Abstract: Hedge fund strategies are not as unique as investors believe. We examine 18 strategy indexes and find that three factors capture more than 87% of the variation in returns. Most strategies are redundant, which has several implications for portfolio construction. Investors should focus on finding quality funds independent of strategy.
Diversification is powerful. Most investors understand that it can substantially improve portfolio performance. Too much diversification can be just as detrimental as too little, however, if it causes investors to diversify into less attractive investments.
Benartzi and Thaler (2001)1 found that investors in defined contribution plans tend to divide their assets equally among available options, even when doing so results in poor asset allocations. Institutional investors, although usually much more sophisticated than retail investors, often make a similar mistake by over-diversifying into a wide array of asset classes and investment strategies.
It makes sense for institutional portfolios to include each of the most common hedge fund strategies if each contributes something unique, but is this really the case? In this report, we analyze hedge fund indexes using four different tools—correlation, clustering, principal components, and optimization—to determine which strategies are, in fact, distinct.
Eqira produces 30 hedge fund indexes. When we restrict our universe to top-level strategies with at least 15 years of history through December 2016, we are left with 18. We can assess the uniqueness of each strategy by calculating its mean correlation against each of the other 17 indexes in the sample.
Figure 1 provides the mean correlation and highest single correlation for each of the 18 strategies. Three strategies—commodities, managed futures, and equity short-bias—appear significantly less correlated than the others. Commodities and managed futures are highly correlated with each other, but relatively uncorrelated with most other strategies. Equity short-bias is either negatively correlated or uncorrelated with the rest of the sample.
The remaining 15 strategies appear to overlap. Each bears a mean correlation between 0.48 and 0.69. Many have maximum correlations above 0.90. Each appears closely related to at least one other strategy. There is little to distinguish these strategies from one another, which suggests that it might be appropriate to classify our indexes into three groups: equity short-bias, trend following strategies, and everything else.
We can confirm the suitability of this grouping by conducting a cluster analysis, a common technique in statistical data analysis that is particularly popular in the machine learning community. A cluster analysis systematically identifies and groups related elements within a data set.
There are many different clustering algorithms. We use one of the most common, k-means. It partitions data into clusters such that each data point belongs to the cluster with the nearest mean. The algorithm requires us to specify the number of clusters, k. We would ideally choose k such that elements within a cluster are as similar as possible and elements in different clusters are as dissimilar as possible.
The algorithm requires us to define a distance between each pair of elements. Correlation works well for this purpose. We could also use covariance, but doing so would likely cause the algorithm to partition data by volatility rather than by shared risk, grouping the most volatile strategies separately from the least volatile.
To identify an appropriate value for k, we perform the analysis multiple times using different values. In each case, we measure the fit by summing the distance between each element and its cluster mean. Since we can always reduce this sum by increasing k, the goal is to select the smallest k that provides suitable segmentation.
Figure 2 charts the total distance for several values of k. Increasing k from one to two and then from two to three substantially improves performance. These gains decelerate rapidly with values larger than three. Three is most likely the appropriate value for k, but we can confirm this by choosing a higher value of five.
Our goal is to maximize the correlation within each cluster while minimizing the correlation between each cluster. We calculate cluster returns by creating equally-weighted portfolios of strategies within each cluster. We then use the correlations between these portfolios to represent the correlations between clusters. Figure 3 provides these correlations.
Clusters one and four are very highly (0.85) correlated with each other. Clusters one and five (0.69), two and five (0.67), and four and five (0.57) are also highly correlated. This suggests that we have too many clusters and should therefore reduce our value of k.
We repeat this exercise with k set to three and show the results in Figure 4. Here we see that cluster three is only moderately correlated with the others and clusters one and two are negatively correlated with each other. The intra-cluster correlations are also sufficiently high. Setting k to three segments the data much more effectively.
