Financial Toolbox™

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.

Examples

See Information Ratio Example.

References

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