The Myth of Persistent Sharpe Ratio

No value as a forward-looking investment tool

SIEWLING LAY, SENIOR ANALYST, GFIA

GFIA’s conclusion is that investing in Asian hedge funds with historically strong Sharpe ratios is likely to result in poor performance. The Sharpe ratio may provide historical insights, but it has little or no value as a forward-looking investment tool. In this paper, GFIA looks at the persistency of the Sharpe ratio, over a multi-year time frame, across the Asian hedge fund universe. The findings reveal little persistency of the measure when applied in the context of Asian hedge funds, and hypothetical investments using historical Sharpe ratio produced dismal results in subsequent periods. The study was then repeated at the strategy level for the five biggest strategy groups, to remove strategy bias, so as to better investigate the persistency of the Sharpe ratio. This approach again showed little persistency of the measure, though we did observe an improvement in the number of funds which remained in the same category over the subsequent time horizon. Hypothetical investments using historical Sharpe ratio had also produced poor performance in the subsequent periods.

The Sharpe ratio – a commonly used measure of risk adjusted returns
Investors typically aim to maximise returns of their investments per unit of risk. The Sharpe ratio is one of the most commonly used measures by investors to determine an investment’s risk adjusted returns. Essentially, the Sharpe ratio measures the return of an investment relative to its volatility, adjusting for the underlying cost of capital. Many investors use the Sharpe ratio to categorise conveniently the risk-adjusted return profile of their funds, and use it as a core input into their decision-making process. Managers often (and legitimately) therefore “game” their return profile to maximise their Sharpe ratio. While the fundamental validity of the Sharpe ratio should be questioned, should investors decide to include it in their assessments of a fund’s attractiveness for investment, its persistence and reliability would clearly be important We tested whether in fact Sharpe ratios persisted on a multi-year time frame, specifically in relation to Asian hedge funds which form the majority of our investment universe. One specific concern is that Sharpe ratios, for a given group of funds, may well not have been calculated over uniform periods (and therefore market environments). In order to ensure that the Sharpe ratio of a fund is not a function of the market environment during the specific period of evaluation, or of the number of months the fund has been running, we used a consistent time period to evaluate the Sharpe ratio of all funds. To balance between the relatively short track record of most Asian hedge funds, and the need to have a meaningful sample size for our study, we ran the study based on returns of funds from 2007 till July 2009, and only funds that were incepted on or before July 2007 were included in the study. In order to better measure the persistency of a fund’s Sharpe ratio, funds that had ceased to report their numbers to AsiaHedge before May 2009 were excluded. The resulting universe consisted of 331 funds, as shown in Fig.1.

GFIA1

Does the Sharpe ratio persist across different time horizons?
We calculated the Sharpe ratio of each fund, before ranking them in ascending order. Since the aim of our study is to compare the Sharpe ratio of all funds in the sample, we assumed a risk free rate of zero to simplify the calculation (and to be consistent with the normal market practice of assessing performance, for performance fee calculations, over a hurdle of zero). These funds were then grouped into four categories based on their ranking. Each category contained 83 funds with Sharpe ratios as follows:

• < 25th percentile
• 25th to <50th percentile
• 50th to <75th percentile
• ≥ 75th percentile

GFIA2+3

GFIA4-6

We looked at the strategy breakdown of the groups of top performing and worst performing funds each year (see Figs.2 and 3). These showed:

• No consistency in the strategy mix of the worst performing funds, over different time periods; and
• No consistency in the strategy mix of the best performing funds, over different time periods.

On a year on year basis, there is little consistency in the mix of strategies that fall below the 25th percentile. The same can be said of the breakdown of strategies with funds above the 25th percentile. No strategy had a constant proportion of funds falling within the top quartile over the period considered for the study, nor for the bottom quartile:

• Fund rankings in the year 2007 versus 2008, showing that no more than 28% of funds in one category remained in the same category subsequently.
• Fund rankings in the year 2008 versus 2009, showing that no more than 20% of funds in one category remained in the same category subsequently.
• Fund rankings in the year 2007-2008 versus 2009, showing that no more than 27% of funds in one category remained in the same category subsequently.

No more than 50% of all funds in the same category remained in that category in the subsequent year. In fact, the highest percentage (46%) is represented by funds which were doing better than the 75th percentile in 2008 but which in the following year were among the worst performing funds as measured by the Sharpe ratio!

The worst performing funds were seldom the worst performers in a subsequent period
Overall, very few funds which were in the top quarter continued to be the top performing funds in the subsequent year. The same can be said of the worst performing funds in each year. Having established this pattern, we looked at the performance of funds with different Sharpe ratios. We assumed that we had invested in the categories of funds based on their Sharpe ratio. We repeated the study for 2007, 2008 and 2007-2008. The performances of these are plotted in Figs 4, 5 and 6.

