Question

Consider securities in this table:

                                                                        A         B

Standard deviation (%)                                   40        10

Correlation with the market portfolio              0.2       0.6

The expected return on the market portfolio is 9%, and the volatility of the market return is 15%.   The risk free rate of return is 2%.

Calculate the beta of each security?

What is the expected return of each security?

Answer 1

Answer:

Beta of Stock = Correlation of stock with market portfolio * (Standard deviation of stock return / Standard deviation of market return)

Hence:

Beta of Security A = 0.2 * 40% / 15% = 0.533

Beta of Security B = 0.6 * 10% / 15% = 0.40

Beta of Security A = 0.53

Beta of Security B = 0.40

Expected return = Risk free return + Beta * (Market return - Risk free return)

Expected return of Security A = 2% + 0.533 * (9% - 2%) = 5.73%

Expected return of Security B = 2% + 0.40 * (9% - 2%) = 4.80%

Expected return of Security A = 5.73%

Expected return of Security B = 4.80%