Sharpe Ratio & Information Ratio

How do you select funds?

The most simple approach would be peformance i.e. returns.

But is it sufficient to track only returns?

There is something more...

The reliability of the scheme too is a critical aspect. Reliability is nothing but volatility.

A scheme giving good returns but extremely volatile or unreliable may not find favor

with a larger number of investors.

This calls for a measure of performance which takes into account both returns as well

as volatility / reliability.

Here it is…

The ratio Returns/Volatility expresses this measure. The measure will be high if

returns are high and volatility is low. A good fund will have a higher ratio.

This ratio is the basis for Sharpe Ratio as well as Information Ratio.

However it is interesting to understand the diffference between them.

Prof. Simply Simple will try to simplify the explanation by drawing an analogy with

cricket.

Analogy

Imagine a cricket series has just got over and we are analysing the performance of

Sehwag, M S Dhoni (MSD) and Sreesanth

Lets assume the team played four one day internationals. In these matches their

scores were as follows:-

1. Sehwag (0, 0, 120, 160) – Average 70 & Standard Deviation = 71.41

2. MSD - (60, 60, 70, 70) – Average 65 & Standard Deviation = 10

3. Sreesanth – (0, 0, 5, 20 ) – Average 6.25 & Standard Deviation = 8.19

What do we learn fromthese scores?

We realize that both Sehwag and MSD have had a good run.

The average of Sehwag at 70 is higher than Dhoni’s 65. But the story does not end

here.

Dhoni’s standard deviation is only 10 while Sehwag’s is 71.41.

Keeping the above measures in mind one is likely to go with Dhoni for his

performance + reliability as long as other parameters like strike rate etc are

comparable.

Sharpe Ratio decides as follows…

Sehwag : 70 – 6.25 /71.41 = .9

Dhoni : 65 – 6.25 / 10 = 5.8

6.25 was the average of Sreesanth, the worst batsman in the series.

The rationale over here is that 6.25 runs were scored by the worst batsman. Any

thing above that is display of batsman ship.

But…

A single measure is insufficient as the measure of average would have made

Sehwag a better bet and the measure of standard deviation would have made

Sreesanth better than Sehwag and Dhoni.

Thus the Sharpe ratio takes both measures of performance and reliability into

account to arrive at the quality of the batsmen and thereby supporting our decision of

selecting Dhoni over Sehwag.

Mathematically…

Sharpe ratio: (Rp- r) / Sp

Where

Rp – Return of the fund or the portfolio

r – The risk-free rate

Sp – The volatility of the fund or the portfolio

Principally, higher the Sharpe ratio better is the fund.

So…

One important feature that is observed while calculating Sharpe Ratio when applied to

cricket is that we compare the average runs of a batsman with that of a bowler. In the

world of finance the bowler is the risk free investment option of Government bonds.

Hence we should compare the average of the batsmen with the average of another

batsman who could be treated as a benchmark. That would throw more light on the

batting performance.

Similarly in funds we should compare the performance with the benchmark fund’s

performance both for returns as well as volatility.

This measure is called the Information Ratio.

Now…

1. Let’s assume Dravid is the benchmark batsman for India in the series.

2. In our example Information Ratio would compare the performance of the batsman

(Sehwag and Dhoni) with Dravid.

3. Let’s say Dravid scored 80, 75, 85, 70 in the same series. His standard deviation

turns out to 5.59. His average is 77.5. Both his measures are better and hence he

is chosen as the benchmark.

On comparison with Dravid…

The information Ratio is calculated as :The information Ratio is calculated as :

IR = IR = Difference in averages of player compared to benchmark / difference in Difference in averages of player compared to benchmark / difference in

standard deviation of player compared with benchmark.standard deviation of player compared with benchmark.

So, IR of Dhoni = 0.34So, IR of Dhoni = 0.34

Thus…

Information Ratio measures the excess return of an investment manager divided

by the amount of risk the manager takes relative to a benchmark.

The Sharpe Ratio on the other hand compares the return of an asset against the

return of a risk-free instrument such as Treasury Bills.