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# Sharpe Ratio

The Sharpe ratio is calculated by dividing the mean excess return of the index by its volatility, annualized over the horizon under consideration. In some years, the risk-free rate used to compute excess returns can be negative. The higher the Sharpe ratio, the higher the excess returns for a unit of risk.

where:

$//$ denotes the annualised mean Excess Returns of the index.
$//$ denotes the annualised Index Return Volatility measure.

We compute sharpe ratios depending on the choice of currency to report returns, assuming that for the 'risk-free' asset for any given investor is the domestic 3-month risk-free asset. A Sharpe Ratio based on local currency returns and risk-free rates is also computed using local currency excess returns, as described  here.

We also compute an Adjusted Sharpe ratio to account for the skewness and excess kurtosis in the returns distribution

where:

$//$ is the skewness of the return distribution

$//$ is the excess kurtosis of the return distribution

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