Using the Information Ratio
Introduction
Although originally called the "appraisal ratio"
by Treynor and Black, the information ratio is the ratio of relative
return to relative risk (known as "tracking error").
Whereas the Sharpe ratio looks at returns relative to a riskless
asset, the information ratio is based on returns relative to a risky
benchmark which is known colloquially as a "bogey."
Given an asset or portfolio of assets with random returns designated
by Asset and a benchmark with random returns designated
by Benchmark, the information ratio has the form:
Mean(Asset - Benchmark) / Sigma (Asset - Benchmark)
Here Mean(Asset - Benchmark) is the mean
of Asset minus Benchmark returns,
and Sigma(Asset - Benchmark) is the standard deviation
of Asset minus Benchmark returns.
A higher information ratio is considered better than a lower information
ratio.
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Information Ratio Example
To calculate the information ratio using the example data, the
mean return of the market series will be used as the return of the
benchmark. Thus, given asset return data and the riskless asset return,
compute the information ratio with
load FundMarketCash
Returns = tick2ret(TestData);
Benchmark = Returns(:,2);
InfoRatio = inforatio(Returns, Benchmark)
which gives the following result:
InfoRatio =
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 software). Its standard deviation
of relative returns in the denominator is 0.
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 | Using the Sharpe Ratio | | Tracking Error |  |
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