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Mutual Funds | There’s no conflict between Sharpe Ratio and Treynor Ratio

Any difference in mutual fund rankings based on these two ratios is due to the difference in the level of portfolio diversification 

July 06, 2022 / 04:40 PM IST
 (Photo by Spencer Platt/Getty Images)

(Photo by Spencer Platt/Getty Images)

Risk and return are two dimensions of investment performance. Investors tend to focus on return, with little regard to the risk involved, while they should look at the risks along with the return. There are many risk-adjusted return ratios, and their performance measures assess the performance of investments in terms of return per unit of risk.

Mutual funds periodically communicate their performance in a document called factsheet. There are a few fund tracking entities providing such information as well. In a typical mutual fund factsheet, investors see return disclosed for different periods of times i.e. since the inception of the fund, last 10 years, last five years, last three years, last one year, etc.

Factsheets also provide information of various measures of risk such as standard deviation and Beta. Standard deviation is a measure of the total risk, while Beta is a measure of market risk. In addition to return and risk, factsheets provide information of some risk-adjusted return measures such as Sharpe Ratio and Treynor Ratio. These risk-adjusted performance measures assess the performance of a fund in terms of return per unit of risk.

Sharpe Ratio calculates the fund’s return in excess of the risk-free return and divides the excess return by the portfolio’s standard deviation. The Sharpe Ratio is a measure of relative performance. It enables investors to compare across investment opportunities. Higher the Sharpe Ratio, better is the ‘Reward to Variability’. A fund with a higher Sharpe Ratio in relation to another is preferable as it indicates that the fund has generated better return for every unit of risk.

Treynor Ratio is computed by dividing a portfolio's excess return, by its Beta. Like Sharpe Ratio, it is a measure of relative performance. The Treynor Ratio is also known as the reward-to-volatility ratio.

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Sharpe and Treynor ratios are used for ranking mutual funds. Sharpe Ratio uses standard deviation of return as the measure of risk, whereas the Treynor Ratio uses Beta (systematic risk). Since the denominator of the Sharpe ratio is a different measure of risk than the Treynor Ratio, it is possible that the ranking of funds on the basis of Sharpe ratio differ from the ranking of the funds on the basis of Treynor Ratio.

Though for a well-diversified portfolio, the two measures would give identical ranking, because the fund would have mostly the non-diversifiable market risk, for a poorly-diversified portfolio, the ranking based on the Treynor Ratio could be higher than that of the Sharpe Ratio. This is because the Treynor Ratio ignores unsystematic risk. Thus, any difference in mutual fund rankings based on these two ratios is due to the difference in the level of portfolio diversification.

In such situation investors have to make a choice between the ranking given on the basis of the Sharpe Ratio or the Treynor Ratio. The thumb rule in the market is that the Sharpe Ratio is more suitable to evaluate the mutual fund’s performance for an investor who has not achieved adequate diversification on their wealth as a whole, and the Treynor Ratio should be used for investors who hold their wealth in well-diversified portfolios.

Given the limited cognitive ability, investors are bound to get confused if the ranking of mutual funds is different on the basis of these two popular ratios. However, when it comes to various kinds of equity funds in India, investors need not worry on this account. The table below shows the Spearman’s Rank Correlation Coefficient (SRCC) between the ranking of various equity funds on the basis of Sharpe and Treynor measures.

Spearman's correlation coefficient measures the strength and direction of association between two ranked variables. The value of the coefficient lies between +1 to -1. Plus-one (+1) indicates a perfect association of ranks, zero indicates no association between ranks, and -1 indicates a perfect negative association of ranks. The table below gives the correlation coefficient between the ranks assigned on the basis of Sharpe and Treynor ratios.

Spearman’s Rank Correlation Coefficient For Equity Funds

Spearman’s Rank Correlation Coefficient For Equity Funds

*Data for calculation is for three-year period

It is clear that there is a close to +1 correlation coefficient across the categories of funds chosen. This shows that whether these funds are outperforming their benchmarks or not, they are ranked almost the same on the basis of both the ratios.

Given that investors are rationally bound, it is a good news. This means that there is no ranking conflict — which means that is one less thing to worry about while choosing a fund.
Rachana Baid is faculty at the National Institute of Securities Management (NISM). Views are personal.
first published: Jul 6, 2022 04:40 pm
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