and 20% hedge funds, 30% stocks, 30% bonds and 40% hedge funds, etc. From the monthly returns on the resulting portfolios we calculated four different sample statistics: the mean, standard deviation, skewness, and kurtosis. For hedge fund allocations ranging from 0% to 100%, the 5th, 10th, etc. percentiles of the frequency distributions of these four statistics are shown in figure 1-4.

Many will argue that investors (including fund of funds managers) do not select portfolios by random sampling. This is certainly true. However, although many investors spend a lot of time and effort selecting hedge funds, this does not necessarily mean that in many cases a randomly sampled portfolio is not a good proxy for the portfolio ultimately selected. So far, there is no evidence that some investors are consistently able to select future out-performers² nor of the existence of specific patterns or anomalies. When corrected for possible biases, there is no significant persistence in hedge fund performance nor is there any significant difference in performance between older and younger funds, large and small funds, etc. In addition, older funds may be (more or less) closed for new investments. Investors that are relatively new to hedge fund investing are therefore often forced to invest in funds with little or no track record. If so, selecting funds based on (the statistical properties of) their track record is not an option. The fund prospectus and interviews with managers may provide some information, but in most cases this information will only be sketchy at best and may add more confusion than actual value.

Figure 1 shows the frequency distributions of the mean portfolio return for varying hedge fund allocations. A portfolio of 50% stocks and 50% bonds has a mean return of 0.95%. Since the mean return of a portfolio is simply the weighted average of the means of its components, the introduction of hedge funds makes the median mean return change linearly from 0.95% when no hedge funds are included to 0.99% (the mean return on the median basket of 20 hedge funds) when 100% is invested in hedge funds. Figure 2 shows the frequency distributions of the standard deviation of the portfolio return. Here a more interesting picture emerges. Starting at 2.49% for the case of no hedge funds, the median standard deviation drops first but rises later to end at a standard deviation of 2.44% when 100% is invested in hedge funds. The drop represents the relatively low correlation of hedge funds with stocks and bonds. The median standard deviation reaches its minimum at a hedge fund allocation of 50%, which makes it very clear that to obtain at least some diversification benefits investors will have to allocate a very substantial part of their wealth to hedge funds.

The frequency distributions of the skewness of the portfolio return are shown in figure 3. The graph shows a remarkable similarity with that of the standard deviation. Starting at -0.32, the median skewness drops first and rises later to end at -0.52 when 100% is invested in hedge funds. The median reaches a minimum of -0.86 at a hedge fund allocation of 55%. Finally, figure 4 shows the frequency distributions of the kurtosis of the portfolio return. Starting at 2.90, the median kurtosis rises gradually towards the kurtosis level of the median portfolio of hedge funds (5.39). The graph is somewhat S-shaped though, meaning that most of the rise takes place for hedge fund allocations between 25% and 65%. For allocations smaller than 25% the effect from the inclusion of hedge funds on the kurtosis of the overall portfolio return is relatively limited.

Overall, it appears that the case for using hedge funds for diversification purposes is not as straightforward as is often suggested. Hedge funds can indeed be expected to reduce a portfolio's standard deviation, but only at the cost of lower skewness and increased kurtosis. In addition, and not completely unexpected, figure 1-4 show that to realize at least some of the diversification effect investors will have to invest a large proportion of their assets in hedge funds; much more than most of them are currently contemplating.

IV. YIELD ENHANCEMENT WITH HEDGE FUNDS

Another application of hedge funds that is often suggested is to use hedge funds to replace bonds. A good example can be found in McFall Lamm (1999). The idea is that since hedge funds have a relatively high mean and low standard deviation and are only loosely correlated with equity, replacing bonds by hedge funds will substantially raise the expected return without an accompanying rise in standard deviation. To investigate the exact workings of this, we again created 500 different portfolios containing 20 hedge funds and combined every one of these hedge fund portfolios with stocks and bonds. Doing so, the equity allocation was kept constant at 50%. In other words, starting with 50% stocks and 50% bonds, the hedge fund allocation is assumed to come fully out of the bond allocation. This gives rise to portfolios like 50% stocks, 40% bonds and 10% hedge funds, 50% stocks, 30% bonds and 20% hedge funds, etc. As before, from the monthly returns on the resulting portfolios we calculated the mean, standard deviation, skewness, and kurtosis. For hedge fund allocations ranging from 0% to 50%, the 5th, 10th, etc. percentiles of the frequency distributions of these four statistics are shown in figure 5-8.

