inforatio

Calculate information ratio for one or more assets

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

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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.

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.

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

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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

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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.