Question

Ebenezer Scrooge has invested 45% of his money in share A and the remainder in share B. He assesses their prospects as follows:

	A		B
Expected return (%)	12		22
Standard deviation (%)	15		24
Correlation between returns		0.4

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.)

b. How would your answer change if the correlation coefficient were 0 or –0.40? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

c. Is Mr. Scrooge’s portfolio better or worse than one invested entirely in share A, or is it not possible to say?

• Better

• Worse

• Not possible to say

Answer 1

Working Note 1

Calculation of Expected return of portfolio

E(R) of A = 12% Weight A = 45%

E(R) of B= 22% Weight B = 55% ( Remainder)

E (Portfolio)= 12 *.45 + 22 * .55

= 17.5%

Working Note 2

Calculation of Standard Deviation of Portfolio

S (D) of Portfolio is σP = (wA2σA2 + wB2 σB2 + 2wAwBσAσBρAB)1/2

where,

ωA = weight of asset A in the portfolio;

ωB = weight of asset B in the portfolio;
σA = standard deviation of asset A;
σB = standard deviation of asset B; and
ρAB = correlation coefficient between returns on asset A and asset B.

S(D) of portfolio ={ (.45*.45*.15*.15)+(.55*.55*.24*.24)+(2*.55*.45*.15*.24*.4)}^1/2

= {0.029108}^1/2

=0.170611

Rounded off to 0.17

If Correlation is 0 then SD= 0.15

If Correlation is -0.4 then SD = 0.12

It would be worse of he invest entire in Share A