From figure 5 we see that, as intended, when the hedge fund allocation increases the median expected return rises in a linear fashion from 0.95% on a portfolio without hedge funds to 1.24% on a portfolio of 50% equity and 50% hedge funds. From figure 2, which shows the frequency distributions of the standard deviation of the portfolio return, we see that replacing bonds by hedge funds in the way we did does not leave the portfolio standard deviation completely untouched. Over the range studied, it rises from 2.4% with no hedge funds to 3.1% with 50% hedge funds.

So far things are not too different from what investors (are told to) expect when replacing bonds by hedge funds. However, this is no longer the case if we look at the skewness of the portfolio return distribution. Figure 7 shows very clearly that replacing bonds by hedge funds will lead to a very substantial reduction in skewness. In addition, as shown by figure 8, it also causes a substantial rise in the return distribution's kurtosis. The drop in skewness is very interesting. With the median hedge fund portfolio exhibiting a skewness of only -0.52, it is clear that in terms of skewness hedge funds and equity do not mix very well. In economic terms, the data suggest that when things go wrong in the stock market, they also tend to go wrong for hedge funds. In a way, this makes sense. A significant drop in stock prices will often be accompanied by a widening of a multitude of spreads, a drop in market liquidity, etc. As a result, many hedge funds will show relatively bad performance as well. A similar reasoning explains why the median portfolio of 50% hedge funds and 50% equity already has a kurtosis that is almost as high as that of 100% hedge funds (5.39).

We reach a similar conclusion as before. The improvement in expected return that is observed when bonds are replaced by hedge funds is not a free lunch. The higher expected return is obtained at the cost of substantially lower skewness as well as substantially higher kurtosis. Figure 5-8 also confirm our previous conclusion with respect to the required size of the hedge fund allocation. To see at least some effect, investors will have to make an allocation to hedge funds that is much higher than what most are currently contemplating.

V. BRINGING IT TOGETHER

From the previous discussion it is clear that the beneficial effect of hedge funds on the mean or standard deviation of the portfolio return tends to go hand in hand with an opposite effect on the return distribution's skewness and kurtosis. As a result, the overall shape of the portfolio return distribution can be expected to change substantially as a result of the inclusion of hedge funds. Figure 9 shows the return distribution of a portfolio of 50% stocks and 50% bonds as well as the return distribution of the median portfolio of 30% stocks, 30% bonds and 40% hedge funds.

Comparing both distributions we see that they intersect several times. Reading the graph from left to right, the net effect of the inclusion of hedge funds consists of: (1) a higher probability of a very large loss, (2) a lower probability of a smaller loss, (3) a higher probability of a low positive return, and (4) a lower probability of a high positive return. Most investors that use hedge funds for diversification will expect to trade in profit potential for reduced loss potential on a more or less equal basis. However, as shown clearly by figure 9, because of the increase in negative skewness the trade-off is not symmetrical. Investors can expect to give up more on the upside than on the downside.

Figure 10 shows the return distribution of a portfolio of 50% stocks and 50% bonds as well as the return distribution of the median portfolio of 50% stocks and 50% hedge funds. Comparing both graphs we see that the net effect of replacing bonds by hedge funds consists of (1) a higher probability of a large loss, (2) a lower probability of a smaller (positive or negative) return, and (3) a higher probability of a higher positive return. Most investors who replace bonds by hedge funds will expect the return distribution to simply shift to the right without changing shape. Figure 10, however, makes it clear that this shift will be accompanied by an extension of the left tail, i.e. a higher probability of a large loss.

The above confirms that the case for hedge funds is less straightforward than often suggested and requires investors to make a trade-off between profit and loss potential. In essence, hedge funds offer investors a way to modify the risk-return characteristics of their portfolio.³ Whether the resulting portfolio makes for a more attractive investment than the original is primarily a matter of taste though, not a general rule. The next question is of course what type of investor would be interested in trading in skewness for a higher mean return and/or a lower standard deviation. Since in general institutional investors will be better equipped to deal with a relatively large loss (they can raise premiums for example) than retail investors, one could argue that hedge funds are more suitable for institutional investors than for retail investors. So far, however, private investors have been the main investors in hedge funds. Driven by low interest rates, declining stock markets, and substantial marketing and peer pressure, institutional investors are showing interest but, apart from a number of US endowments, not many have made a significant allocation to hedge funds yet.

