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Suppose assets A and B have expected returns r_A, and r_B, standard deviations sd_A and sd_B,...

Suppose assets A and B have expected returns r_A, and r_B, standard deviations sd_A and sd_B, and are positively correlated. What is the standard deviation of a portfolio which contains both A and B?

A. sd_A + sd_B

B. Greater than sd_A + sd_B

C. Less than sd_A + sd_B

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Answer #1

We know that a portfolio having stocks which are not positively correlated brings diversification and reduces teh risk of the portfolio which is measured by standard deviation.

Let the weight of stock A be W1 and weight of stock B be W2 also let teh correlation be r between stock A & B.

Standard deviation of portfolio = [ W1^2*sd_A^2 +W2^2*sd_B^2 + 2*W1*W2*sd_A*sd_B*r ] ^0.50

Here stock A and stock B are positively correlated which means r>1. Hence the third component of the formula will be positive which will add up to sd_A & sd_B.

Hence standard deviation of a portfolio which contains both A and B will be

B.. Greater than sd_A + sd_B

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