Question

1. With the limited information below on monthly returns for a stock and the S&P 500 market index, what would you guess is this stock's CAPM beta?

Month 1: Stock -7.4%, Market -2.0%

Month 2: Stock -4.0%, Market -4.0%

Month 3: Stock +2.2%, Market +0.5%

Month 4: Stock +13.4%, Market +10.8%

Group of answer choices:

a) Beta is greater than one

b) Beta is one

c) Beta is between zero and one

d) Beta is zero

e) Beta is negative

2. A stock has a correlation with the S&P 500 of 0.85. The standard deviation of the stock's returns is 27%. The standard deviation of the S&P 500 is 16%. The S&P 500 is expected to return 7% over the next year, and one-year treasury bills are yielding 1.7%. What return does a diversified investor require to invest in this stock? Group of answer choices:

a) 6.6%

b) 7.2%

c) 8.9%

d) 9.3%

e) 10.5%

f) 12.2%

Answer 1

Answer for question no.1

The correct option is option a. The beta is greater than 1.

When the beta of a stock is more than 1, its returns are more than that of the market , when the market return is positive. The stock's return is lower than market return, when market return is negative.

The stock has displayed these characteristics in 3 out of 4 months. In the second month the stock's return was same as market returns.

Hence, the stock most likely has a beta greater than 1

Answer for question no.2

The formula for calculating Beta of a stock = (correlation between stock and market) * standard deviation of stock / standard deviation of the market or index

Hence, Beta of the stock = 0.85 * 0.27/0.16 = 1.434

US Treasuries are considered risk-free, hence their yield is considered risk-free interest rate

Now that we know the beta of the stock, we can find out the required rate of return on the stock, using the CAPM formula

expected rate of return = risk-free interest rate + { Beta of stock * (market return - risk-free rate of return) }

= 1.7% + {1.434* (7% - 1.7%)}

1.7% + (1.434* 5.3%) = 1.7% + 7.6% = 9.3%

Hence, option D is the right answer