VI. MEAN-VARIANCE OPTIMAL PORTFOLIOS

The allocation rules that we have studied so far are quite ad hoc, i.e. do not rely on more detailed information with regard to the statistical properties of the asset classes involved. To solve this we performed two standard mean-variance optimisations; one with only stocks and bonds and one with stocks, bonds and hedge funds as the available asset classes. The results of both optimisations can be found in table 1 and 2. The differences between the case with and the case without hedge funds can be found in table 3. Throughout we concentrate on the median case.

In table 1-3 the mean-variance efficient set is approached in two different ways. In the first part of each table we look at the highest possible mean for a given standard deviation. This is the mean-variance equivalent of the yield enhancement strategy discussed in section IV. In the second part of each table we look at the lowest possible standard deviation for a given mean return. This is the mean-variance equivalent of the diversification strategy discussed in section III. The remaining columns show the required portfolio allocations as well as the skewness and kurtosis of the resulting return distributions. Starting with the case without hedge funds (table 1), we see that moving upwards over the efficient frontier results in a straightforward exchange of bonds into stocks. Since stocks have a higher mean and a higher standard deviation than bonds, if we increase the standard deviation (mean), the mean (standard deviation) also goes up. While this happens the skewness of the return distribution drops quite significantly as stock returns are more negatively skewed than bond returns. The kurtosis of the return distribution remains more or less unchanged.

Next, we added hedge funds and recalculated the efficient frontier (table 2). Moving upwards over the efficient frontier again, we observe interesting changes in the asset allocation. Starting with a mix of 50% bonds and 50% hedge funds, bonds are exchanged for stocks while the hedge fund allocation remains more or less constant. When the bond allocation nears depletion, the equity allocation continues to grow but now at the cost of the hedge fund allocation, just as bonds are exchanged for stocks in the case without hedge funds. This process is graphically depicted in figure 11. Similar to the case without hedge funds, if we increase the standard deviation (mean), the mean (standard deviation) goes up, while the skewness of the return distribution goes down.

At the same time, the degree of leptokurtosis rises. Unlike what we saw before, skewness does no longer drop in a more or less linear fashion though. This is also shown in figure 12, which for given standard deviations shows the mean return and skewness of the portfolios on the mean-variance efficient frontier. From figure 11 and 12 we see that skewness drops as long as bonds are being replaced by equity. The lowest level of skewness is reached when the bond allocation reaches 0%, i.e. with around 45% invested in stocks and 55% in hedge funds. After that, as hedge funds start to be replaced by equity, skewness rises again, reaching -0.80 when 100% is invested in equity. A similar but reverse phenomenon is observed for kurtosis. This confirms what we saw already saw before in section III and IV: in terms of skewness and kurtosis hedge funds do not combine very well with equity.

What are the most striking differences between both mean-variance efficient sets (table 3)? First, as expected, introducing hedge funds allows for a higher mean at a given standard deviations and a lower standard deviation at a given mean. The largest improvement is observed for relatively low means and standard deviations. For high means and standard deviations the effect is only small though.⁴ Second, skewness drops with the drop being most striking for those cases where the mean or standard deviation improves most. This emphasizes that the improvement in mean and/or standard deviation is not a free lunch. Third, kurtosis rises with the highest rise occurring when the hedge fund allocation is highest. Again, we also see that to actually realize the above effects investors will have to invest a high portion of their assets in hedge funds. A meaningful improvement in mean return or standard deviation requires a hedge fund allocation of at least 25-30%.

VII. MEAN-VARIANCE-SKEWNESS ANALYSIS

From the above it is painfully obvious that standard mean-variance portfolio decision making is no longer appropriate when hedge funds are involved. Given the statistical properties of portfolios of stocks, bonds and hedge funds we need a decision-making framework that not only incorporates the mean and standard deviation of the portfolio return distribution, but also (at least) its skewness. Mean-variance-skewness portfolio selection models received quite some attention in academia in the 1970s,⁵ but interest faded in later years, partly because traditional asset classes tend to exhibit relatively little skewness. To assess where the mean-variance optimal portfolios that we calculated in the previous section fit into the mean-variance-skewness opportunity set, we first plotted the mean-variance efficient portfolios for the case with (red) and without (green) hedge funds in mean-variance-skewness space. The result can be found in figure 13. From the graph we clearly see that both efficient sets are significantly different, not only in terms of mean and variance, but especially in terms of skewness. The efficient set for the case with hedge funds offers more attractive mean-variance properties, but at the cost of much lower levels of skewness.

