Investing in Hedge Funds of Funds

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Funds of hedge funds (FOFs) have become popular investment vehicles for institutional investors and wealthy individuals alike who want exposure to hedge funds but lack the necessary platforms or resources to understand complicated hedge fund strategies, conduct thorough due diligence, perform meaningful risk management, and other operational and administrative activities.

These additional skills provided by FOFs seemingly justify an additional layer of fees on top of the fees already charged by underlying hedge fund managers that includes management fees ranging from 0.5% to 2% plus incentive fees for most FOFs, ranging from 5% to 20%. While past research focus has been on the manger skill of hedge funds, 1 little research has been done on the skills of FOFs managers.

In this chapter, we address whether FOFs truly add value.

FOFs are generally perceived to have lower risk than individual hedge funds because of diversification. Many FOF managers also have extensive investment backgrounds and are believed to have a better understanding of different hedge fund strategies.

Moreover, FOFs typically are well connected with many hedge fund managers, and are often the only way to get access to good hedge funds that are already closed to new money.

Given these competitive advantages, one might expect FOFs to out-perform average hedge funds. However, as shown in Figure 1 (on the next page), on average, FOFs actually under-perform the hedge fund universe as measured by two industry-standard hedge fund benchmarks — HFR’s Composite Hedge Fund Index and the Van Global Hedge Fund Index — by an annual return difference of about 3% and 5% respectively, with slightly
lower risk (represented by standard deviation) from January 1998 to July 2005.

Hedge funds have earned an average of 9.72% annually from January 1998 to July 2005, as measured by the HFR Composite Hedge Fund Index (and an even higher 11.58% as measured by the Van Global Hedge Fund Index). If we assume the fee structure of a typical FOF includes a 1% management fee and a 10% performance fee, FOFs would have earned about 7.85% if these FOFs had invested in average hedge funds. However, the average return of FOFs was actually 6.54% annually during this period.

One could argue that the FOFs index cannot directly be compared to the HFR Hedge Fund Composite Index, since some FOFs may intentionally have lower target return because of risk constraints.

In this chapter, we apply a methodology developed by Sharpe (1992) to decompose FOFs return into two components: returns attributed to strategy allocation and returns attributed to hedge fund selection.

By separating these, we can evaluate both asset allocation ability and manager selection ability of average FOFs.

Data and methodology of Investing in Funds of Funds
This study uses the HFR FOFs Composite Index and the four sub-FOF indices based on broad strategies which FOFs employ. Although the Van Companies have their own proprietary database, we choose to use HFR data instead of our own data, so other researchers can replicate our study.

While analyses at the individual FOF level would be more useful, the backfilling bias in the HFR database will make the fund level analyses unreliable. HFR groups FOFs into four categories and provides sub-indices for each group. The brief definitions of these four groups are as follows:

Conservative: invests in ‘conservative’ strategies, such as market neutral or convertible arbitrage, to achieve lower return volatilities.

Diversified: invests in a variety of strategies among multiple managers; usually have similar risk/return profile as FOF Composite Index.

Defensive: invests in funds that generally engage in short-biased strategies such as short selling and managed futures; usually have negative correlation with general market benchmarks.

Strategic: primarily invests in funds that generally engage in more opportunistic strategies; usually have higher return and higher risk.

Following the style analysis methodology developed by Sharpe (see Sharpe [1988] and Sharpe [1992]), the exposure of FOF indices to each hedge fund strategy is determined by the following quadratic programming:

Here, the 15 HFR hedge fund indices for each strategy serve as factor Fs, similar to the traditional asset classes  in the mutual fund style analysis. As Sharpe points out, the style analysis method is not designed to find a style that makes the FOFs look good or bad. Rather, the goal is to infer as much as possible about the fund’s exposure to variations in the returns of the asset class, in this case, different hedge fund strategies during the period studied.

Following Sharpe (1992), starting from January 1998, for each month ‘t’, we conduct the analysis as follows:

• The strategy exposure of each sub-FOF index is estimated using returns from month t-12 through t-1.

• The return on the resultant style is calculated from month t. This is the return FOFs should earn if average hedge fund mangers are selected in the strategies they expose.

• The difference between the sub-FOF index in month t and that of the style benchmark determined in step 1 and 2 is computed. This difference is defined as the FOF’s manager selection return for month t.

The above analysis was conducted with the HFR FOF Composite Index as well as the four sub-FOF indices.

Since all indices are calculated based on returns net of fees charged by FOFs, some adjustment is needed to reflect the raw return earned by FOFs. Figure 2 illustrates the fee structure of FOFs using data from the Van Hedge Fund Database. The majority of FOFs charge a 1% management fee and a 10% performance fee, or 1% to 2% management fee without an incentive fee. The return before fees for all FOF indices was calculated by assuming the underlying FOF managers charge a 1% management fee and a 10% performance fee.

