Question

A portfolio is composed of two stocks, A and B. Stock A has a standard deviation of return of 20%, while stock B has a standard deviation of return of 26%. Stock A comprises 60% of the portfolio, while stock B comprises 40% of the portfolio. If the variance of return on the portfolio is 0.035, the correlation coefficient between the returns on A and B is _________.

A .157

B.392

C.235

D.102

Answer #1

Weight of stock A in the portfolio = wA = 60%, Weight of stock B in the portfolio = wB = 40%

Standard deviation of stock A = σA = 20%, Standard deviation of stock B = σB = 26%

Correlation coefficient between stock A and stock B = ρ

Variance of the portfolio = σ2 = 0.035

Variance of the portfolio is calculated suing the formula:

σ2 = wA2*σA2 + wB2*σB2 + 2*ρ*wA*wB*σA*σB = 0.035

(60%)2*(20%)2 + (40%)2*(26%)2 + 2*ρ*60%*40%*20%*26% = 0.035

0.0144 + 0.010816 + 0.02496*ρ = 0.035

0.025216 + 0.02496*ρ = 0.035

0.02496*ρ = 0.035 - 0.025216

0.02496*ρ = 0.009784

ρ = 0.009784/0.02496 = 0.39198717948718 ~ 0.392 (Rounded to three decimals)

**Answer -> 0.392 (Option B)**

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Multiple Choice
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QUESTION 12
The investor is presented with the two following stocks:
Expected Return
Standard Deviation
Stock A
10%
30%
Stock B
20%
60%
Assume that the correlation coefficient between the stocks is
-1. What is the standard deviation of the return on the portfolio
that invests 30% in stock A?
A.
26%
B.
49%
C.
30%
D.
33%

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is -.23.
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14%
15.6%

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rate of return is 5%. The proportion of the optimal risky portfolio
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Multiple Choice
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