What are alpha and beta in mutual funds?

The relationship between risk and return is a foundational concept in investments. You cannot get higher returns without taking risks. A good understanding of risk and risk adjusted returns is required when you evaluate mutual fund performance. For example, if a mutual fund gives high returns you should try to understand if it is due to higher risk taken by the fund manager? In this article, we will discuss different measures of risk and returns - what is alpha and beta in mutual fund - so that you can understand various performance parameters of a mutual fund scheme and make informed investment decisions.

How is risk measured?

In layman terms, risk is the deviation from expected or average returns. A common measure of risk is standard deviation. Standard deviation is a statistical metric which measures the dispersion of returns from the average returns. Higher the standard deviation higher is the volatility. Standard deviation is an absolute measure of risk. For example, standard deviation of returns on equity fund is likely to be higher than a debt fund. Similarly, standard deviation of returns of large cap funds is likely to be lower than midcap funds.

What is beta in mutual funds - A more useful understanding of risk is in relation to the market or rather the relevant market benchmark. Beta of a mutual fund scheme is the volatility of the scheme relative to its market benchmark. If beta of a scheme is more than 1, then scheme is more volatile than its benchmark. If beta is less than 1, then the scheme is less volatile than the benchmark. If a scheme outperformed its benchmark you should try to understand, whether the beta of the scheme was high or the fund manager was able to deliver superior risk adjusted returns.

How are risk adjusted returns measured?

Risk adjusted return factors in the risk taken by the scheme. You should always try to invest in schemes with good track record of superior risk adjusted returns to ensure that you get superior performance without taking more risks than what is required according to your risk appetite. A common measure of risk adjusted returns is the Sharpe Ratio. Sharpe ratio is the ratio of the excess returns of the scheme over risk free rate to the standard deviation of the scheme. Higher the Sharpe Ratio, higher is the risk adjusted returns.

The limitations of Sharpe Ratio are as twofold. Firstly, Sharpe Ratio does not distinguish between good and bad volatility. When a scheme gives high returns, its standard deviation will also be high, but this is good volatility. When a scheme gives low returns, its standard deviation will be high but this is bad volatility. This limitation of Sharpe Ratio is solved by using a ratio called Sortino ratio. The calculation of Sharpe and Sortino ratio is almost the same with one major difference – Sortino ratio only shows downside volatility i.e. volatility in down markets. The second limitation of Sharpe ratio, as well as the Sortino ratio, is that it does not distinguish between market risk and excess risk over market.

What is alpha in mutual funds - Both the limitations of Sharpe Ratio are addressed by using a metric known as alpha. Alpha is the excess returns relative to market benchmark for a given amount of risk taken by the scheme. Alpha in mutual funds is probably the most important performance measures of a mutual fund scheme. If a scheme outperformed the benchmark, then alpha will tell you whether the outperformance was due to higher risk or the fund manager’s skill of delivering superior risk adjusted returns.

So far we have discussed what is alpha and beta in mutual fund, let us see how alpha and beta in mutual fund are calculated.

Calculation of alpha and beta in mutual funds

To understand alpha and beta, one needs a basic understanding of Capital Asset Pricing Model (CAPM). CAPM is the mathematical relationship of fund returns and market risk. The mathematical equation of CAPM is as follows:-

If you rearrange the above equation then, you get the formula for beta:-

Please note that this is a simplistic formula for beta for the purpose of your understanding. Actually, beta is calculated statistically by fitting a line through a plot of excess monthly returns of the fund over risk free rate (on Y-axis) versus excess monthly returns of market benchmark over risk free rate – the slope or gradient of the best fit line through this plot is the Beta of the fund. Beta is calculated in Excel using Regression tool in the Data tab. You may need to install data analysis pack in Excel unless it is already installed.

From the point of view of investors, the calculation of beta is not as important as the understanding of beta. Beta of a scheme is disclosed on a monthly basis in the scheme factsheet.

Let us assume that a scheme’s beta is 1.5 and its benchmark is Nifty – 100. If Nifty – 100 rises by 10% in a year, then according to CAPM, the fund returns will be = 4% + 1.5 X (10% - 4%) = 13% (assuming risk free rate is 4%). However, if Nifty – 100 falls by 5%, the fund return will be = 4% + 1.5 X (-5% - 4%) = -9.5%. Clearly higher the beta, higher is the risk. You should check the beta of a fund and invest according to your risk appetite.

In the above example, we saw that CAPM predicted the fund to outperform the benchmark when market was up. The actual returns of a fund may be different from what is predicted by CAPM. The difference in actual returns versus what is predicted by CAPM is known as Alpha in mutual funds. The mathematical equation for alpha is:-

Continuing with the previous example, CAPM predicted that the fund will give 13% when Nifty – 100 rises by 10%, but the actual return of the fund was 15%. Where did this extra 2% come from? This extra 2% return is the value added by the fund manager of the scheme through superior stock selection. This 2% is the Alpha of the fund. If the fund manager is able to maintain this alpha in down-market also, then if Nifty – 100 falls by 5%, then fund return will be = 4% + 1.5 X (-5% - 4%) + 2% = -7.5%. You can see that alpha is not just about giving high returns in bull markets, but also limiting downside when market is down.

Conclusion

In this article we discussed different risk ratios of mutual funds. Alpha and beta in mutual fund are the two most important risk ratios. What is a good alpha and beta? Anything more than zero is a good alpha; higher the alpha ratio in mutual fund schemes on a consistent basis, higher is the potential of long term returns. Generally, beta of around 1 or less is recommended. If your fund beta is less than 1, make sure that the fund alpha is high enough so that you can meet your financial goals. If you are fund beta is more than 1, then make sure that you are comfortable with the risk, as per your risk capacity.

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