# Sharpe Ratio: Risk Adjusted Return of Mutual Funds

Sharpe ratio is an important mutual fund performance metric.

This is the second part of a series which focuses on a few important mutual fund performance parameters.

The first part of the series focused on two important mutual fund parameters – rolling returns and standard deviation.

It is essential that you read the first part before proceeding to read about Sharpe ratio.

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A quick recap of the first part –

Trailing returns are like the scores of Sachin Tendulkar and Harbhajan Singh in the last match. Just because Harbhajan scored a rare century and Tendulkar got out on a rare duck doesn’t make Harbhajan a better batsman than Tendulkar.

Rolling returns are like the scores of Tendulkar and Harbhajan of last 200 innings ** averaged**. The averaging score will make sure that you select the better batsman when compared to trailing returns.

Trailing returns are used by most mutual fund ranking portals and are deceptive most of the times.

A good mutual fund selection framework will use rolling returns and not trailing returns.

However, rolling returns alone is not enough. You also require standard deviation as a mutual fund performance metric.

This was explained using two scores of two batsmen. One batsman either gets a low score (close to 0) or gets a high score (close to 100). The other batsman consistently scores in a narrow range of about 35-50.

Over 10 innings, the total scores of the batsmen are the same – 500. However, the standard deviations were very different – for the first batsman it is 55 and for the second batsman it is 20.

**Standard deviation indicates volatility or risk. So, a higher standard deviation is not desirable.**

All in all, you need to know the following…

Moving on to Sharpe ratio…

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## Sharpe Ratio

Sharpe ratio is calculated as follows…

**R _{mf}** is the return of a mutual fund for a period like 1 or 3 years

**R**is the risk free rate of return (usually the rate of return of 10 year government bond)

_{rf}**Std Dev**is the standard deviation of the mutual fund for the considered period

See how Sharpe Ratio integrates returns and risk as indicated by rolling returns and standard deviation?

This is why it becomes very important to understand rolling returns and standard deviation before you attempt to understand Sharpe ratio.

And for the same reason Sharpe ratio is a metric of “**risk-adjusted returns**.”

In addition to the rolling returns and standard deviation of the mutual funds, Sharpe ratio calculation requires another variable – **risk-free rate of return**.

What is the most risk-free rate of return in the market? Something that is absolutely guaranteed.

Did you say fixed deposits? Surprise surprise! You are wrong.

Fixed deposits are neither guaranteed nor are they 100% insured. Every bank account is insured only up to Rs. 1,00,000 – this includes the principal and interest of your fixed deposits, savings account and even recurring deposits.

Convert your fixed deposits in to a source of stable monthly income

The only instrument that is completely risk free is government bonds or G-secs. And for the Sharpe ratio calculation the ideal rate of R_{rf} to plug is 10-year G-sec yield.

Let’s have a look at a quick example of Sharpe ratio calculation…

Let us say for Fund A the 3-year rolling return has been 15%. The 10-year government bond has a yield of 5%. Additionally, the standard deviation of 3-year rolling returns of fund A is 8%. The Sharpe ratio will be calculated as follows…

### Interpretation of Sharpe Ratio

Let’s try to logically understand why **a high Sharpe ratio is desirable**.

The numerator – which increases the value of Sharpe ratio – is the extra return you earn over the risk-free rate of return. Ideally, you would want the extra return to be as high as possible.

The denominator – which decreases the value of Sharpe ratio – is the risk (standard deviation) you take to earn the extra return. Ideally, you want the risk to be as low as possible.

Now you know why a higher Sharpe ratio is desirable.

If the Sharpe ratio of fund A is greater than that of fund B, does it mean that fund A is fund B *always*?

*Depends*.

As we saw for rolling returns and standard deviation, you cannot compare them for funds belonging to different categories. Every fund category has a different risk-return profile.

Additionally, even if the funds belong to the same category you cannot compare them for different time periods. You cannot compare the rolling return of fund A since 2005 to the rolling return of fund B since 2011.

The same logic applies to Sharpe ratio.

### Limitations of Sharpe Ratio

On the face of it, Sharpe ratio sounds like a very good metric to assess a mutual fund’s performance. Further, since you can compare it across funds, Sharpe ratio can also tell you the better of two comparable funds.

This is until you try to think about the shortcomings of Sharpe ratio.

**Too much weight to risk**

As a measure of risk and return, Sharpe ratio gives too much weight to *risk*. In my view, this makes sense in the short term.

However, for investment instruments that are intended to be held for long term, much higher emphasis should be placed on returns.

**Even upside deviation is penalized**

Sharpe ratio uses standard deviation to measure risk. And standard deviation penalizes upside and downside deviation equally.

Let’s say the expected return is 15%.

What standard deviation says is, any deviation from 15% is a risk. This is perfectly applicable to 10% return.

However, for an investor, a 20% return doesn’t sound like a risk. A bonus maybe, but not risk.

Standard deviation penalizes this instance of 20% return too!

To solve this problem, what we recommend at Finpeg is that risk and return parameters should be kept separate. Merging them may create a problem instead of creating a short cut.

At Finpeg, we make use of what is called Downside Deviation to measure risk.

Downside deviation and other parameters that we use to assess and rank funds are explained here –

How to select the best mutual funds using the Finpeg CRAFT Framework