**Risk-Adjusted Return is one of the concept investors should be aware when comparing returns of mutual funds.***One way of comparing the returns between two different funds is to look at the their relative returns over a period. However, a weakness of this approach is that it does not differentiate between two schemes that have assumed*

*different levels of risk*in pursuit of the same investment objective.

It is possible that although two schemes share the benchmark, their risk levels will differ, and sometimes quite dramatically as well. Evaluating performance, purely based on relative returns, may be unfair towards the fund manager who has taken lower risk but generated the same return as a peer.

*An alternative approach to evaluating the performance of the fund manager is through 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. 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.**There are various measures of risk-adjusted returns. We’ll look at the three most commonly used :

**Sharpe Ratio**An investor can invest with the government, and earn a risk-free rate of return (Rf). T-Bill index is a good measure of this risk-free return.

Through investment in a scheme, a risk is taken, and a return earned (Rs).

The difference between the two returns i.e. Rs – Rf is called risk premium. It is like a premium that the investor has earned for the risk taken, as compared to government’s risk-free return.

This risk premium is to be compared with the risk taken.

*It is calculated as*

**Sharpe Ratio uses Standard Deviation as a measure of risk.**(Rs minus Rf) ÷ Standard Deviation

Thus, if risk free return is 5%, and a scheme with standard deviation of 0.5 earned a return of 7%, its Sharpe Ratio would be (7% – 5%) ÷ 0.5 i.e. 4%.

*scheme is not to be compared with the Sharpe Ratio of a debt scheme.*

**Sharpe Ratio is effectively the risk premium per unit of risk. Higher the Sharpe Ratio, better the scheme is considered to be.**Care should be taken to do Sharpe Ratio comparisons between comparable schemes. For example, Sharpe Ratio of an equity

**Treynor Ratio**Like Sharpe Ratio, Treynor Ratio too is a risk premium per unit of risk.

Computation of risk premium is the same as was done for the Sharpe Ratio.

**However, for risk, Treynor Ratio uses Beta.**Treynor Ratio is thus calculated as: (Rf minus Rs) ÷ Beta

Thus, if risk free return is 5%, and a scheme with Beta of 1.2 earned a return of 8%, its Treynor Ratio would be (8% – 5%) ÷ 1.2 i.e. 2.5%.

**Higher the Treynor Ratio, better the scheme is considered to be. Since the concept of Beta is more relevant for diversified equity schemes, Treynor Ratio comparisons should ideally be restricted to such schemes.**

**Alpha**The Beta of the market, by definition is 1. An index scheme mirrors the index. Therefore, the index scheme too would have a Beta of 1, and it ought to earn the same return as the market. The difference between an index fund’s return and the market return, as seen earlier, is the tracking error.

Non-index schemes too would have a level of return which is in line with its higher or lower beta as compared to the market. Let us call this the optimal return.

The difference between a scheme’s actual return and its optimal return is its Alpha – a measure of the fund manager’s performance. Positive alpha is indicative of out-performance by the fund manager; negative alpha might indicate under- performance.

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

*These quantitative measures are based on historical performance, which may or may not be replicated.*

*Such quantitative measures are useful pointers. However, blind belief in these measures, without an understanding of the underlying factors, is dangerous. While the calculations are arithmetic – they can be done by a novice; scheme evaluation is an art – the job of an expert. *

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*Source : NISM*More on Mutual Funds