Question

Consider the following information on a portfolio of three stocks:

State of Economy	Probability of State of Economy	Stock A Rate of Return	Stock B Rate of Return	Stock C Rate of Return
Boom	.14	.05	.35	.47
Normal	.52	.13	.25	.23
Bust	.34	.19	–.24	–.38

Required:
(a)	If your portfolio is invested 42 percent each in A and B and 16 percent in C, what is the portfolio’s expected return, the variance, and the standard deviation? (Do not round intermediate calculations. Round your variance answer to 5 decimal places (e.g., 32.16161) and input your other answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

Expected return	%
Variance
Standard deviation	%

(b)	If the expected T-bill rate is 4.4 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Expected risk premium

%

Answer 1

A

Expected return in Boom=0.42*0.05+0.42*0.35+0.16*0.47 = 0.2432

Expected return in normal=0.42*0.13+0.42*0.25+0.16*0.23 = 0.1964

Expected return in Bust=0.42*0.19+0.42*-0.24+0.16*-0.38 = -0.0818

portfolio Expected return = Prob. of boom* Expected return in boom+Prob. of Normal* Expected return in Normal+ Prob. of bust* Expected return in bust

=0.14*0.2432+0.52*0.1964+0.34*-0.0818 =0.10836= 10.84 %

Expected Variance= Prob. of boom* (Expected return in boom- Portfolio Expected return)^2+(Prob. of Normal* Expected return in Normal- Portfolio Expected return)^2+ Prob. of bust* (Expected return in bust- Portfolio Expected return)^2

=0.14*(0.2432-0.10836)^2+0.52*(0.1964-0.10836)^2+0.34*(-0.0818-0.10836)^2

=0.018871

Expected Standard Deviation=Variane^1/ = 0.018871^1/2 =0.13737=13.74%

B Expected risk premium = Expected return-Risk free rate= 10.84%-4.4%=6.44%