Next, we calculated the complete mean-variance-skewness opportunity set, which is depicted in figure 14. Figure 14 shows that when combining stocks, bonds and hedge funds the nature of the opportunity set is such that the most attractive mean-variance combinations are found at the lowest skewness levels. It is exactly these portfolios that mean-variance optimisation singles out for us, i.e. mean-variance optimal portfolios are also minimum skewness portfolios. From figure 14 we also see that the skewness effect can partially be avoided by opting for a lower mean and/or higher standard deviation. Unfortunately, doing so simply takes us back to the case without hedge funds.

VIII. SOME OTHER CONSIDERATIONS

Apart from the fact that the only way to capitalize on the low volatility and low correlation properties of hedge funds seems to be to allocate quite a significant part of one's wealth to hedge funds and accept the additional negative skewness and increased kurtosis that tends to come with it, there are a number of other important points to consider before making an allocation to hedge funds. In this section we briefly discuss three of them, all relating to the validity of the inputs used in the portfolio decision nmaking process.

Biased Data

Apart from reporting and data entry errors and survivorship bias, monthly hedge fund return data exhibit another type of bias as well. As shown in Brooks and Kat (2001) and Kat and Lu (2002) for example, the available monthly returns of hedge funds involved in convertible arbitrage, risk arbitrage or distressed securities tend to exhibit a high degree of positive serial correlation. The explanation for this phenomenon lies in the difficulty for these types of hedge funds' administrators to generate up-to-date valuations of their positions. When confronted with this problem, administrators either use the last reported transaction price or an estimate of the current market price, which may easily create lags in the evolution of these funds' net asset value. As a result of the autocorrelation, estimates of the standard deviation of monthly hedge fund returns may be biased downwards by a significant amount. Brooks and Kat (2001) show that when corrected for serial correlation the standard deviation of the monthly return on the CSFB/Tremont Convertible Arbitrage index for example increases from 1.36% to 2.42%. Incorporation of this bias will make certain types of hedge funds more risky and their inclusion in the portfolio less attractive.

Illiquidity

Many hedge funds employ long lock-up and advance notice periods. Such restrictions are not only meant to reduce managing costs and cash holdings but also allow managers to aim for longer-term horizons and invest in relatively illiquid securities, including exotic OTC derivatives. As a result of the above, hedge fund investments are substantially less liquid than investments in common stocks or bonds. If this relative illiquidity is incorporated in the portfolio decision-making process, for example by lowering the expected return by an amount equal to the cost of securitization of the hedge fund portfolio, this will reduce the benefits of hedge funds.

Estimation Error

Since most data vendors only started collecting data on hedge funds around 1994 and hedge funds report into these databases only once a month, the available data set on hedge funds is very limited. Apart from spanning a very short period of time, the available data on hedge funds also span a very special period: the great bull market of the 1990s. This sharply contracts with the situation for stocks and bonds. Not only do we have return data over differencing intervals much shorter than one month, we also have those data available over a period that extends over many business cycles. This has allowed us to gain insight into the main factors behind stock and bond returns and also allows us to distinguish between normal and abnormal market behaviour. The return generating process behind hedge funds on the other hand is still very much a mystery and so far we have little idea what constitutes normal behaviour and what not. Risk arbitrage funds used to show impressive performance during the recent bull market but, with M&A volumes at their lowest level since 1996, are currently confronted by a serious lack of merger activity that can be expected to greatly impact their performance. Many investors are therefore switching to other relative value strategies like convertible arbitrage for example.

With institutional interest in hedge funds on the increase another question that arises is when the hedge fund industry will reach capacity. Schmidt (2001) notes that while the hedge fund industry has experienced strong growth over the last five years more hedge funds are showing similar and lower returns. This could be taken as a first indication there may not be enough opportunities in the global capital markets to allow hedge funds to continue to deliver the sort of returns that we have seen so far. However, it could also simply be the result of sampling error or, following the collapse of LTCM, the implementation of improved risk management procedures and a reduction in the overall degree of leverage employed by hedge funds. Although this is by no means an easy task, the above uncertainties should be properly incorporated in the portfolio decision-making process. Of course, doing so will again reduce the attractiveness of hedge funds.

