Alternative Investment Management Association Representing the global hedge fund industry
In today’s market there is a wide range of Fund of Funds (FoF) competing for investors’ capital. Many investors are concerned about directional exposure to underlying markets when making a FoF investment decision. To make a comprehensive investment decision, an investor should evaluate the historical performance to assess what underlying exposures the FoF has and whether it fits into the existing portfolio. Using a multi-factor model approach, can shed some light on what the main bets are, as well as the magnitude of those bets. A FoF with directional market exposure is usually less attractive to investors, as they already have that exposure in their existing portfolio or can access it cheaply. Also, directionality to underlying markets usually has an effect on the volatility and thus the risk adjusted return of the FoF. So it is also of interest for investors to assess the linkage between market exposures and the risk of a FoF.
In this brief article the objective is to answer the following questions by using relatively simple mathematical concepts: What general market exposures do FoF have? What type of exposure combination is most beneficial to investors? What is the relationship between market exposure and the risk-adjusted return?
Data, Model and Methodology
There have been numerous studies about the underlying exposures of hedge funds over the last couple of years. Most of them have focused on the difference in exposures between different hedge fund strategies, using indices. This study will only look at the exposures of different FoF using single fund performance, instead of indices. The FoF selected for the study is some of the largest (in terms of assets), most well known multi-strategy funds in existence. The funds selected have to be labelled as multi-strategy and have a track record going back to January 2000 and at least up to December 2005, so the evaluation period is six years (72 observations). The study is not meant to be exhaustive, so the number of funds included is 25.
The factors have been selected to be as broad as possible. The following factors are included with the proxy in parenthesis: equity (MSCI World), sovereign debt (Citigroup World Government Bond Index), high yield debt (Citigroup High Yield Index), commodities (Goldman Sachs Commodity Index), Volatility (VIX Index) and credit spread (Moody’s Baa index – 10-year Treasuries). The model used to evaluate the exposures is a simple multiple regression with the FoF return as the dependent variable and the different indices the independent variables. All data comes from Bloomberg.
The explanatory level of the model is fairly dispersed with R-squared from 4% to 65% with the average being 32%. The graph shows the distribution of the R-squared and most of them are centred from 10% to 40%. The results indicated that over the period in question the FoF in the study had relatively low directional exposure to the underlying markets. However, it can vary substantially depending which one you pick. In general the FoF with higher R-squared are dependent on the direction of the equity market and obviously the FoF with low R-squared have not significant exposure. In total there are seven FoF that have no significant exposures (at 95% confidence interval).
Figure 1: Distribution of R-squared
Looking at how the individual factors fared in the regressions, indicates that there is no prevalent factor that is considerably more stable and stronger than the others. Table 1 shows the ranges of the betas for the regressions and also how many times each factor is significant.
Figure 2: Range, Average and Significance of Betas
The most significant Beta is high yield debt which is significant in nine cases. The stability of it appears to be quite low and on average it does not have much effect. However, in the cases where the Betas are significant they’re around 0.1 to 0.18. So the implication is that it could have a detrimental effect in a month like March 2005 when high yield was down -3% implying a hit of between 30bps to 60bps to the FoF. The equity Beta has the same characteristics. In cases where it is significant, it is roughly 0.2 so drawdowns in equity markets tend to have a more negative affect on these funds compared to others. Most of the other factors are significant in a handful of situations and the stability quite low.
From this sample of FoF the conclusion is that both the exposures and significance can vary quite a lot. Some FoF have higher correlation to market whereas others provide returns uncorrelated to major factors. Investors on average would probably like FoF to generate returns without directionality and there are a few that manage to do that. The reason for this can have many different sources, for example, the underlying hedge funds manage their exposures actively or the FoF manager tactically selects the right strategies at the right time.
The next task is to evaluate if there is any relationship between the level of market exposures and risk-adjusted returns; in this case, Sharpe ratio. All the FoF in the sample can be viewed as successful since they have been in existence for a rather long time and also have a significant amount of assets under management. Graph 2 shows the distribution of the Sharpe ratios using a risk-free rate of 3%. The range is fairly wide with the lowest one being -0.15 and the highest 2.17 so not all of the FoF could be considered successful, at least not in terms of risk-adjusted returns. The average Sharpe ratio for the sample is 1.24 which suggests favourable risk-adjusted returns.
Figure 3: Distribution of Sharpe Ratios
The subsequent analysis would be to observe if there is any relationship between the degree of market exposures of the FoF and the Sharpe ratios. The simplest way to do this is by using the correlation coefficient. The first item is to test if there is any relationship between the R-squared of the multifactor regression and the volatility of the FoF. The answer is that the correlation is +0.5. Hence, more market directionality could increase the volatility of the FoF performance. The second thing to evaluate is if the R-squared is correlated to the Sharpe ratio. This result is more interesting as the correlation coefficient is -0.5. In other words, it appears to be a pattern where higher market exposure leads to lower risk adjusted returns.
FoF tend to differ quite substantially when it comes to exposures to underlying markets. As most investors would like to limit directionality in their FoF allocation, evaluating the magnitude of exposure produces quite useful information. Depending on whether an investor would like have a certain market exposure or try to avoid market exposures, using a multifactor regression model can help make an assessment during the initial screening process. If the investor also has a designated risk budget for the FoF allocation, it could also make sense to evaluate the peer group’s market exposures to the risk adjusted returns. The degree to which a FoF is correlated with the underlying market can have a significant effect on the risk-adjusted performance.