Understanding the notion of a risk-adjusted return requires some maturity to think beyond mere returns. While comparing funds, a fund that offers a lower return with lower risk is better than one with higher return with higher risk.

There are many risk-adjusted measures and one of them is the information ratio. The information ratio is a measure of how effective the fund manager is in beating the benchmark.

The information ratio has always been part of the **mutual fund risk-return analyzer**. I started to pay more attention to it when Dr. Uma Shashikant remarked at FB group, Asan Ideas for Wealth in a thread on star ratings: *"Information ratio is my key quantitative indicator". *

So that got me curious and I included a new sheet which plots the information ratio for each period in the **year-on-year risk-return analyzer**

In this post, let us look at what the information is, how it can be interpreted, and what are its limitations. First published Apr 26 2015. Republished now with updated graphs.

**What is the information ratio? **It is a measure of outperformance per unit risk associated with the outperformance.

**How is the Information ratio calculated?**

To calculated the information ratio, the follow steps are necessary:

- Calculate daily or month returns of the fund and benchmark (I use daily returns) for a given duration.
- Calculate the difference between the two. This is known as the excess return (we hope it will be positive!)
- Calculate the average of the return difference for the duration. Call this
**Avg** - Calculate the standard deviation of the return difference. Call this
**Stdev.**This is a measure of how much individual excess returns deviate from the average. - Information ratio = Avg/Stdev

Or it is the average excess return divided by volatility associated with the excess return.

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

Higher average excess returns and lower volatility (standard deviation) are desirable. 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 numerator, the average excess return is negative. The denominator, the standard deviation is always positive.

Here is an example:

The top graph is for different investment durations: 1 year to 8 years. The bottom graph represents year-on-year information ratios.

For all investment durations, Quantum Long Term Equity has consistently produced excess returns at minimal risk.For a few years (bottom graph), the fund has not been able to produce excess returns (on average).

However, the information ratio has a flaw. A fund can have negative information ratio and could have still beat the benchmark comfortably or a fund with positive information ratio could have lagged behind the benchmark.

Take the case of HDFC Top 200. The SIP and lump sum returns for different investment durations are plotted below.

Although it does not make for spectacular viewing, HDFC Top 200 has managed to beat BSE 200 (excluding dividends!!) on many occasions.

Yet all the information ratios are negative!

This is misleading as it suggests that HDFC Top 200 **never** produced excess returns wrt BSE 200 in the past 8 years.

This is because the information ratio considers the arithmetic average of excess returns and ignores the way in which the excess returns can compound and produce alpha.

The so-called **geometric information ratio** is the way out of this discrepancy.

The geometric information ratio for HDFC Top 200 is computed below

For all investment durations (except the last Y - top graph) the geometric information ratio is positive.The geometric version is a better estimate of risk-adjusted returns.

**Download the information ratio calculator** (the format is the same as the risk-return analyser but only the returns and information ratio are computed here)

Ashal JauhariNow people may understand, why WE are in comfort zone with respect to Quantum Long Term Eq. fund.

Thanks

Ashal

freefincalPost authorThanks Ashal.

Ashal JauhariNow people may understand, why WE are in comfort zone with respect to Quantum Long Term Eq. fund.

Thanks

Ashal

freefincalPost authorThanks Ashal.

Raghu RamamurthyIt is getting more and more complicated.From one of your previous posts I

have observed you are thinking of change of jobs.Is the new job anything connected with

financial planning?If so, count me as one of your potential customer!!!!

Raghu RamamurthyIt is getting more and more complicated.From one of your previous posts I

have observed you are thinking of change of jobs.Is the new job anything connected with

financial planning?If so, count me as one of your potential customer!!!!

moronbuffett5.Information ratio = average/standard-deviation

dr.murari,

isnt this mu/sigma ? looks like good old signal to noise ratio to me !

isn't it better to do all your calculations on a log scale? i think we can overcome the -ve values

also, your post-mortem on HDFC Top200 looks like confirmation bias 🙂

You are fitting the calculations to confirm your a priori results!

freefincalPost authorThe STD is for excess returns not just returns. not the same.

