## Using the Sharpe Ratio

### Introduction

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`.

### Sharpe Ratio

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

```load FundMarketCash 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.