In the end, each FOF index return is separated into three parts: return attributed to strategy allocation; return attributed to hedge fund manager selection; and fees.

Empirical results
Table 1 reports yearly returns of both the Van Global Hedge Fund Index and the HFR Hedge Fund Composite Index, as well as the HFR FOF Composite Index and four sub-FOF indices. On average, all four sub-FOF indices under-perform the HFR Hedge Fund Composite Index during the 1998 to 2005 period.

The Conservative Index and Defensive Index have significantly lower volatility, albeit with lower returns relative to the HFR Hedge Fund Composite Index, while the Diversified Index shows similar volatility with lower returns than both the HFR Hedge Fund Composite Index and the FOF Composite Index.

The Strategic Index has the highest return among all indices, with much higher volatility than both the HFR Hedge Fund Composite Index and other FOFs indices.

The underperformance of FOFs, especially diversified FOFs and strategic FOFs, could be a result of either deficient asset allocation, poor manager selection or both. Thus, asset allocation and manager selection were examined separately to identify the underlying reasons of this underperformance.

Table 2 reports the asset allocation efficiency of FOFs relative to the HFR Hedge Fund Composite Index, which can be treated as a special FOF with passive strategy allocation. Every month we first estimate the style return for each FOFs’ index as described in the previous section, and then calculate the difference between style returns and HFR Hedge Fund Composite Index return. A zero difference means no attribution from asset allocation, while a positive (negative) difference implies positive (negative) attribution from asset allocation. The statistics in Table 2 are calculated using monthly return data from January 1998 to July 2005. The mean monthly style return difference for the HFR FOF Composite Index is -0.21% with standard deviation of 0.71%, and the ‘t’ statistic is significant at the 1% level. This suggests that asset allocation of FOFs as a whole is not as efficient as the passive composite index.

Not surprisingly, both the Conservative Index and the Market Defensive Index show negative asset allocation biases due to their risk-averse nature. However, there is evidence that FOFs in the diversified group have done a sub-optimal job in strategy allocation relative to the passive hedge fund index. On the other hand, the Strategic Index shows no sign of a positive asset allocation edge during this period. We will discuss the asset allocation for each sub-group in detail later.

Table 3 provides statistics that reflect manager selection ability of FOFs during the 1998 to 2005 period. All statistics are calculated based on the monthly manger selection return described in the methodology section. It should be noted that the manger selection return, ie, the month-to-month deviations of the fund return from that of the estimated style, could be partially caused by style changes (See Sharpe [1992]). However, it is reasonable to assume that these return deviations are mostly attributed to manager selection because of the relative illiquid nature of hedge funds.

Results in Table 3 suggest FOFs overall have some competitive edge in manager selection. The average monthly manager selection return, though not statistically significant, is 0.10%. Moreover, all of the four sub-FOF indices exhibit positive biases in manger selection. Since managers with better tracking records are more likely to be selected by FOFs, this positive bias suggests that returns of selected managers are persistent. This seems to contradict the well-documented, non-persistence or short-term persistence in hedge fund returns reported in numerous academic studies (See Agarwal and Naik 2000, Brown et al 1999 among many others). In our opinion, this discrepancy could be a result of methodologies used in most studies.

Typically, hedge funds are first ranked based on certain criteria, which could be just returns or certain risk-adjusted returns.

Then the next period returns or risk-adjusted returns are calculated, and the new ranks are compared with ranks in previous period to test the persistency. A major drawback of these methodologies is that hedge funds are always ranked based on characteristics that can be quantified, but typically with no qualitative control involved. In practice, the quantitative rank only serves to screen funds, and is just the starting point of the whole complicated due diligence process.

Higher ranked funds could be knocked out during the due diligence process because of qualitative reasons, such a poor risk management, high operational risk, or other qualitative factors. In fact, it is exactly these types of funds that tend to experience a reverse in return during the next period. As a result, hedge funds selected through both quantitative and qualitative standards are more likely to exhibit return persistency than funds selected only based on quantitative standards.

Another possible explanation of this persistency is that FOFs typically pick the top managers in their strategy, not only the winners defined as the top 50% in most academic studies. The details of VAN’s hedge fund persistence study (which were conducted to test the viability of constructing an investable index fund to track the 16-year plus track record of the VAN Global Hedge Fund Indices) are beyond the scope of this chapter. However, using a scoring system based on several quantitative factors, VAN found statistically significant persistence. Top-quartile funds, chosen with VAN’s proprietary scoring system, in a given year generate performance in the top quartile for the subsequent year approximately 40% of the time. Furthermore, these top-quartile funds end up in the bottom 50% of funds the following year only 30% (rather than 50% of the time, as one would expect if performance were random). Finally, VAN finds that negative performance persists as well.

