# sharpe

Compute Sharpe ratio for one or more assets

## Syntax

``sharpe(Asset)``
``sharpe(Asset,Cash)``
``Ratio = sharpe(Asset,Cash)``

## Description

example

````sharpe(Asset)` computes Sharpe ratio for each asset.```

example

````sharpe(Asset,Cash)` computes Sharpe ratio for each asset including the optional argument `Cash`.```

example

````Ratio = sharpe(Asset,Cash)` computes Sharpe ratio for each asset including the optional argument `Cash`.```

## Examples

collapse all

This example shows how to compute the Sharpe ratio using the mean return of a cash asset as the return for the riskless asset.

Given asset return data and the riskless asset return, the Sharpe ratio is calculated:

```load FundMarketCash Returns = tick2ret(TestData); Riskless = mean(Returns(:,3))```
```Riskless = 0.0017 ```
`Sharpe = sharpe(Returns, Riskless)`
```Sharpe = 1×3 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 is calculated with the mean of cash returns. The Sharpe ratio can also be calculated with the cash return series as input for the riskless asset.

`Sharpe = sharpe(Returns, Returns(:,3))`
```Sharpe = 1×3 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.

## Input Arguments

collapse all

Asset returns, specified as a `NUMSAMPLES x NUMSERIES` matrix with `NUMSAMPLES` observations of asset returns for `NUMSERIES` asset return series.

Data Types: `double`

(Optional) Riskless asset, specified as a either a scalar return for a riskless asset or a vector of asset returns to be a proxy for a “riskless” asset. In either case, the periodicity must be the same as the periodicity of `Asset`. For example, if `Asset` is monthly data, then `Cash` must be monthly returns. If no value is supplied, the default value for `Cash` returns is `0`.

Data Types: `double`

## Output Arguments

collapse all

Sharpe ratios, returned as a `1`-by-`NUMSERIES` row vector of Sharpe ratios for each series in `Asset`. Any series in `Asset` with standard deviation of returns equal to `0` has a `NaN` value for its Sharpe ratio.

Note

If `Cash` is a vector, `Asset` and `Cash` need not have the same number of returns but must have the same periodicity of returns. The classic Sharpe ratio assumes that `Cash` is riskless. In reality, a short-term cash rate is not necessarily riskless. `NaN` values in the data are ignored.

 Sharpe, W. F. "Mutual Fund Performance." Journal of Business. Vol. 39, No. 1, Part 2, January 1966, pp. 119–138.