IX. CONCLUSION

In this paper we have studied the diversification effects from including hedge funds into a portfolio of stocks and bonds. We saw that introducing hedge funds in a portfolio of stocks and bonds will improve that portfolio's mean-variance characteristics but at the cost of lower skewness and higher kurtosis. In addition, our results make it clear that to have at least some impact on the overall portfolio, investors will have to make an allocation to hedge funds which far exceeds the typical 1-5% that many institutions are currently considering.

Strictly speaking our conclusions are only valid for the median hedge fund portfolio, i.e. an average portfolio of 20 funds with a strategy allocation more or less in line with the composition of the industry. We chose this portfolio because it resembles the average (fund of fund) portfolio that people invest in. It would be interesting to see whether it is possible to reduce the observed skewness and kurtosis effects, while maintaining the benefits in terms of mean and standard deviation, by changing the strategy allocation and/or including only funds with certain characteristics. Research in this area is currently underway.

Hedge funds are not necessarily good or bad. They are just very different from what most investors are used to and require a more elaborate approach to investment decision-making than currently in use by most investors.⁶ When studied in the traditional mean-variance framework, the inclusion of hedge funds in a portfolio appears to pay off impressive dividends. However, when taking into account the complexity of hedge fund returns, their relationship with each other and other asset classes, the illiquidity, and the lack of (reliable) data, the matter becomes quite a lot more complicated. Clearly, it will take a substantial research effort before these issues can be dealt with in a satisfactory manner.

FOOTNOTES

1. Recent announcements by major institutions such as CalPERS and ABP that they will invest up to one billion in hedge funds are often used in the marketing of (funds of) hedge funds to smaller institutions. One should keep in mind, however, that, given the size of these institutions, these hedge fund allocations often amount to not more than 1% of total assets.

2. Although funds of hedge funds often claim to possess superior fund selection skills, it is shown in Kat and Lu (2002) that over the period 1994 -2001 the average fund of funds underperformed an equally-weighted portfolio of randomly selected hedge funds by almost 3% per annum. Likewise, Amin and Kat (2001a) found a difference in efficiency between the average fund of funds and the average hedge fund index of almost 5%.

3. The question whether hedge funds are the most efficient way to accomplish this modification is dealt with in detail in Amin and Kat (2001a).

4. It should be noted that much of this is due to the specific nature of the hedge fund portfolio used. Typically, when adding hedge funds the largest improvement takes place around the hedge funds portfolio's mean and standard deviation. For example, a portfolio of convertible arbitrage funds can be expected to improve especially the mean and standard deviation at the lower end of the efficient frontier, while a portfolio of long/short equity funds on the other hand will primarily improve the upper end.

5. See for example Jean (1971, 1973) or Simkowitz and Beedles (1978).

6. A similar point can be made for other types of alternative investments such as venture capital, non-principal protected structured notes and bonds, etc. In this context it is interesting to note that the bulk of the outstanding catastrophe-linked bonds is held by only a handful of hedge funds. As long as no major catastrophe occurs these funds can be expected to perform quite well. However, when a catastrophe does eventually occur, they may be left with a large loss.

REFERENCES

Amin, G. and H. Kat (2001a), Hedge Fund Performance 1990-2000: Do the Money Machines Really Add Value?, forthcoming Journal of Financial and Quantitative Analysis.

Amin, G. and H. Kat (2001b), Welcome to the Dark Side: Hedge Fund Attrition and Survivorship Bias 1994-2001, Working Paper ISMA Centre, University of Reading.

Amin, G. and H. Kat (2002), Portfolios of Hedge Funds: What Investors Really Invest In, Working Paper ISMA Centre, University of Reading.

Brooks, C. and H. Kat (2001), The Statistical Properties of Hedge Fund Index Returns and Their Implications for Investors, Working Paper ISMA Centre, University of Reading.

Jean, W. (1971), The Extension of Portfolio Analysis to Three and More Parameters, Journal of Financial and Quantitative Analysis, Vol. 6, pp. 505-515.

Jean, W. (1973), More on Multidimensional Portfolio Analysis, Journal of Financial and Quantitative Analysis, Vol. 8, pp. 475-490.

Kat, H. and S. Lu (2002), The Statistical Properties of Individual Hedge Fund Returns, Working Paper ISMA Centre, University of Reading.

McFall Lamm, R. (1999), Portfolios of Alternative Assets: Why Not 100% Hedge Funds?, Journal of Alternative Investments, Winter, pp. 87-97.