Next, each of the four sub-FOF indices was examined in detail to identify the drivers behind their performance. Figure 3 shows the yearly style return for the Conservative Index versus the HFR Hedge Fund Composite Index from 1998 to 2005.

The return of the Conservative Index has been relatively stable during this period, outperforming the Composite Index in down/mediocre markets (2000–2002) and underperforming the Composite Index in bull markets. As reported in Table 2, the underperformance of the Conservative Index between 1998 and 2005 is largely due to strategy allocation, which reduced the index return by 0.16% per month. Interestingly, the Conservative Index has the smallest manager selection bias, which is about 1 base point per month. The result suggests that conservative FOF managers may not only choose conservative strategies but also select ‘conservative’ hedge funds within strategies. Clearly, the Conservative Index has its own unique risk/return characteristics that cannot be achieved by simply investing in average hedge funds or the HFR Hedge Fund Composite Index.

Figure 5 illustrates the yearly style return for the Market Defensive Index relative to the HFR Hedge Fund Composite Index since year 1998, and Figure 6 compares the strategy returns with index returns before fees during the same periods. Similar to the Conservative Index, the Market Defensive Index exhibits lower volatility than the Composite Index. More importantly, the strategy return outperformed the Composite Index handily in 1998 and 2002, and this is precisely what investors would have expected from this type of FOFs. Table 2 and Table 3 show an 18 pbs reduction in index return per month due to style selection, but with an increase of about 11 bps per month because of positive manager selection returns.

The positive strategy return was more than offset by the negative hedge fund manager selection returns in 1998, and the Market Defensive Index earned an impressive 8.2% return in 2002. The negative correlation with broad market benchmarks combined with its low risk profile would make this type of FOF a valuable component in institutional investors’ portfolios.

Figure 7 and Figure 8 depict the style return and index return before fees for the Diversified Index. While the Diversified Index has been closely tracking the performance of the Composite Index as shown in Figure 7, the strategy return underperformed the Composite Index in six out of eight years since 1998. In 1998, the strategy allocation contributed to a return of -4.6% when the Composite Index increased by 2.6%. The average monthly return deduction due to deficient asset allocation in the Diversified Index is 0.23% per month, and this is statistically significant at a 1% level. In fact, this is the only sub-FOF index that exhibits a statistically significant negative asset allocation bias. The diversified FOFs may be diversified, but evidently their strategy allocations are sub-optimal even compared with the passive Composite Index. Though the diversified FOFs show the largest manager selection premium, which is roughly 12 bps per month, it is still not enough to offset the negative effects due to poor strategy allocation.

As a result, the Diversified Index has much lower return than both VAN Global Hedge Fund Index and HFR Hedge Fund Composite Index historically, with roughly the same volatility. The results suggest that these FOFs would perform better had they just followed the passive strategy allocation and spent their time choosing good managers. Given the rapid growth since 2003 of the so-called Investable Hedge Fund Index that follows passive strategy allocation, we believe the growth of FOFs in this category will be limited.

Figure 9 illustrates the yearly style return for the Strategic Index relative to the composite index since 1998, and Figure 10 compares the strategy returns with index returns before fees during the same periods. The Strategic Index does have much higher volatility as shown in Table 1, with annual standard deviation of 14.97% compared to 10.64% of the HFR Composite Index and 11.87% of VAN Global Hedge Fund Index. However, as shown in Table 2 and Figure 9, there is little evidence that hedge funds engaged in opportunistic strategies out-performed other strategies during the 1998 to 2005 period. According to the results in Table 3 and Figure 10, strategic FOFs seem to have the ability to pick above-average managers, with monthly premium of 4 bps per month, but this premium fluctuated significantly year-by-year.

Conclusion
This study examines an average FOFs manager’s skill using the monthly HFR Fund of Hedge Fund Indices. Using the methodology developed by Sharpe (1992) to decompose FOFs return into returns attributed to strategy allocation and returns attributed to hedge fund selection, we are able to analyse both the strategy allocation efficiency and manager selection ability of FOFs mangers during the January 1998 to July 2005 period.

Our main findings are as follows:

1. Overall, FOFs have inefficient strategy allocation relative to the passive strategy allocation of the Van Global Hedge Fund Index and the HFR Composite Hedge Fund Index. On the other hand, contrary to many previous studies, we find FOFs, on average, have shown ability in selecting good hedge fund managers.

2. The conservative FOFs and market defensive FOFs have their unique risk/return characteristics that cannot be achieved by a passive hedge fund index, and are valuable components in investors’ portfolios.

3. There is statistically and economically significant inefficiency in strategy allocation in diversified FOFs. Investors will be better off by simply investing in an Investable Hedge Fund Index designed to track the whole hedge fund universe if they just want to get diversification effects.

4. Strategic FOFs have much higher volatilities, but yield little reward in returns relative to the HFR Hedge
Fund Composite Index.

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