The following table gives the expected returns and probabilities of various states of nature for securities A and B:

State Probability Return on Asset A Return on Asset B

Boom 0.10 45% 30%

Normal 0.60 20% 25%

Recession 0.30 -10% -5%

Determine:

i. the expected return on each stock.

ii. the standard deviation of returns of each stock.

iii. the coefficient of variation for each stock.

iv. which stock is more volatile. Why

Suppose you use $1 000 000 to construct a portfolio comprising stocks A and B such that you invest $600 000 in A and $400 000 in B. Also, you have done some research and estimated the beta of the stocks to be A = 1.5 and B = 0.75. Use expected returns calculated for each stock in A., above to calculate the expected:

i. return on the portfolio.

ii. beta of the portfolio.