Schmidt, J. (2001), Performance Quartiles of Single & Multi-Manager Hedge Funds 1996-2001, Allenbridge Hedgeinfo Study 2/2001.

Simkowitz, M. and W. Beedles (1978), Diversification in a Three-Moment World, Journal of Financial and Quantitative Analysis, Vol. 13, pp. 927-941.

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RISK DISCLOSURE WHEN CONSIDERING ALTERNATIVE INVESTMENTS YOU SHOULD CONSIDER VARIOUS RISKS INCLUDING THE FACT THAT SOME PRODUCTS USE LEVERAGE AND OTHER SPECULATIVE INVESTMENT PRACTICES THAT MAY INCREASE THE RISK OF INVESTMENT LOSS, CAN BE ILLIQUID, ARE NOT REQUIRED TO PROVIDE PERIODIC PRICING OR VALUATION INFORMATION TO INVESTORS, MAY INVOLVE COMPLEX TAX STRUCTURES AND DELAYS IN DISTRIBUTING IMPORTANT TAX INFORMATION, ARE NOT SUBJECT TO THE SAME REGULATORY REQUIREMENTS AS MUTUAL FUNDS, OFTEN CHARGE HIGH FEES, AND IN MANY CASES THE UNDERLYING INVESTMENTS ARE NOT TRANSPARENT AND ARE KNOWN ONLY TO THE INVESTMENT MANAGER. WITH RESPECT TO ALTERNATIVE INVESTMENTS IN GENERAL, YOU SHOULD BE AWARE THAT: RETURNS FROM SOME ALTERNATIVE INVESTMENTS CAN BE VOLATILE. YOU MAY LOSE ALL OR PORTION OF YOUR INVESTMENT. WITH RESPECT TO SINGLE MANAGER PRODUCTS THE MANAGER HAS TOTAL TRADING AUTHORITY. THE USE OF A SINGLE MANAGER COULD MEAN A LACK OF DIVERSIFICATION AND HIGHER RISK. MANY ALTERNATIVE INVESTMENTS ARE SUBJECT TO SUBSTANTIAL EXPENSES THAT MUST BE OFFSET BY TRADING PROFITS AND OTHER INCOME. A PORTION OF THOSE FEES IS PAID TO CAPITAL MANAGEMENT PARTNERS, INC. TRADING MAY TAKE PLACE ON FOREIGN EXCHANGES THAT MAY NOT OFFER THE SAME REGULATORY PROTECTION AS US EXCHANGES. WITH RESPECT TO AN INVESTMENT IN A FUND, YOU SHOULD BE AWARE THAT: THERE IS OFTEN A LACK OF TRANSPARENCY AS TO THE FUND'S UNDERLYING INVESTMENTS. AS TO FUND OF FUNDS, THE FUND'S MANAGER HAS COMPLETE DISCRETION TO INVEST IN VARIOUS SUB-FUNDS WITHOUT DISCLOSURE THEREOF TO YOU OR TO US.  BECAUSE OF THIS LACK OF TRANSPARENCY, THERE IS NO WAY FOR YOU TO MONITOR THE SPECIFIC INVESTMENTS MADE BY THE FUND OR TO KNOW WHETHER THE SUB-FUND INVESTMENTS ARE CONSISTENT WITH THE FUND'S HISTORIC INVESTMENT PHILOSOPHY OR RISK LEVELS. A FUND OF FUNDS INVESTS IN OTHER FUNDS AND FEES ARE CHARGED AT BOTH THE FUND AND SUB-FUND LEVEL.  THUS THE OVERALL FEES YOU WILL PAY WILL BE HIGHER THAT YOU WOULD PAY BY INVESTING DIRECTLY IN THE SUB-FUNDS.  IN ADDITION, EACH SUB-FUND CHARGES AN INCENTIVE FEE ON NEW PROFITS REGARDLESS OF WHETHER THE OVERALL OPERATIONS OF THE FUND ARE PROFITABLE. THERE IS NO SECONDARY MARKET FOR FUND INTERESTS.  TRANSFERS OF INTERESTS ARE SUBJECT TO LIMITATIONS.  THE FUND'S MANAGER MAY DENY A REQUEST TO TRANSFER IF IT DETERMINES THAT THE TRANSFER MAY RESULT IN ADVERSE LEGAL OR TAX CONSEQUENCES FOR THE FUND. A FUND'S OFFERING MATERIALS OR A MANAGER'S DISCLOSURE DOCUMENT DESCRIBES THE VARIOUS RISKS AND CONFLICTS OF INTEREST RELATING TO AN INVESTMENT AND TO ITS OPERATIONS.  YOU SHOULD READ THOSE DOCUMENTS CAREFULLY TO DETERMINE WHETHER AN INVESTMENT IS SUITABLE FOR YOU IN LIGHT OF, AMONG OTHER THINGS, YOUR FINANCIAL SITUATION, NEED FOR LIQUIDITY, TAX SITUATION, AND OTHER INVESTMENTS. KEEP IN MIND THAT THE PAST PERFORMANCE OF ANY INVESTMENT IS NOT NECESSARILY INDICATIVE OF FUTURE RESULTS.  YOU SHOULD ONLY COMMIT RISK CAPITAL TO A FUND INVESTMENT.  ALTERNATIVE INVESTMENT PRODUCTS, INCLUDING HEDGE FUNDS, ARE NOT FOR EVERYONE AND ENTAIL RISKS THAT ARE DIFFERENT FROM MORE TRADITIONAL INVESTMENTS.  