Question

1A) Risk-averse investors who hold a single stock would require a higher rate of return on a stock whose standard deviation is 0.33 than on a stock whose standard deviation is 0.18. But, if these stocks are held as part of a portfolio, it is possible for the stock with the higher standard deviation to have the lower required return. True/False?

1B) Ceteris paribus, a change in the beta of a firm's stock will change the required rate of return on that stock, as well as the stock's price. True/False?

1C) The distributions of rates of return for companies Alpha and Beta are as follows:

State of the           Probability of

Economy             This State Occurring       Alpha        Beta  

Boom                         0.2 30% -10%

Normal                       0.6 10% 5%

Recession 0.2 -5% 50%

Given the numbers above, we can conclude that a risk-averse investor would be better off adding company Beta to a well-diversified portfolio over company Alpha. True/False?

Answer 1

1a). False - The rate of return of a stock contributes to the return of a portfolio but is not dependent on it so the stock with higher volatility will have a higher return.

1b). False - Beta measures the changes in the stock price (or volatility) so it is dependent upon stock price and not the other way round.

1c).  False - A risk-averse investor will prefer a stock with lower volatility. So, the investor will prefer adding Alpha which has a lower volatility than Beta. (Alpha = 3.3% and Beta = 4.9%. Calculated using STDEV function in excel.)