Testing the Significance and Uncertainty of an Information Ratio

Summary

The document asks how to assess uncertainty in an estimated information ratio based on portfolio returns relative to a benchmark. It explains that the information ratio resembles a t-statistic and can be used to test whether average active returns differ from zero. This provides a way to assess the significance of the estimated mean active return.

The response distinguishes that test from estimating uncertainty in the information ratio itself. It offers classic bootstrapping as a possible approach for the latter, but gives no procedure, assumptions, or example calculations. The discussion is therefore a brief conceptual pointer rather than a complete guide to inference. It does not specify how sample size, serial dependence, or other properties of the return data affect the test or confidence interval, so those details would need separate treatment.

Key ideas

• The information ratio is similar to a t-statistic and can test whether mean active returns differ from zero.
• Testing the mean active return does not by itself quantify uncertainty in the information ratio estimate.
• Bootstrapping is suggested as a way to estimate uncertainty in the information ratio.
• The response does not provide implementation details or discuss assumptions about return data.

Tags

# Test significance for information ratio


# Test significance for information ratio












Suppose that we have an estimated Information Ratio $IR^*$ calculated from the relative returns between a portfolio and a benchmark.

I am looking for a way to quantify the uncertainty of this calculated value by either testing for significance of the value or by estimating a confidence interval.

I've read that the Information Ratio is very similar to a t-statistic. What further calculations are required to transform it to estimate significance?

## Answer by Rylan (score 1)

https://quant.stackexchange.com/a/76798

The Information Ratio is indeed quite similar to a $t$-statistic; you could use that value to test whether your returns from active management are different from zero. In other words, the Information Ratio is a way of testing significance of the estimated mean of active returns.

If you want to quantify the uncertainty of the information ratio itself, I'm not familiar with anything beyond classic bootstrapping (hopefully someone more knowledgeable than me can provide a better answer there.)

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