Initial conclusion: investing based on Sharpe ratio produced dismal results on a multi-year view!
As evidenced from the graphs, investing in funds based on the ranking of their Sharpe ratio, that were calculated using between a one- and two-year history of data, often produced dismal results. Our initial conclusion, therefore, is that risk-adjusted performance across Asian hedge funds on a multi-year view exhibit little consistency. Investing based on historical Sharpe ratio alone has not been a successful strategy. However, different strategies might perform better under different market environments, and comparing the Sharpe ratio across funds of the same strategy might give a better indication of the measure. We repeated the study of Sharpe ratios at the strategy level, using the same data set. In order to have a meaningful result, the analysis was only conducted on the larger strategy groups with more than 30 funds:

• Asian equity excluding Japan – 52 funds
• Asian equity including Japan – 59
• Chinese equity – 53
• Japanese equity – 61
• Macro/multi-strategy – 34

Does the Sharpe ratio persist across strategies?
The Sharpe ratios of each fund were calculated as per the previous study and ranked in ascending order within their respective strategy buckets. The funds were then grouped into four categories based on their ranking in the strategy bucket. Each category within the same strategy bucket contained approximately the same numbers of funds, with Sharpe ratios as before. The study was run based on the returns of funds from 2007 to July 2009, to maintain consistency. We used two different time periods to calculate the Sharpe ratio of the funds during 2007 to 2008 and in 2008. We then looked at the funds’ Sharpe ratios in 2009. The results showed:

• Asia equity excluding Japan fund rankings show no more than 46% of funds in one category remained in the same category subsequently.
• Asia equity including Japan fund rankings show that no more than 33% of funds in each category remained in the same category subsequently.
• Chinese equity fund rankings show that no more than 43% of funds in each category remained in the same category subsequently.
• Japan equity fund rankings show that no more than 33% of funds in each category remained in the same category subsequently.
• Macro/multi-strategy fund rankings show that no more than 44% of funds in each category remained in the same category subsequently.

Consistent with the previous conclusion, no more than 50% of funds in one category remained in the same category the subsequent year. However, with the exception of the macro/multi-strategy funds, Sharpe ratios of funds in 2008 did give a better indication of 2009 Sharpe ratios for the best and worst performing funds, unlike Sharpe ratios calculated using data from 2007 to 2008. This could indicate that more recent data used in the calculation of Sharpe ratio gives a better projection of the fund’s Sharpe ratio in the immediately subsequent time period; there appears to be some short-term persistence. The persistence of the ratio is particularly high for the Asia equity ex Japan funds, which saw 46% of the worst performing funds in 2008 based on Sharpe ratio remaining at the bottom of the pack in 2009, and 38% of the best performing funds still at the top of the pack in 2009.

Macro/multi-strategy showed least persistence in Sharpe ratios over different time periods
Macro/multi-strategy funds showed least persistence in Sharpe ratios over different time periods. No funds in the lowest quartile remained in that quartile for the subsequent time period. In fact, 63% of funds in the top quartile moved on to the lowest quartile in the subsequent time horizon. Although long short funds also saw a significant number of managers moving from the top quartile to the worst quartile and vice versa, this figure is low compared to the macro/multi-strategy managers. Since 2008 Sharpe ratios seemed to have some persistence into 2009, we carried out the next part of the study using the funds’ 2008 Sharpe ratio. We assumed that we invested in the four categories of funds based on their Sharpe ratio. The performances of these revealed the following:

• Asia ex Japan long-short only shows persistence for poor Sharpe ratio.
• Asia long-short shows no persistence of Sharpe ratio.
• China long-short shows no persistence of Sharpe ratio.
• Japan long-short shows inverse relationships.
• Macro/ multi-strategy shows inverse relationships.

Investing in funds based on the best Sharpe ratio is likely to create weak investment performance
Once again, we see that investing in funds based on the best Sharpe ratio in 2008 produced dismal results in all cases. In four out of the five cases, funds with the best Sharpe ratio in 2008 actually generated the worst subsequent returns among the four simulated investment strategies. Particularly for the Japan equity long short funds and the macro/multi-strategy funds, the ranking of the eventual performance of the funds in 2009 were in reverse order of the ranking of their Sharpe ratio calculated using 2008 data. In conclusion, we find no persistency in using the Sharpe ratio as a tool for portfolio construction in the hedge fund universe. Bluntly, while we have no comment on its validity as a historical measurement, the Sharpe ratio has no validity as an investment decision tool.

Siewling Lay joined GFIA Pte Ltd in 2006 and is currently senior analyst at the firm, responsible for researching emerging market hedge funds