Question

Consider the following information about three stocks: Probability of Rate of Return if State of Economy State State Occurs Stock A Stock B Stock C 0.24 Boom 0.35 0.36 0.55 0.13 Normal 0.50 0.17 0.09 -0.28 Bust 0.15 0.00 -0.45 a. What is the expected return of Stock A? The standard deviation? (6 points) b. If your portfolio is invested 40% each in A and B and 20% in C, what is the portfolio expected return? The standard deviation? (13 points) c. If the expected T-bill rate is 3.8% and the portfolio has a beta of 1.6, what is expected market risk premium? (4 points)

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

A В C E F 1 State of Economy Probability Stock A 2 Stock B Stock C 33 Normal 35.00% 24.00% 36.00% 55.00% 4 50.00% 17.00% 13.00% 9.00% Вoom 15.00% -28.00% 0.00% -45.00% Bust Expected return 14.90% 6 17.00% 16.90% 7 Standard deviation 7.78% 33.38% 20.83% Portfolio's Stock Weight Stock A Stock B Stock C 10 40% 40% 11 12 20% 13 14 Covariance(A,B) 0.016109 Covariance (A,C) Covariance (B,C) 15 0.025120 16 0.068720 17 Variance of Portfolio 0.03253 18 19 Expected return of Stock A Standard deviation of Stock A 16.90% 20 a. 7.78% 21 22 Expected return of Portfolio Standard deviation of Portfolio 23 b. 16.12% 18.04% 24 25 T-bill rate Portfolio beta 26 3.80% с. 27 1.6 7.70% Expected market risk premium 28 29 LO

Cell reference -

A В D F 1 State of Economy Probability Stock A Stock B Stock C 2 Normal 0.24 0.17 0.35 0.36 0.55 4. 0.09 Вoom 0.5 0.13 Bust 0 5 0.15 -0.28 -0.45 -SUMPRODUCT($C$3:$C$5,E3:E5) -SQRT(SUMPRODUCT((D6-D3:D5)^2, $C$3:$C$5)) -SQRT(SUMPRODUCT((E6-E3:ES)^2,$C$3:$C$5)) =SQRT(SUMPRODUCT(( F6- F3: F5)^2,$C$3:$C$5)) Expected return Standard deviation -SUMPRODUCT($C$3:$C$5,D3:D5) -SUMPRODUCT($C$3:$C$5,F3:F5) 6 7 8 Portfolio's Stock Stock A Stock B Weight 9 0.4 10 0.4 11 Stock C 12 -1-C10-C11 13 -SUMPRODUCT((D6-D3 :D5), ( E6-E3:E5),C3:C5) -SUMPRODUCT((D6-D3 :D5), (F6-F3:F5),C3 :C5) -SUMPRODUCT((E6-E3:E5), (F6-F3:F5),C3 :C5) Covariance(A,B) Covariance (A,C) Covariance (B,C) 14 15 16 17 -(C10*D7)A2+ (C11*E7)^2+(C12* F7^2+2*C10*C11*c14+2*C10*C12* c15+2*C11*C12*c16 Variance of Portfolio 18 19 20 a. Expected return of Stock A Standard deviation of Stock A =D6 21 =D7 22 23 b. Expected return of Portfolio Standard deviation of Portfolio =C10*D6+C11* E6+C12* F6 =SQRT(C18) 24 25 26 c. T-bill rate 0.038 Portfolio beta 1.6 27 Expected market risk premium(C23-C26)/C27 28 29

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