A portfolio has 25% of its funds invested in Security C and 75% of its funds invested in Security D. Security C has an expected return of 8% and a standard deviation of 6%.Security D has an
Expected return of 10% and a standard deviation of 10%.The securities have a coeﬃcient of
Correlation of 0.6.Which of the following values are the portfolio return and variance?
A).090; .0081
B).095; .001675
C).095; .0072
D).100; .00849
E)Cannot calculate without the number of covariance terms.

Question

Quizplus · Accepted Answer

To calculate the portfolio return, we need to take a weighted average of the expected returns of Security C and Security D:

Portfolio return = 0.25(8%) + 0.75(10%) = 9.5%

To calculate the portfolio variance, we need to use the formula:

Portfolio variance = w1^2 * σ1^2 + w2^2 * σ2^2 + 2*w1*w2*σ1*σ2*ρ12

where w1 and w2 are the weights of Security C and Security D respectively, σ1 and σ2 are the standard deviations of Security C and Security D respectively, ρ12 is the correlation coefficient between the two securities.

Substituting the given values, we get:

Portfolio variance = 0.25^2 * 6%^2 + 0.75^2 * 10%^2 + 2*0.25*0.75*6%*10%*0.6 = 0.0072 or 0.72%

Therefore, the answer is C, 0.095 and 0.0072.

A Portfolio Has 25% of Its Funds Invested in Security