Source: RAPA Capital Introduction – http://rapacapintro.com/journal/journal/noticeboard#sharpe

Recently, we came across a paper that shows that Sharpe ratios of funds with short history are considerably smaller than Sharpes of funds with longer trading history. We decided to check if this result is correct.

To check the argument we divided all funds into four categories:

- Funds that have more than one year of trading history,
- Funds that have more than two years of history,
- Funds that have more than five years of history,
- Funds that have more than ten years of history.

For each category, we calculate the Sharpe ratios and we fit these numbers to the Student t-distribution. The choice of t-distribution is natural because of the Sharpe ratio’s formula with the standard deviation of returns in the denominator. We will see that indeed, the distribution of Sharpe ratios possess heavier tails than the normal distribution.

On the chart below we plot the fitted densities of the obtained distributions. We clearly see that the observed average Sharpe ratios for each category are roughly the same and is approximately equal to ~0.65. It is interesting that this value of Sharpe is of the same order as the Sharpe ratio of the broad market (S&P 500 before the GFC).

What is more interesting on this chart – are the degrees of freedom of the fitted t-distributions. For the 1yr data the number of degrees of freedom is equal to 2, while for the 10yr data this number is 4. Recall, that the number of degrees of freedom measures overall weight in the tails of t-distributions. We see that for the 1yr data, the number of strange or abnormal funds is much larger than for the 10yr data and Sharpe ratios for the funds that survived more than 10yrs are much more stable. We conjecture that funds with abnormally high Sharpe ratios are in general not capable of surviving enough time and will eventually suffer from big drawdown’s and liquidation.

To conclude, in our study we established that funds with a longer history on average have the same Sharpe ratio as the funds that survived only a few years. However, the distribution of Sharpe ratios around the mean possess much heavier tails for the funds with less history than for funds with large trading history.

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