The cluster analysis substantiates the findings of our correlation analysis. We again find three unique groups and once again most strategies wind up in the same partition. As with our correlation study, equity short-bias exists on its own while commodities and managed futures are paired once again, this time joined by global macro.
Principal Component Analysis
Correlation is a useful measure for evaluating the relationship between elements, but it is not necessarily the best measure. Consider, for example, our findings for equity short-bias. Both of our methods have determined that the strategy belongs in a group by itself, but does this make sense? Although short-bias is negatively correlated with most strategies, it involves shorting equity risk, a risk most other strategies go long. If short-bias achieves its negative correlation by taking the opposite side of a common risk factor, it is not really that different after all.
We can investigate shared strategy risk by performing a principal component analysis (PCA). PCA is another popular statistical technique often used for dimension reduction and data compression. It works by transforming a set of possibly correlated variables into a set of linearly uncorrelated variables called principal components. The algorithm chooses these components such that each successive component explains as much of the variation in the data as possible while remaining uncorrelated with all preceding components.
If a limited number of components describe most of the risk in the system, we can reduce the complexity of the data set by ignoring the less significant components. The components we choose to include behave like factors in a factor model: they allow us to approximate behavior using a smaller number of variables.
This is not unlike more commonly known factor models such as the Capital Asset Pricing Model (CAPM). Unlike such models, however, PCA does not require us to specify the factors to include. Instead, the algorithm identifies statistical factors that optimally represent the data.
These statistical factors often lack economic meaning, making them difficult to interpret. Sometimes, however, this is not the case. If fact, if you were to perform a PCA on a large group of equities, the first principal component should behave similarly to the market return and each stock’s loading on the component should resemble its CAPM beta.
Principal components are useful for illustrating the structure of a data set and the amount of unique risk it contains. We can measure a component’s significance by its relative variance. If a handful of components capture most of the variance in a data set, then we can conclude that the variables they describe have much in common. If each component captures an identical amount of risk, then we can infer that each variable is independent.
Related financial securities usually derive the bulk of their risk from a small number of components. Hedge fund indexes are no different. Figure 5 illustrates the proportion of variance explained by each component in a PCA conducted on our strategy correlation matrix. The first component alone explains nearly 69% of the total variation in the system. The first two together capture more than 81% and the first four explain more than 90%.
These indexes clearly contain a high degree of shared risk. Rudin and Morgan (2006)2 proposed a method for measuring the diversification potential provided by a set of assets. It relies upon the proportion of risk captured by the asset’s principal components. The method produces a number between one and n, where n is the number of assets. We can interpret this value as the number of uncorrelated factors needed to capture the variation in the assets. A value of one means that the assets are not at all diversified, and that we can represent them all using a single factor. A value of n means that the assets are independent.
When we apply the Rudin and Morgan method to our hedge fund PCA, we obtain a value of 2.99, meaning that our 18 hedge fund indexes are equivalent to about three unique risks. This is suboptimal. When we perform the same task on a universe of 16 liquid asset classes (see the Appendix) we get a value of 4.8. If we use 25 traditional and alternative risk premiums we get 10.2. In terms of diversification, hedge fund indexes fall far short of other investment options. As with our correlation and cluster analyses, we once again find that most hedge fund strategies are not unique.
Each principal component is actually a portfolio of hedge fund indexes. We can try to determine the risk a component represents by inspecting the weights it assigns to each index. As we’ve mentioned, this usually isn’t that helpful because components often don’t have simple economic interpretations. In our case, however, we are fortunate because the first three components do appear to convey meaning. Figure 6 provides weights for the first three principal components. The first component draws substantial risk from every strategy except managed futures and commodities. It takes roughly equivalent exposure to each included strategy and loads in the same direction on all but one. We can therefore think of the first principal component as representing hedge fund beta, the common risk shared between all strategies.
The second principal component loads primarily on managed futures, commodities, and global macro, three strategies that depend to varying degrees on trend following and momentum. The third principal component loads in one direction on arbitrage strategies and in the opposite direction on long equity strategies. This is a bit like being long tail risk and short equities. So, hedge fund beta, trend following, and tail risk appear to be the dominant risks within hedge fund indexes.
