  Sharpe ratio (sometimes also referred to as information ratio) is widely used
in asset management to compare and benchmark funds and asset managers. It
computes the ratio of the (excess) net return over the strategy standard
deviation. However, the elements to compute the Sharpe ratio, namely, the
expected returns and the volatilities are unknown numbers and need to be
estimated statistically. This means that the Sharpe ratio used by funds is
likely to be error prone because of statistical estimation errors. In this
paper, we provide various tests to measure the quality of the Sharpe ratios. By
quality, we are aiming at measuring whether a manager was indeed lucky of
skillful. The test assesses this through the statistical significance of the
Sharpe ratio. We not only look at the traditional Sharpe ratio but also compute
a modified Sharpe insensitive to used Capital. We provide various statistical
tests that can be used to precisely quantify the fact that the Sharpe is
statistically significant. We illustrate in particular the number of trades for
a given Sharpe level that provides statistical significance as well as the
impact of auto-correlation by providing reference tables that provides the
minimum required Sharpe ratio for a given time period and correlation. We also
provide for a Sharpe ratio of 0.5, 1.0, 1.5 and 2.0 the skill percentage given
the auto-correlation level.
