Question

Ebenezer Scrooge has invested 60% of his money in share A and the remainder in share B. He assesses their prospects as follows:

	A		B
Expected return (%)	15		20
Standard deviation (%)	20		22
Correlation between returns		.5

a. What are the expected return and standard deviation of returns on his portfolio? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Expected return	17.00 %
Standard deviation	18.08 %

b. How would your answer change if the correlation coefficient were 0 or –.5?

Answer 1

Solution:-

(a)

Expected return (Portfolio)= Expected return (Asset A) * Weight of asset A + Expected return (Asset B) * Weight of asset B

Expected return (Portfolio)= 15%*0.6 + 20%*0.4

Expected return (Portfolio)= 17%

The standard deviation of a two asset portfolio is represented as follows:

SD (P)= [(SD A)² * (W A)² + (SD B)² * (W B)² + 2*(SD A)*(SD B)*(W A)*(W B)*Correlation]^(1/2)

where,

SD (P)= Standard deviation of the portfolio

SD A= Standard deviation of asset A

SD B= Standard deviation of asset B

W A= Weight of asset A in the portfolio

W B= Weight of asset B in the portfolio

Thus, putting the values we get as follows:

SD (P) =[(0.20)² * (0.6)² + (0.22)² * (0.4)² + 2*(0.20)*(0.22)*(0.6)*(0.4)*0.5]^(1/2)

SD (P)= (0.0144 + 0.007744 + 0.01056)^(1/2)

SD (P)= 18.08%

Therefore, the standard deviation of the portfolio is 18.08%

(b)

If correlation coefficient was zero, the expected return would still be the same, however the standard deviation would be as follows:

SD (P) =[(0.20)² * (0.6)² + (0.22)² * (0.4)² + 2*(0.20)*(0.22)*(0.6)*(0.4)*0]^(1/2)

SD (P)= (0.0144 + 0.007744)^(1/2)

SD (P)= 14.9%

If correlation coefficient was -0.5, the expected return would still be the same, however the standard deviation would be as follows:

SD (P) =[(0.20)² * (0.6)² + (0.22)² * (0.4)² + 2*(0.20)*(0.22)*(0.6)*(0.4)*(-0.5)]^(1/2)

SD (P)= (0.0144 + 0.007744 - 0.01056)^(1/2)

SD (P)= 10.8%