# inforatio

Calculate information ratio for one or more assets

## Syntax

``inforatio(Asset,Benchmark)``
``[Ratio,TE] = inforatio(Asset,Benchmark)``

## Description

example

````inforatio(Asset,Benchmark)` computes the information ratio for each asset relative to the `Benchmark`.```

example

````[Ratio,TE] = inforatio(Asset,Benchmark)` computes the information ratio and tracking error for each asset relative to the `Benchmark`.```

## Examples

collapse all

This example show how to calculate the information ratio using `inforatio` with example data, where the mean return of the market series is used as the return of the benchmark.

You can use inforatio to compute the information ratio for the given asset return data and the riskless asset return.

```load FundMarketCash Returns = tick2ret(TestData); Benchmark = Returns(:,2); InfoRatio = inforatio(Returns, Benchmark)```
```InfoRatio = 1×3 0.0432 NaN -0.0315 ```

Since the market series has no risk relative to itself, the information ratio for the second series is undefined (which is represented as `NaN` in MATLAB®.

This example show how to calculate the tracking error using `inforatio` with example data, where the mean return of the market series is used as the return of the benchmark.

Given an asset or portfolio of assets and a benchmark, the relative standard deviation of returns between the asset or portfolio of assets and the benchmark is called tracking error.

```load FundMarketCash Returns = tick2ret(TestData); Benchmark = Returns(:,2); [InfoRatio, TrackingError] = inforatio(Returns, Benchmark)```
```InfoRatio = 1×3 0.0432 NaN -0.0315 ```
```TrackingError = 1×3 0.0187 0 0.0390 ```

Tracking error, also know as active risk, measures the volatility of active returns. Tracking error is a useful measure of performance relative to a benchmark since it is in units of asset returns. For example, the tracking error of 1.87% for the fund relative to the market in this example is reasonable for an actively managed, large-cap value fund.

## 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`

Returns for a benchmark asset, specified as a `NUMSAMPLES` vector of returns for a benchmark asset. The periodicity must be the same as the periodicity of `Asset`. For example, if `Asset` is monthly data, then `Benchmark` should be monthly returns.

Data Types: `double`

## Output Arguments

collapse all

Information ratios, returned as a `1 x NUMSERIES` row vector of information ratios for each series in `Asset`. Any series in `Asset` with a tracking error of `0` has a `NaN` value for its information ratio.

Tracking errors, returned as a `1 x NUMSERIES` row vector of tracking errors, that is, the standard deviation of `Asset` relative to `Benchmark` returns, for each series.

Note

`NaN` values in the data are ignored. If the `Asset` and `Benchmark` series are identical, the information ratio is `NaN` since the tracking error is `0`. The information ratio and the Sharpe ratio of an `Asset` versus a riskless `Benchmark` (a `Benchmark` with standard deviation of returns equal to `0`) are equivalent. This equivalence is not necessarily true if the `Benchmark` is risky.

 Grinold, R. C. and Ronald N. Kahn. Active Portfolio Management. 2nd. Edition. McGraw-Hill, 2000.

 Treynor, J. and Fischer Black. "How to Use Security Analysis to Improve Portfolio Selection." Journal of Business. Vol. 46, No. 1, January 1973, pp. 66–86.