# Can we use the information ratio to analyze index funds?

Published: May 13, 2023 at 6:00 am

Last Updated on May 13, 2023 at 8:33 am

A member of the freefincal investor circle asks, Can we use the information ratio to analyze index funds?

What is the information ratio? It is a measure of outperformance per unit risk associated with the outperformance. In other words, the information ratio is a risk-adjusted measure of the fund manager’s effectiveness in beating the benchmark.

How is the Information ratio calculated? To calculated the information ratio, the follow steps are necessary:

1. Calculate daily or month returns of the fund and benchmark (I use daily returns) for a given duration.
2. Calculate the difference between the two. This is the excess return in the case of an active fund. For a passive fund this should be a low negative number.
3. Calculate the average of the return difference for the duration.
4. Calculate the standard deviation of the return difference. This is also known as the tracking error or the relative volatility. This measures how much individual excess returns deviate from the average.

Information ratio = Avgerage return difference divided by the tracking error.

Or it is the average excess return divided by volatility associated with the excess return. It can be defined in a bit more friendly way as:

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Information Ratio =(Portfolio ReturnBenchmark Return​)/Tracking Error

The information ratio is part of our comprehensive mutual fund analysis tool for freefincal investor circle members.

In contrast, the Sharpe ratio also calculates excess return per unit average risk but for a fixed risk-free return.

Higher average excess returns and lower relative volatility (tracking error) are desirable for an active fund. So higher the information ratio, the better.  Since the ratio depends on the duration considered, it is difficult to say what value is good. In general, a high positive value is acceptable.

A negative information ratio implies that the average excess return is negative for the numerator. The denominator, the standard deviation, is always positive. So the information ratio for most passive funds will be negative.

So, can we use the information ratio to analyze index/passive funds?

For a passive fund, the excess return should be small and negative. The tracking error should be small. So for a passive fund, we want both the numerator and denominator to be small, and the information ratio will be negative.

So it easy to see that the information ratio will not be intuitive when used for an index fund or ETF. A ratio should either be small or big. The numerator should be small (big) and the denominator big (small) for the ratio to be small (big). It is hard to appreciate the ratio if both need to be small, as is the case for index funds.

Insead, we simply look at tracking difference – defined as fund fund difference minus index difference for different periods. Say the last 1Y, 2Y etc. We can also do the same with tracking errors and choose a fund with consistently low tracking difference and low tracking errors. We adopt this approach in our monthly index fund tracking error screeners.

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