# Documentation

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# inforatio

Calculate information ratio for one or more assets

## Syntax

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

## Arguments

 `Asset` `NUMSAMPLES`-by-`NUMSERIES` matrix with `NUMSAMPLES` observations of asset returns for `NUMSERIES` asset return series. `Benchmark` `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` must be monthly returns.

## Description

Given `NUMSERIES` assets with `NUMSAMPLES` returns for each asset in a `NUMSAMPLES x NUMSERIES` matrix `Asset` and given a `NUMSAMPLES` vector of benchmark returns in `Benchmark`, `inforatio` computes the information ratio and tracking error for each asset relative to the `Benchmark`.

To summarize the outputs of `inforatio`:

• `Ratio` is 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.

• `TE` is 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.

## References

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

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