When the sign of the ratio matters to me, I cannot plot it in log scale.

It is a well known fact that T200 has generated significant alpha in the past. The standard information ratio does not reflect that. Hence the geometric version is need. This is a well known fact. You want to think it is my bias, go ahead.

moronbuffett5.Information ratio = average/standard-deviation

dr.murari,

isnt this mu/sigma ? looks like good old signal to noise ratio to me !

isn't it better to do all your calculations on a log scale? i think we can overcome the -ve values

also, your post-mortem on HDFC Top200 looks like confirmation bias 🙂

You are fitting the calculations to confirm your a priori results!

freefincalPost authorThe STD is for excess returns not just returns. not the same.

When the sign of the ratio matters to me, I cannot plot it in log scale.

It is a well known fact that T200 has generated significant alpha in the past. The standard information ratio does not reflect that. Hence the geometric version is need. This is a well known fact. You want to think it is my bias, go ahead.

Pattabiraman MurariAgree sir. Felt the same way. I am not going to change job. Just my research area. Thank you for your confidence.

moronbuffettjust curious,

are there any backtesting tool or research available for indian equities ?

I would really love to see your screener back tested just for academic reasons.

Pattabiraman MurariAgree sir. Felt the same way. I am not going to change job. Just my research area. Thank you for your confidence.

moronbuffettjust curious,

are there any backtesting tool or research available for indian equities ?

I would really love to see your screener back tested just for academic reasons.

A.SundaramDear Pattu,

1) Comforting post-over the last month have focused on QLTEF for increased allocation.But contrary to popular opinion,it was the cash holding which made me look at QLTEF with confidence.

2) Having been shut out out of FB,did not know about your plans to get into financial research/planning.I sincerely wish you the very best.Good luck,my dear friend.

A.SundaramDear Pattu,

1) Comforting post-over the last month have focused on QLTEF for increased allocation.But contrary to popular opinion,it was the cash holding which made me look at QLTEF with confidence.

2) Having been shut out out of FB,did not know about your plans to get into financial research/planning.I sincerely wish you the very best.Good luck,my dear friend.

rayn leI was wanted to know that in Morning star India, when you check any mutual fund stats, you can go to the section "Factsheet" and there is Information ratio given but does not tell you for what duration it is? Any one ?

rayn leI was wanted to know that in Morning star India, when you check any mutual fund stats, you can go to the section "Factsheet" and there is Information ratio given but does not tell you for what duration it is? Any one ?

DadaHi,

Dec 31, 2015.

All PICTURES and the EXCEL file are GONE / inaccessible.

Please reupload them all again, ASAP.

Thanks.

freefincalPost authorRestored. Pl. check now.

DadaThanks. Now please clarify to me these few things.

I quote:

"1. Calculate DAILY or MONTH(LY) returns of the fund and benchmark (I use daily returns) for a given duration."

My #1 question to that is--though not common--, is it ACCEPTABLE to calculate IR or GIR on YEARLY Returns? Say, for a given duration of 5 years..?

My #2 question is , is there a MINIMAL Number of duration for calculating them to make it a reliable conclusion? For monthly returns, I see people only use the 12-months duration. So, I would reckon--for Yearly Returns--3 years of period is OK. What's your thought on that?

Hope to get reply from you soon.

freefincalPost authorYou can choose to calculate with any duration return you like and over any period. To identify trends, you need enough (large no) mutual funds which fit your criterion.

DadaThank you, Sir.

Tanveer SehgalHey,

Firstly, thank you for the great articles.

The problem I am experiencing when using the excel sheet is

Run-time error '438':

Object doesn't support this property or method

I am using Excel on Mac. Any idea what is causing the problem?

freefincalPost authorThank you. Will not work on a Mac. I am slowly making my sheets Mac compatible. Check out: Personal Finance Calculators for Mac Excel 2011