Examples
Suppose the asset has an expected return of 15% in excess of the risk free rate. We typically do not know if the asset will have this return; suppose we assess the risk of the asset, defined as standard deviation of the asset's excess return, as 10%. The risk-free return is constant. Then the Sharpe ratio (using the old definition) will be 1.5 ( and ).
For an example of calculating the more commonly used ex-post Sharpe ratio - which uses realized rather than expected returns - based on the contemporary definition, consider the following table of weekly returns.
| Date | Asset Return | S&P 500 total return | Excess Return |
|---|---|---|---|
| 7/6/2012 | -0.0050000 | -0.0048419 | -0.0001581 |
| 7/13/2012 | 0.0010000 | 0.0017234 | -0.0007234 |
| 7/20/2012 | 0.0050000 | 0.0046110 | 0.0003890 |
We assume that the asset is something like a large-cap U.S. equity fund which would logically be benchmarked against the S&P 500. The mean of the excess returns is -0.0001642 and the (sample) standard deviation is 0.0004542, so the Sharpe ratio is -0.0001642/0.0004542, or -0.3615359.
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