Question

Consider the following information about three stocks:

  

				Rate of Return If State Occurs
State of	Probability of
Economy	State of Economy			Stock A			Stock B			Stock C
Boom		.20			.28			.40			.56
Normal		.45			.22			.20			.18
Bust		.35			.00			−.20			−.48

  

a-1	If your portfolio is invested 30 percent each in A and B and 40 percent in C, what is the portfolio expected return? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Portfolio expected return

%

a-2	What is the variance? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.)

  

Variance

  

a-3	What is the standard deviation? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Standard deviation

%

b.	If the expected T-bill rate is 4.20 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected risk premium

%

  

c-1	If the expected inflation rate is 3.80 percent, what are the approximate and exact expected real returns on the portfolio? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Approximate expected real return	%
Exact expected real return	%

c-2	What are the approximate and exact expected real risk premiums on the portfolio? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Approximate expected real risk premium	%
Exact expected real risk premium	%

Answer 1

probability expected return weighted return state of economy rate of return if state occurs (weight x return) Expected return Stock A Stock B Stock C Stock A Stock B stock c (sum of weighted return) Boom | 0.28 0.40 0.56|| 0.08 0.12 0.22 42.80% Normal 0.22 0.20 0.18 0.07 0.06 0.07] | 19.80% Bust | 0.00 -0.20 -0.48|| 0.00 -0.06] -0.19 -25.20% deviation (weighted return- deviation^2 deviation ^2x probability expected return) 34.15% 11.66% 10.02332450 | 11.15% 1.24% 0.00559451 -33.85% 11.46% 0.04010379 0.20 0.45 0.35 8.56% 8.91% -8.82% 8.65% Weight 30.00% 30.00% 40.00% Variance 0.0690 la-1) la-2) [a-3) Portfolio expected return = 8.65% Variance = 0.06902 Standard deviation = variance^0.5= 26.27% Expected risk premium = (8.65%-4.20%) = 4.45%, Real return(approximate) = 4.85%(8.65%-3.80%) Real return(exact) 4.67%(1.0865)/(1.0381-1 (-2) Risk premium(approximate) = Risk premium(real) = 4.45% 4.85%-10.042-0.038) 4.29% 4.67%(1.042/1.0381-1)