Recently, an article here on Seeking Alpha titled "The Value of Hedge Funds: 2 Differing Conclusions" presented two sides of the case about whether or not hedge funds create value, or alpha. On the pro hedge fund side was a paper, "The value of the hedge fund industry to investors, markets, and the broader economy," which was prepared by Investment Management KPMG and the Alternative Investment Management Association (AIMA) based on analysis performed by the Centre for Hedge Fund Research at London's Imperial College. The report wholeheartedly comes down in favor of hedge funds as providers of significant risk-adjusted returns, above what can be achieved in the broader markets, even with their high fees. Given the leanings of the authors (they cater to the hedge fund industry), we wondered whether there might be any bias in the report.

An issue we have with the report is that the authors do not account for the significant smoothing that appears in hedge fund returns and the impact it has on the statistics they report and conclusions they draw. In technical jargon, hedge fund returns have significant temporal correlation which is at odds with the efficient market hypothesis. In contrast, the overall stock market, represented by the S&P 500 say, has no smoothing (statistically speaking). The root cause of this smoothing in hedge fund returns is not known exactly although Andrew Lo et. al. elucidate the probable causes in his must-read book, "Hedge Funds: An Analytical Perspective." As an example, the Dow Jones/Credit Suisse Broad Hedge Fund Index had a 21% correlation between adjacent monthly returns (1994 to 2011) while the Fixed Income Arbitrage sub-strategy, which I am personally familiar with, had a 53% correlation. These are significant and they affect performance statistics in subtle ways.

Without getting into the gore of financial statistics, a simple example will illustrate the problem with the KPMG/AIMA report and smoothed returns, in general. We took the monthly returns of the S&P 500 index and created three fictitious hedge funds. The first fund, Fund 1, was created by smoothing the S&P 500 returns over three months. Specifically, Fund 1's return for any given month was 70% of this month's S&P 500 return, 20% of the prior month's, and 10% from two months before. In other words, Fund 1 did nothing more than invest in the S&P 500 and report smoothed returns. We are not suggesting that any fund is nefarious enough to do such a thing but are simply using this for illustration. The second fund, Fund 2, does the same smoothing but using 50%, 30%, and 20% over the last 3-months S&P returns (i.e., a thicker smoothie). Lastly, Fund 3 is just a 50/50 weighting of Fund 1 and 2 so it can be viewed as a simple hedge fund index.

Statistics of S&P 500 and Three "Smooth" Hedge Funds(1994-2011)

S&P500 | Fund 1 | Fund 2 | Fund 3 | |
---|---|---|---|---|

Mean | .73 | .72 | .72 | .72 |

Stdev | 4.54 | 3.42 | 2.93 | 3.14 |

SRatio | .55 | .73 | .85 | .80 |

10% VaR | -5.5 | -3.6 | -2.9 | -3.5 |

Beta | N/A | .72 | .52 | .62 |

Alpha | N/A | .20 | .34 | .27 |

% Alpha | N/A | 28% | 47% | 38% |

The results of our little experiment are shown in the table above. They are all monthly numbers except for the Sharpe Ratios (SRatio) which are annualized in accordance with industry standard. What is clear, from the second row which is the standard deviation, is that smoothing has a significant impact on apparent volatility. Fund 1, which produces correlations like the DJCS broad index, results in a 25% reduction in volatility. This produces an improvement in computed Sharpe Ratios, a widely used performance statistic, with Fund 2 appearing to have a significant risk-adjusted "edge" over the S&P 500. Clearly, smoothing returns can make a fund look better than it is. Interestingly, the Sharpe Ratio of Fund 3, the 50/50 index, is biased towards Fund 2 which implies that indices built from smoothed hedge fund returns will be biased more than their weightings suggest.

Looking at the 10% Value-at-Risk (10% VaR) in row 4, it appears that our Funds have much lower tail risk even though it is simply an artifact of the artificial smoothing that occurred. The fact that the KPMG/AIMA cite these types of statistics for their conclusions gives one pause in accepting their results. What is most interesting from the experiment is that the "Funds" have betas less than one and seem to deliver significant alpha, which presumably is what one pays those hefty fees for. In particular, Fund 2 appears to have almost half of its average return generated by alpha, divorced from the overall market. This is traditionally a sign of a hedge fund manager's prowess but, given what we know now, we need to cautiously approach any track record that has temporal smoothing.

The moral to our story is fairly straightforward: "Don't believe every statistic that you see" and "buyer beware." Looking at hedge fund returns through the myopic lens of simple statistics, which rely heavily on assumptions such as independence in time, leads one down a very slippery slope. Whether hedge funds have smooth returns due to illiquidity or mispricings is unknown. What is known, however, is that without considering these correlations, to uncover the true risk investing in any hedge fund, one will invariably find out if they are just smooth operators the hard way.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.