Hedge fund beta can consist of many different risks. It can include traditional betas such as long equity and fixed income exposures, but it can also include alternative betas like currency carry, as well as risk unique to hedge funds. Given that hedge fund beta represents such a large portion of overall hedge fund risk, we would hope that this “beta” is mostly unique risk that investors cannot capture elsewhere.
We can identify the risks underlying this beta if we regress the returns to the first principal component on a set of explanatory variables. We use our Market Factors—a set of financial time series we’ve developed to capture most of the systematic risks taken by investors—as our explanatory variables. These factors span a universe of traditional and alternative betas.
Our regression model, fit via a well-known machine learning algorithm known as elastic net, yields an in-sample R2 of 0.97, even after performing cross-validation to reduce overfitting. This means that systematic risk factors capture 97% of the component’s variation, leaving only a scant 3% for residual idiosyncratic risk. Equity beta alone represents 46% of this risk. Traditional risk factors across all asset classes capture 91%. This implies that the dominant risk across hedge fund strategies is not alpha-driven. Investors could source the majority of this risk from passive, low-cost index products.
When we repeat this exercise on the second and third principal components we find that systematic factors explain 74% and 88% of the variance, respectively. Again, most of the risk is systematic, not idiosyncratic.
This shouldn’t come as a surprise. When we model each of our hedge fund indexes using our Market Factors we are able to produce an R2 of a least 0.67 for each strategy and an R2 above 0.90 for most strategies. This suggests that hedge fund indexes are not taking on new risks, but rather repackaging common risks to which investors are already exposed.
We can evaluate the uniqueness of individual hedge fund strategies by decomposing their risks by principal component. Figure 7 provides the cumulative percentage of variance each strategy draws from the first three principal components. We can see that most strategies lean heavily on the first component. Event driven, for example, derives 94.5% of its risk from this single factor, providing nearly undiluted exposure. Multi-strategy (93.4%), equity long/short (92.2%), and relative value (89.9%) also depend almost exclusively upon the first principal component.
Managed futures sources the bulk of its risk (85.9%) from the second principal component. Commodities (66.7%) and global macro (49.4%) do as well. Equity short-bias (21.9%), fixed income arbitrage (21.4%), and convertible arbitrage (19.4%) draw substantial risk from the third.
Equity short-bias derives more than 61% of its risk from the first principal component. Even though the strategy is negatively correlated with most other strategies, it obtains most of its risk from the same source. The only difference is that it is short this exposure, rather than long. This confirms our earlier suspicion that the strategy may not be unique. Equity short-bias doesn’t diversify by adding large amounts of unique risk. It instead offsets risk found in other strategies. This is wasteful for investors, who wind up paying fees on net zero exposure when they combine equity short-bias with these strategies. Since investors will always pay performance fees on one side of this offsetting exposure, the larger the return to any one side, the larger the loss.
It goes without saying that investors should rarely, if ever, allocate to equity short-bias. If we eliminate the strategy from our investable universe, we remove one of our three strategy clusters, thereby leaving only two types of hedge fund indexes: trend following/macro and everything else.
Suppose that we would like to produce a portfolio of hedge fund strategies that maximizes diversification. We can do this by constructing a minimum variance portfolio using strategies that have each been scaled to the same level of expected volatility. Doing so provides two pieces of interesting information. Firstly, we can analyze the portfolio weights to determine which strategies provide the most diversification. Secondly, we can observe the total risk reduction achieved via optimization. The better the diversification, the greater this risk reduction.
Figure 8 contains the weights to this maximum diversification portfolio. We exclude equity short-bias given its inefficiency, and we restrict weights to non-negative values. Managed futures receives the largest allocation, which is not surprising since it provides the purest exposure to the second principal component. Fixed income arbitrage and convertible arbitrage, two strategies well-represented in the third principal component, receive healthy weights as well. Other notable strategies include equity value, merger arbitrage, commodities, and equity market neutral. The optimization almost universally ignores strategies that load heavily on the first principal component.
