**Sharpe ratio measures risk adjusted returns**

Despite its well-documented weak points, the Sharpe ratio is still one of the most commonly used measures by investors to gauge the quality of funds of hedge funds from a risk-adjusted point of view. In essence the Sharpe ratio measures the return achieved per unit of risk. Ratio is calculated by dividing the excess return of the analysed fund – over a predefined hurdle-rate – by the volatility of the funds return. The discussion whether the Sharpe ratio is a suitable measure for evaluating the risk-adjusted performance of hedge funds is still ongoing, both in academia and in practice. The most common objection against the usage in the case of hedge funds is their underlying asymmetric risk-return profile. Due to the fact that volatility is a symmetric risk measure, it’s widely accepted that the Sharpe ratio is not able to incorporate the non-normality of the return distributions caused by the asymmetric risk-return profiles of hedge funds. However, given the inherent diversification of funds of hedge funds their return distributions are not so extremely away from the normal distribution as single hedge funds. Nevertheless, they still do exhibit high autocorrelations, which cause the classical Sharpe ratio to be biased. That finding is documented by Lo (The Statistics of Sharpe Ratios in Financial Analysts Journal, Vol. 58 No. 4, pp. 36-52.), which provides a robust calculation of the Sharpe ratio, which takes into account serial correlation in monthly returns. Notwithstanding the mentioned shortcomings, many investors still use the Sharpe ratio as a core input into their decision-making process, mainly due to its easy calculation and being readily availability. Some fund managers even promote their funds based on an exceptional Sharpe ratio. If we accept the shortcomings and to base your decision on it, as many investors do, the important question then becomes: how reliable are Sharpe ratios, especially, how persistent is the performance of funds of hedge funds with a historical high Sharpe ratio? We tested whether in fact Sharpe ratios persisted on a multi-year time frame, especially in relation to multi-strategy fund of hedge funds. In order to ensure that the Sharpe ratio of a fund is not a function of the environment during specific period of evaluation, or of the number of months the fund has been running, we used a rolling time period window to evaluate the Sharpe ratio for all funds. The rolling approach also enables us to incorporate funds that stop reporting during the sample period. These funds are normally classified as dead funds. Due to the fact that the study also considers dying funds, our results should not be heavily exposed to the classical survivorship bias. Furthermore, we are not limited to funds, which reportthroughout the whole period. Therefore, the number of analysed funds can increase or decrease whether more funds begin reporting to Eurekahedge or stop reporting and vice versa. The analysed universe starts with 71 funds in January 1995 while that number increases to 584 in August 2008 before dropping down to 455 in December 2009 (see Fig.1). For the sake of the analyses we focus on US-Dollar denominated multi-strategy funds of hedge funds.

**Are Sharpe ratios stable over time?
**

We calculated the Sharpe ratio of each fund on a rolling basis over a time window of 36 months. We assumed a risk free rate of 3% for its calculation and adjust it for the bias of serial correlation by using the methodology provided by Lo. After ranking them in ascending order, these funds were then grouped into four categories based on their ranking.

• < 25th percentile

• 25th to <50th percentile

• 50th to < 75th percentile

• ≥75th percentile

Figure 2 displays the evolution of the dispersion of Sharpe ratios across the sample throughout time. One can clearly see that both the range between the maximum and minimum Sharpe ratio as well as the cross sectional distribution of Sharpe ratios varies considerably throughout the months. An investor faces the question: what are my odds of ending up again in the first quartile in the following investing period, when the investor decides to invest in a fund of hedge fund that was classified as a first quartile fund during the observation period. Finally we determine what percentage of funds in the first quartile in the formation period are again in the first quartile during the investing period or have transitioned to the second, third or even fourth quartile. This procedure yields the first row in our Markov transition matrix. To obtain a complete Markov transition matrix, the previous step also has to be constructed for the funds in the second, third and fourth quartiles during the formation period.

Figure 3 shows the graphical visualisation of the four Markov transition matrices. The individual graph reads the following way: each bar represents a quartile of the formation period, e.g. the left bar of the upper left graph displays the 1st quartile of funds in the formation period from January 1995 until December 1997 ranked on December 1997 based on their serial correlation adjusted Sharpe ratios. The lower dark part of that bar represents the percentage of funds, which were again in the first quartile after the investing period from January 1998 until December 2000. That percentage was almost 30% and one can easily see that roughly 80% of the 1st quartile funds were at least in the 2nd quartile if not in the 1st quartile during the investing period. Looking at Figure 3 one can see that until December 2006 there was a relatively high persistence of 1st quartile funds ending up at least in the 2nd quartile and 4th quartile funds ending up at most in the 3rd quartile.

However, given the market turmoil during 2008 that persistency broke down with regard to the 1st quartile funds, of which almost 60% moved into the 4th quartile, mainly due to the reason that they stopped reporting to the database. That phenomenon can also be documented for the 2nd and 3rd quartile as well. On the other hand, the probability of a fund ending up in the 1st quartile in December 2009 was almost identical for all funds regardless its quartile membership on December 2006. That finding is quite unusual compared to the previous periods, where that probability has been increasing when moving from the 4th quartile up to the 1st quartile. Given these findings, one could conclude that the persistency of Sharpe ratios can also be interrupted by market turmoil. But during calm periods there is clearly a persistency for 1st and 4th quartile funds staying in the quartile or moving just one quartile down or up, respectively.

**Fund of Funds with best Sharpe ratio**

What can investors expect when investing in funds of hedge funds based on the best Sharpe ratio? It is important to recall that persistency of Sharpe ratios does not implicate consistent outperformance of highly ranked funds based on the Sharpe ratio. That is due to the scenario that a fund can still exhibit a high Sharpe ratio although its return has fallen below the mean of its peers while having successfully reduced its volatility in order to keep the ratio high. That said we tested a simple trading strategy based on the Sharpe ratio ranking of the analysed funds, by which we start investing in January 1998 based on the Sharpe ratio rankings in December 1997 while rebalancing the portfolio every year on January based on the ranking of the rolling 36 month Sharpe ratio in the previous month of December.

Given the fact that such a strategy’s performance could be highly dependent on the starting point – which our analysis clearly indicates – we calculated the quartile specific returns for all possible starting months ending up with 12 different portfolios for each quartile. To come up with a valid estimate for the mentioned strategy for each month we took the average across all the 12 different portfolio returns for each quartile. Figure 4 displays the cumulative performance of the annually rebalanced four quartiles from January 1998 until December 2009. Although the picture seems to be quite clear, the 1st quartile outperforming over the long haul while the 4th quartile underperforming, the investor should keep in mind that these are just the averages of the 12 portfolios with the different starting months.

A more detailed look at a higher granularity reveals that the dispersion of the compounded returns for the 12 underlying portfolios for each quartile is quite high, e.g. for the 2nd quartile the difference between the maximum and minimum compounded return is 1.04% and for the 3rd quartile is 1.13%. Due to that dispersion some portfolios of the 1st quartile have a lower compounded return than portfolios of the 3rd quartile. Given the high mortality rate over the last 12 months, readers should keep in mind that a liquidation bias, which is caused by the fact that real performance is not available for funds that stop reporting, could have an impact on the results. Although, it is difficult to generalise the outcome of a strategy investing in highly ranked funds based on the Sharpe ratio, we can conclude that investors should avoid multi-strategy funds of hedge funds with a low Sharpe ratio compared to its peers, as these funds consistently underperform.

**Oliver Schwindler**, is Managing Partner, HF-Analytics GmbH, a quantitative research driven hedge fund consulting boutique that specializes in funds of hedge funds.

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