YOU SHOULD OBTAIN INVESTMENT AND TAX ADVICE FROM YOUR ADVISERS BEFORE DECIDING TO INVEST. CAPITAL MANAGEMENT PARTNERS, INC. (CMP) HAS ENTERED INTO SELLING AGREEMENTS WITH SOME OF THE FUNDS DESCRIBED ON THIS WEBSITE, PURSUANT TO WHICH IT IS PAID FEES BY THE FUND OR ITS MANAGER IN CONNECTION WITH FUND SALES MADE BY CMP. IN ADDITION, CMP MAY ACT AS AN INTRODUCING BROKER FOR INDIVIDUALLY MANAGED FUTURES ACCOUNTS AND TO SOME OF THE FUNDS AND AS SUCH, MAY RECEIVE A PORTION OF THE COMMODITY BROKERAGE COMMISSIONS THEY PAY IN CONNECTION WITH THEIR FUTURES TRADING OR RECEIVE A PORTION OF THE INTEREST INCOME (IF ANY) EARNED ON AN ACCOUNT'S ASSETS.  CERTAIN CTAS MAY ALSO PAY CMP A PORTION OF THE FEES THEY RECEIVE FROM ACCOUNTS INTRODUCED TO THEM BY CMP.  BEFORE SEEKING ANY ADVISOR'S SERVICES OR MAKING AN INVESTMENT IN A FUND, INVESTORS MUST READ AND EXAMINE THOROUGHLY THE RESPECTIVE DISCLOSURE DOCUMENT OR OFFERING MEMORANDUM. Information presented on this site has been obtained from sources that CMP believes to be reliable.  However, CMP has not and cannot verify the accuracy of such information, and potential investors should be aware that such information is subject to change without notice.  Not all products and services described on this website are available in all jurisdictions, and certain investments may not be suitable for all investors.  Certain investment products that are available to U.S. persons have not been registered with any federal or state regulator, and as a result are available only to certain qualified investors.  Qualifications vary from product to product. Any information on this website referring specifically to investment products offered by CMP is only available to view by qualified persons with a username and password, which can be obtained by registering and qualifying.  By registering you understand that CMP may, at its sole discretion, send you information (electronically or otherwise) on various products it offers that it believes are suitable for you and you expressly consent thereto.  You may notify CMP in writing, at any time to remove your name from its product distribution list.  The information on this website should not be construed as investment advice.  You should obtain independent investment and tax advice before deciding to invest. Past results are not indicative of future results.  There is risk of loss when investing in managed futures or funds. The information contained in this website may not be reproduced, reorganized or used to create a financial product including an index.  This information is for informational purposes only and is provided on an "as is" basis.  The user assumes the entire risk of its use.  CMP expressly disclaims all warranties of originality, merchantability, of fitness for any particular purpose.  Without limiting the foregoing, in no event will CMP or employees have any liability in connection with the use by any person of the information or data presented in this website. CMP is a broker/dealer firm registered with the Securities Exchange Commission (SEC) and is a member of the Financial Industry Regulatory Authority (FINRA). Website: http://www.finra.org CMP is also an introducing broker and a commodity trading advisor registered with the Commodity Futures Trading Commission (CFTC) and is a member of the National Futures Association and Managed Futures Association.

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