Maximum diversification reduces portfolio standard deviation by 34%. This is approximately the same amount of diversification that a portfolio of 2.3 uncorrelated assets would provide, which is not very much considering the freedom hedge funds have to pursue alternative strategies. Consider that a simple portfolio of equities and government bonds alone would provide two uncorrelated return streams. As a comparison, the 16 liquid asset classes used in our earlier PCA study could reduce risk by more than 50%. The 25 risk premiums could reduce risk by nearly 80%.
Hedge funds could be doing a much better job of sourcing risk. By merely harvesting these risk premiums they could substantially increase their diversification potential, even without generating any idiosyncratic risk or alpha.
What About Idiosyncratic Risk?
Thus far we’ve largely ignored idiosyncratic risk. We can, however, conduct these same analyses, substituting idiosyncratic strategy returns for total returns. To do so, we first estimate idiosyncratic returns by fitting a factor model to each strategy index. We then perform a PCA upon these unique returns.
The results are similar to our initial analysis. Although we require more principal components to explain the variation in the data, we find many of the same relationships between strategies. Those that loaded heavily on the first component in our original PCA tend to load heavily on the first component in our new PCA. Those that loaded on the second follow suit. This means that alphas, too, are shared across strategies.
Idiosyncratic returns provide more diversification than total returns. A maximum diversification portfolio constructed from these unique risks reduces total risk by 54%. If we could somehow invest directly in these unique risks, we could produce a much more efficient portfolio. Unfortunately this is not possible, as most strategies produce only a limited amount of idiosyncratic risk. Figure 9 provides the R2 for each of our strategy index factor models. It also provides the percentage of risk each strategy obtains from traditional betas like long equity and fixed income exposures. 14 of our 18 models have produced an R2 above 0.86. 13 strategies have sourced at least 70% of their risk from traditional risk factors.
What does this mean for hedge fund investors? The primary takeaway is that most strategies are redundant. One can create a portfolio using just two or three strategies that is almost as well-diversified as a portfolio containing all strategies. Although any strategy may offer opportunistic advantages, there appears to be little need for investors to maintain static allocations to the full spectrum. Investors should instead focus on finding quality funds independent of strategy.
1. Benartzi, Shlomo and Richard H. Thaler, 2001, “Naive Diversification Strategies in Defined Contribution Saving Plans”, American Economic Review, 91:1, 79-98.
2. Rudin, Alexander M. and Jonathan S. Morgan, 2006, “A Portfolio Diversification Index”, The Journal of Portfolio Management 32:2, 81-89.
Asset Class Universe
- US equities
- Developed market equities
- Emerging market equities
- US Treasuries
- US inflation-linked bonds
- US investment grade bonds
- US high yield bonds
- Developed market government bonds
- Developed market investment grade bonds
- Developed market high yield bonds
- US REITs
- Foreign real estate
- Agricultural commodities
- Base metals
- Energy commodities
- Precious metals
Risk Premium Universe
- Equity: US
- Equity: US 1-year momentum
- Equity: US size
- Equity: US value
- Equity: developed market size
- Equity: developed market value
- Equity: global 1-year country momentum
- Equity: global country trend following
- Fixed Income: US Treasury term structure
- Fixed Income: developed market term structure
- Credit: US investment grade spread
- Credit: US high yield spread
- Credit: developed market high yield spread
- Commodity: gold futures
- Commodity: 1-year momentum
- Commodity: trend following
- Commodity: term structure
- Currency: carry
- Currency: momentum
- Currency: value
- Multi-asset class: 1-month momentum
- Multi-asset class: 1-year momentum
- Multi-asset class: trend following
- Volatility: put writing
- Volatility: short equity variance