Because replication funds can capture only the "beta" of hedge fund indexes, we believe their returns generally should differ from those of the indexes by the amount of alpha embedded in them. A replica of an index with positive alpha should return less than the index itself, and vice versa. In all circumstances, however, we believe replication funds should generally have lower volatility than the indexes because alpha is more volatile than beta. This combination of medianlike returns and lower-than-average volatility suggests that successful replication products should have higher Sharpe ratios12 than a majority of the funds in the indexes on which they are based.
As described above, the value of the transactional differences between replication products and their underlying funds requires hedge funds and their indexes to produce higher returns than their replicas. Indeed, one might reasonably attribute a portion of any observed positive alpha as compensation for the transactional disadvantages of individual hedge funds. While alpha oscillates between positive and negative values, however, the transactional advantages of replication funds generally have positive value for investors. This suggests that individual hedge fund returns must exceed the sum of the return of a hedge fund index replication fund and a transactional premium before they deliver any alpha.
Finally, funds of hedge funds offer a third way to assess the potential value of replication funds. These funds market themselves as gatekeepers that select and monitor hedge fund investments for investors who cannot or choose not to do so themselves. Since these services have value, funds of hedge funds should generally return less than hedge funds. Additionally, because their manager selection services ought to outperform the naive selection process inherent in most replication strategies while providing an alternative to their transactional benefits,13 in our view, they ought to perform at least as well as replication funds net of any differences in fees between them. Formal tests of these three hypotheses lie outside the scope of this paper, but Figure 4 provides some visual evidence indicating the results one might obtain from such tests.
Figure 4 shows three data sets14: indexes of hedge fund returns;15 returns from a collection of replication indexes and products;16 and indexes of funds of hedge funds.17 We may interpret trend lines plotted through an estimate of the risk-free rate since 2009 (0.25 percent) for the hedge fund indexes and the replication funds as implied market lines. The location of most of the replication indexes closer to the market line than most of the hedge fund indexes supports the first hypothesis that replication funds deliver only beta while the indexes capture alpha and beta. The broader distribution of the hedge fund indexes lends credence to our assertion that hedge funds have higher volatility than replication strategies because they deliver alpha that may be positive or negative. The almost identical slopes of the trend lines that we may view as estimates of Sharpe ratios for each group (0.83 for the replication indexes versus 0.82 for the hedge fund indexes) do not, in our opinion, refute the second hypothesis, that replication strategies may have higher Sharpe ratios than hedge funds. The data shown does not support, however, the third hypothesis, that funds of hedge funds should outperform replication funds. All five indexes of funds of hedge funds have underperformed the mass of replication indexes over the past four years.