Chapter: 7 Understanding Risk

Section: 3 Beta (ß)

One of the most popular and commonly used measures of risk is beta (β). This measure quantifies a stock’s risk in relation to the market. It is a measure of the extent to which the returns on a given stock move with the stock market. The tendency of a stock to move with the market is reflected in its beta coefficient (β), which is a measure of the stock’s volatility relative to that of the overall market. The market has a beta of 1.0. Hence, a stock with a beta greater than 1.0 will have a greater volatility than the overall market, and vice versa. Beta is the measure of systematic risk and is calculated as:

            Beta (β)            =          Covariance (Market Index, Stock Price)

                                                        Variance of Market Index

To calculate the variance of the market, a broad based market index such as S&P 500 or Tadawul All Share Index is used. To calculate beta of a stock, we first need to calculate the variance of the market and its covariance with that stock. For these calculations, we can use either historical or expected data. Covariance is the measure of the average tendency of two variables to move in tandem. The covariance of the market and a particular stock is the measure of the extent to which the returns tend to vary with each other, or co-vary. If the value of covariance is negative, it shows that the two assets vary inversely, that is, when one performs well, the other performs poorly. The following hypothetical example using historical data will clarify the concept.

 

The Covariance of Market Index and Stock A is calculated as:

Cov (Mkt, A)	=	(18-8.5)(22-12) + (12-8.5)(16-12) + (-4-8.5)(1-12) + (8-8.5)(9-12) 3
	=	82.67

Hence, Beta (β) would be:

(β)

=

82.67  86.3

=

0.96