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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 will have 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 will be 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. ed., 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.