## Using the Sharpe Ratio

The Sharpe ratio is the ratio of the excess return of an asset divided by the asset's standard deviation of returns. The Sharpe ratio has the form:

(Mean − Riskless) / Sigma

Here Mean is the mean of asset returns, Riskless is the return of a riskless asset, and Sigma is the standard deviation of asset returns. A higher Sharpe ratio is better than a lower Sharpe ratio. A negative Sharpe ratio indicates “anti-skill” since the performance of the riskless asset is superior. For more information, see sharpe.

To compute the Sharpe ratio, the mean return of the cash asset is used as the return for the riskless asset. Thus, given asset return data and the riskless asset return, the Sharpe ratio is calculated with

Returns = tick2ret(TestData);
Riskless = mean(Returns(:,3))
Sharpe = sharpe(Returns, Riskless)

which gives the following result:

Riskless =
0.0017
Sharpe =
0.0886    0.0315         0

The Sharpe ratio of the example fund is significantly higher than the Sharpe ratio of the market. As is demonstrated with portalpha, this translates into a strong risk-adjusted return. Since the Cash asset is the same as Riskless, it makes sense that its Sharpe ratio is 0. The Sharpe ratio was calculated with the mean of cash returns. It can also be calculated with the cash return series as input for the riskless asset

Sharpe = sharpe(Returns, Returns(:,3))

which gives the following result:

Sharpe =
0.0886    0.0315         0

When using the Portfolio object, you can use the estimateMaxSharpeRatio function to estimate an efficient portfolio that maximizes the Sharpe ratio. For more information, see Efficient Portfolio That Maximizes Sharpe Ratio.