Question

a. What is the value of the beta of the market portfolio? Explain why the beta of the market portfolio takes that value.

 

b. How do you calculate the beta of a portfolio of securities? Provide a numerical example

 

c. Mention the two statistics you need to estimate beta of a security?

Answer 1

a) Beta is a measure used in fundamental analysis to determine the volatility of an asset or portfolio in relation to the overall market. The overall market has a beta of 1.0, and individual stocks are ranked according to how much they deviate from the market.

Beta is a measure of a stock's volatility in relation to the overall market. By definition, the market, such as the S&P 500 Index, has a beta of 1.0, and individual stocks are ranked according to how much they deviate from the market. A stock that swings more than the market over time has a beta above 1.0


b)Beta could be calculated by first dividing the security's standard deviation of returns by the benchmark's standard deviation of returns. The resulting value is multiplied by the correlation of the security's returns and the benchmark's returns.

For example, if Apple Inc. makes up 0.30 of the portfolio and has a beta of 1.36, then its weighted beta in the portfolio would be 1.36 x 0.30 = 0.408. Add up the weighted beta numbers of each stock. The sum of the weighted betas of all the stocks in the portfolio will give you the portfolio's overall beta


c)The two statistics you need to estimate beta of a security :-

To calculate the beta of a security, the covariance between the return of the security and the return of the market must be known, as well as the variance of the market returns.