Question

Refer to the following information to answer questions from a to d

Economic Condition	Probability	Return
		Stock Fund	Bond Fund
Recession	1/3	-0.0400	0.07
Normal	1/3	0.0800	0.04
Boom	1/3	0.1400	-0.02

a) What is the standard deviation of the expected return of the stock fund? Your answer: _______________%. (Keep two decimals; Do include the “-” if your answer is a negative number.)

b) What is the standard deviation of the expected return of the bond fund? Your answer: _______________%. (Keep two decimals; Do include the “-” if your answer is a negative number.)

c) Construct a portfolio with equal weights in the stock fund and the bond fund. What is standard deviation of the portfolio return?   Your answer: _______________%. (Keep two decimals; Do include the “-” if your answer is a negative number.)

d) Construct portfolios with 5% increments in the weight of the stock fund. What is the weight of the stock fund that creates the minimum-risk portfolio?   Your answer: _______________%. (Keep two decimals; Do include the “-” if your answer is a negative number.)

Answer 1

Total expected return of the portfolio = - .04 * 1/3 = .0133 ; .08 *1/3 = .0267; .14 *1/3 = .0467

Hence expected return = - .0133 + .0267+.0467= 0.0601 ; deviation from expected value^2 =( -.0133-.0601)^2 + (.0267 - .0601)^2 +(.0467-.0601)^2 = .0054 + .0011 + .0002 = .0067

Hence standard deviation of the expected return of stock fund = .0067 (1/3+1/3+1/3) = .0067 which equals 0.67% Ans a)

Ans b) Expected return of bond fund = 0.07*0.33 +0.04*0.33-0.02*0.33 = .0231+.0132-.0066 = .0297 Deviations = .0066^2 +.0165^2+.0363^2 = .00004+ .00027 +.0013 = .00161

Hence standard deviation of expected return of bond funds = .00161 = 0.16%

Ansc) Expected return of bond fund = 0.5 (.07 + .04 -.02) = .035 + .02 - .01 = .045 . Deviation = .01 , .025, .055

Square of deviation = .0001+.0006+.0030 = .0037 ; now for share fund 0.5 (.14 +.08-.04) = .07 +.04 - .02 = .09; Deviation = .02, .05, .11 ; Square of deviation = .0004, .0025, .0121; hence sum of deviation square = .015.

Hence standard deviation of the portfolio return equals = .015 *.5 + .0037*.5 = .0075 +.00185 = .00935 = 0.94% Answer.