Investing in a mutual fund scheme starts with the tedious task of selecting the appropriate one and this is where some investor might be tempted to invest in a mutual fund scheme which yields higher returns. But this Relative returns comparison approach does not differentiate between two schemes that have assumed different levels of risk in pursuit of the same investment objective. Therefore, short-listing schemes, purely based on relative returns, may be misleading as the fund that has taken higher risk might have generated the same return as a peer with lower risk.

On the other hand, higher risk may result in higher return but it could also mean sacrificing the quality of a fund’s portfolio. And that’s why relative returns comparison might not be the foolproof way of selecting a mutual fund scheme and then finding out risk adjusted return of a fund becomes extremely important.

**Risk-adjusted Returns**

An alternative approach to the relative returns comparison to evaluate the performance of the fund is to establish the risk reward relationship. The underlying principle is that return ought to be commensurate with the risk taken. A fund manager, who has taken higher risk, ought to earn a better return to justify the risk taken. Similarly, a fund manager who has earned a lower return may be able to justify it through the lower risk taken.

Such evaluations are conducted through Risk-adjusted Returns and determining risk adjusted returns of various mutual fund schemes is an important part of selecting the right fund for investment. There are various measures of risk-adjusted returns and some most popular measures are Sharpe ratio, Treynor ratio, Alpha and Beta.

**Sharpe Ratio**

The Sharpe ratio, also known as Reward-to-Volatility-Ratio, measures the risk-adjusted performance. This ratio has been named after William F. Sharpe who developed this ratio. It indicates the excess return per unit of risk associated with the excess return.

Mathematically, the measurement of Sharpe Ratio is based on standard deviation, risk free returns and expected return earned by the fund. It is also one of the important indicators of fund’s performance vis-à-vis the risk taken by a fund manager.

It is calculated by subtracting the risk-free rate from the rate of return for a portfolio and dividing the result by the standard deviation of the portfolio returns.

SR = {r - rf} / v

Where

SR – Sharpe ratio

r – Portfolio’s return

rf – Risk free rate

v – Portfolio’s volatility

E.g., if investor gets 7% return on her investment in a scheme with a standard deviation/ volatility of 0.5 and we assume risk free rate is 5%, Sharpe Ratio is (7-5)/0.5 = 4 in this case.

**What is the significance of Sharpe Ratio?**

The greater a portfolio's Sharpe Ratio, the better its risk-adjusted performance. A negative Sharpe Ratio indicates that a risk-less asset would perform better than the security being analyzed. This measurement is very useful because it explains why one portfolio has reaped higher returns than its peers; it is only a good investment if those higher returns do not come with too much additional risk.

Due care should be taken while doing the Sharpe Ratio comparisons between comparable schemes. For example, Sharpe Ratio of an equity scheme is not to be compared with the Sharpe Ratio of a debt scheme.

**Treynor Ratio**

Treynor Ratio is one of the methods to establish the relation between risk free return and expected return from the fund. Also known as reward-to-volatility ratio, Treynor ratio is the excess return generated by a fund over and above the risk free return (government bond yield).

It is similar to Sharpe ratio though one difference is that it uses beta as a measure of risk. The performance of fund is termed as good only if Treynor ratio is higher. Since the concept of Beta is more relevant for diversified equity schemes, Treynor Ratio comparisons should ideally be restricted to such schemes.

Treynor Ratio is thus calculated as:

TR = {r - rf} / β

Where

TR – Treynor ratio

r – Portfolio’s return

rf – Risk free rate

β – Portfolio’s Beta

**Alpha**

It is a measure of performance on the basis of risk adjusted return. It is the difference between scheme’s expected return and its actual return. If value of alpha is positive then fund has outperformed the benchmark and vice versa. It shows how much value the fund manager has added to the portfolio beyond the returns generated by a fund’s benchmark.

**Alpha** indicates the excess return of the fund above risk adjusted market return, given its level of risk as measured by Beta. The excess return of the fund over its benchmark index is a fund’s Alpha.

**Beta** is the measure of the volatility of a security or a portfolio as compared to the market as a whole. It is also known as beta coefficient.

**Significance of Alpha & Beta to the investors?**

An investment with a positive Alpha indicates that the fund has performed better than its benchmark and a negative Alpha indicates that the fund has underperformed its benchmark.

A Beta of one indicates that the volatility of the portfolio will reflect the market volatility exactly. A Beta of less than one indicates that the volatility of portfolio is less than the market volatility while a Beta of more than one signifies that the volatility of portfolio is greater than the market.

For example, if a stock's Beta is 1.2, theoretically it means that the stock is 20% more volatile than the market.

**Why these ratios are considered important?**

Alpha value is important to the investors because it measures the excess returns a fund has generated in relation to the returns generated by its benchmark. Alpha is used to determine whether the fund manager through his stock selection ability has been able to beat the market.

Beta value gives an idea of how a fund will move in relation to the market volatility. In simple words, it is a statistical measure that shows how sensitive a fund is to the market movements. If the Sensex moves up by 10%, a fund's Beta number will help the investor to gauge the fund's movement in relation to the Sensex.

Alpha indicates the performance of a fund manager. Since the concept of Beta is more relevant for diversified equity schemes, Alpha should ideally be evaluated only for such schemes.