Question

you have a portfolio comprising of 40 percent of Stock A and 60 percent of stock B. If the risk-free rate is 4.0%, what is the portfolio risk premium?

Economy State Probability E(R)-A E(R)-B

Boom 0.40 20% 14%

Normal 0.50 11% 9%

Recession 0.10 -23% -5%

Answer 1

Solution:-

Share of stock A in total portfolio= 40% or 0.4

Share of stock B in total portfolio= 60% or 0.6

Economy	Probability	Expected return- A	Expected return- B	Expected return- Portfolio
Boom	0.4	20%	14%	(20%*0.4+14%*0.6)= 16.4%
Normal	0.5	11%	9%	(11%*0.4+9%*0.6)= 9.8%
Recession	0.1	-23%	-5%	(-23%*0.4 - 5%*0.6)= -12.2%

Based on above, the expected return of total portfolio is as follows:

Expected return (Portfolio)= E(R) Boom*Prob. of Boom + E(R) Normal*Prob. of Normal + E(R) Recession*Prob. of Recession

Expected return (Portfolio)= 16.4%*0.4 + 9.8%*0.5 + (-12.2%*0.1) = 10.24%

Therefore, portfolio risk premium= Expected return (portfolio)-risk free rate = 10.24%-4% = 6.24%