Question

Consider the following information on two risky asset: Investment A and Investment B. State of the Economy Probability of State of Economy Return on Investment A (%) Return on Investment B (%) Recession 0.4 16% 12% Normal 0.3 18% 14% Boom 0.3 5% 28% a. What is the expected return for Investment A? b. What is the expected return for Investment B? c. What is the standard deviation for Investment A? d. What is the standard deviation for Investment B? e. What is the expected return on a portfolio that is 40% invested in Investment A and the remainder in Investment B? f. What is the standard deviation of the portfolio in part (e) if the covariance between Investment A and Investment B is -0.0016?

Answer 1

Investment A :

State of Economy	Probability (P)	Return on Investment A (x)	Px	x - mean of x	(x - mean of x)^2	P*(x - mean of x)^2
Recession	0.4000	16.0000	6.4000	2.7000	7.29	2.916
Normal	0.3000	18.0000	5.4000	4.7000	22.09	6.627
Boom	0.3000	5.0000	1.5000	-8.3000	68.89	20.667
Expected Return	13.3000	Variance	30.21

a. Expected return for Investment A = 13.3%

c. Standard deviation for Investment A = 30.21^0.5 = 5.5%

State of Economy	Probability (P)	Return on Investment A (x)	Px	x - mean of x	(x - mean of x)^2	P*(x - mean of x)^2
Recession	0.4000	12.0000	4.8000	-1.3000	1.69	0.676
Normal	0.3000	14.0000	4.2000	0.7000	0.49	0.147
Boom	0.3000	28.0000	8.4000	14.7000	216.09	64.827
Expected Return	17.4000	Variance	65.65

b. Expected return for Investmnet B = 17.4%

d,. Standard deviation for Investment B = 65.65^0.5 = 8.10%

e.

Expecetd return on the portfolio = weighted average of the returns where the weights are the proportion of the amount invested in portfolio

= 0.4*13.3 + 0.6 * 17.4 = 15.76%

f. Standard deviation of portfolio = ( w1^2var1 + w2^2var2 + 2*w1*w2* Cov )^0.5

w1 = weight of Investment A = 0.4

w2= weight of investment B = 0.6

var1 = variance of Investment A = 30.21

var2 = variance of Investment B = 65.65

cov = covariance between Investment A & Investment B = -0.0016

Standard deviation of portfolio = ( 0.4^2* 30.21 + 0.6^2*65.65 + 2 *0.4*0.6* -0016 ) ^0.5

= 28.47^0.5

= 5.34%