**Volatility and Beta**

The word volatility is commonly used with reference to the stock market. Many people hesitate to invest in stocks because of volatility. What exactly is volatility? Volatility is variation in prices of a stock over a period. The higher the variation, more volatile is the stock. If the price of a stock varies frequently, then it indicates it is highly volatile. This increases the risk for an investor who would like to invest money. Investors who prefer less risk would not like to invest in highly volatile stocks.

Is it possible to find out how volatile a stock is? Yes, it can be done by using a measure known as beta. Beta (β) or beta coefficient measures the volatility of returns of a stock as compared to the entire market. This is a measure that helps to understand how sensitive the stock is with reference to changes in the stock market (i.e.: market index). A stock whose prices vary in line with the market is less volatile and less risky. A stock whose prices vary more than the market is more volatile and is riskier.

**Why use Beta?**

In the world of finance, a model called Capital Asset Returns Model is used to help an investor calculate the returns of a stock. This model tells the investor what returns he can hope to expect when he invests money in a particular stock. To make this prediction, the model uses the beta coefficient value. This is why calculating the beta is helpful for investors.

Beta is used because it helps an investor know how volatile a particular stock is. The volatility is determined with reference to the overall market index. Beta helps an investor decide whether to invest in a stock or not. An investor who prefers low risk can avoid investing in highly volatile stocks. Similarly, an investor who is ready to take risks in return for rewards can invest money in volatile stocks. Volatility can be determined through the beta coefficient.

**Calculating Beta**

There are different ways of calculating beta coefficient. Most of them need an understanding of statistics. Here’s a simple way if calculating beta. For this, we need three inputs:

- Risk-free return: What is the return one can expect without taking risks? Usually, this is the value of the returns you can get by investing in treasury bills, where there is no risk.
- Market return: This is the average return from the market, calculated using the market index value, at the start and the end of a period.
- Stock return: Just like market return, you need to estimate how much return you obtained from a stock by using its values at the start and end of a particular period.

Let’s assume the risk-free return for a period of three months (one quarter) is 2.5%.

In the same period, the market return is 8.5%

We are trying to calculate the beta of company XYZ. Its return during the same period is 9.5%.

Now, using these values, let’s calculate the beta coefficient.

We need to make two calculations here. One is the variance of the market return as compared to the risk free return, which can be obtained by subtracting the risk-free return from the market return. Let’s refer to this as B. In this example B = 8.5 – 2.5 = 6

In the same way, we can compute the variance of the stock return for XYZ, which is the difference between the stock return and the risk-free return. Let’s refer to this as A. Here A is 9.5 – 2.5 = 7.

Now it’s time to calculate beta. Beta is calculated as A/B.

In this example beta = 7/6 = 1.17. So, the value of β is 1.17

This is a simple way of calculating Beta. There are beta calculators available online that you can use to easily calculate beta with actual data. Excel has an interesting function called Slope that you can use to calculate beta. You can explore all these if you are interested in doing real calculations.

**What does Beta tell us?**

Now that you have calculated beta coefficient for stock XYZ, let us understand what this means.

If the value of β is 1, then it means the stock is as volatile as the market itself.

If the value of β is greater than 1, then it means the stock is more volatile than the market. This indicates the stock has a higher risk and the returns could also be higher.

If the value of β is less than 1 and is non-zero, then it means the stock is less volatile as compared to the market. It is less risky and the returns may not be high.

If the value of β is less than zero, then it means the value of the stock is much less as compared to the market. Such stocks are poor performers.

In the above example, the β value was 1.17, which tells us that stock XYZ is much volatile than the market and represents a higher risk.

You can use β to calculate the expected rate of return. To calculate the expected rate of return for a stock you need to multiply the value of beta by the difference between market rate of return and risk-free rate.

In this case, 1.17 x (8.5 – 2.5) = 1.17 x 6 = 7.02.

Expected rate of return can be obtained by adding this value to the value of risk-free return. So, for stock XYZ it is 7.02 + 2.5 = 9.52%. This means if you invest in this stock you can expect a return of 9.52% on your investment, which is more than the market rate of return.

However, you must remember that all these calculations use past data. There is no guarantee that future returns will mirror that of the past.

The beta is a good way to help an investor estimate how much he can expect to earn from a stock.