For many investors, the most important test of their mutual fund’s performance is how much their investment grew. In other words, how much returns the fund has given shapes investors’ perceptions about their funds. However, looking at returns only, especially short term returns, can lead you to incorrect conclusions. You should understand that mutual funds are market linked instruments; the returns are also market linked. The same scheme can give different returns in different market conditions. Objective evaluation of a fund’s performance includes both risk and returns. In this article, we will discuss some quantitative measures of fund performance.

Volatility

Standard Deviation is the statistical measure of volatility. In investments, the terms volatility and standard deviation are often used interchangeably. Standard deviation is a measure of dispersion of monthly returns from the Arithmetic Mean or average. In mutual fund performance analysis, volatility is usually measured as the annualized standard deviation of monthly returns over a certain period (e.g. 3 years). In the world of investments, standard deviation is a measure of risk. Higher the standard deviation or volatility, higher is the investment risk and vice versa.

Beta

Beta is a measure of volatility of a scheme. Beta broadly tells us, how much NAV change we can expect, if the market benchmark moves up or down by 1%. The exact mathematical formula of beta is as follows:-

Beta = (Scheme Return – Risk Free Rate) ÷ (Benchmark Return - Risk Free Rate)

The conceptual framework which explains beta is known as Capital Asset Pricing Model. If the beta of a fund is 1.5, risk free rate is 5% and benchmark return is 9%, then scheme return will be 4% X 1.5 + 5% = 11%. On the other hand if benchmark return is -5%, the scheme return will be -10% X 1.5 + 5% = -10%. On other hand if beta is 0.5 and benchmark return is -5%, the scheme return will be -10% X 0.5 + 5% = 0%. Therefore, higher the beta, higher is the risk.

R-Squared

R-Squared is the correlation of a fund’s performance with the benchmark index’s performance. The R-Squared figure demonstrates how much of a fund's NAV changes can be explained by the movements in its benchmark index. The performance of fund whose R-Squared is close to 1 (or 100%) is highly dependent on the benchmark performance. While R squared and beta are closely related they measure different things. Beta measures the NAV sensitivity of the fund to changes in the benchmark, R-Squared measures how much of the fund’s performance can be attributed to benchmark performance. Higher the R-Squared, more relevant is the beta of the fund. R-Squared and beta complement each other as quantitative measures. Used together, Beta and R-Squared can be used to get a picture of how a fund may perform, given a certain performance of the benchmark index.

Sharpe Ratio

Sharpe Ratio is a measure of risk adjusted returns of a mutual fund. Sharpe Ratio tells the investor whether the fund manager delivered high returns by taking more risk or through superior stock selection that will ensure consistent performance in different market cycles. If the return of a fund is high, but the Sharpe Ratio is not high, it means that the fund manager has delivered higher returns by taking more risks. High Sharpe Ratio means that the fund manager has delivered good risk adjusted returns.

Information Ratio

Information ratio is the ratio excess of scheme returns over market benchmark index returns and tracking error of returns. Tracking error is the standard deviation of the difference in returns between the scheme and the benchmark. Information Ratio is a better measure of a fund manager’s performance compared to Sharpe ratio for two reasons:-

• Information Ratio measures performance relative to market benchmark index and not risk free rate. Market benchmark index returns is a more relevant relative measure of equity fund performance compared to risk free rate.
• Information ratio also measures the performance consistency of the fund manager through the tracking error. If the tracking error is low it means that the fund manager is able to outperform the benchmark consistently.

Alpha

Alpha is the excess return over what a scheme would normally get by taking a certain amount of risk. Let us understand this with the help of an example. Let us assume risk free rate is 5%, benchmark return is 9% and beta is 1.5. As per the Beta formula, scheme return should be 4% X 1.5% + 5% = 11%. If the scheme actually delivered 13% return, then the alpha is 2%. Where did you get this extra 2%? From a conceptual standpoint, alpha is the value added by your fund manager. The exact mathematical formula of alpha is as follows:-

Alpha = (Scheme Return – Risk Free Rate) – Beta X (Benchmark Return – Risk Free Rate)

Good fund managers should be able create alphas consistently. Consistently good alphas show the fund manager’s ability of superior stock selection and portfolio construction. Alpha is one of the most important quantitative measures of mutual fund’s performance. You should try to identify funds which consistently deliver good alphas over sufficiently long investment tenures.