Question

Describe what happens to the expected value and standard deviation of the portfolio returns when the coeffi cient of correlation decreases.

Answer 1

Answer:

Given,

To verify what happens to the expected value and standard deviation of the portfolio returns when the coefficient of correlation decreases.

Consider,

Expected value of portfolio of two stocks = E(R)

E(R) = w1*E(P1) + w2*E(P2)

where as

P1,P2 are the proportion of investments

E(P1) , E(P2) are expected values

Here by observing the formula, we can say that in the given formula there is no coefficient of correlation, so there will be no change in the expected value of portfolio returns.

Now consider,

V(R) = p1^2 * V(R1) + p2^2 * V(R2) + 2p1p2Cov(R1,R2)

= p1^2 + p2^2 + 2p1p2

Here in the formula, is the correlation coefficient

p1 , p2 are the proportion of investments

E(R1) , E(R2) are the expected values

1,1 are the standard deviations

By observing formula , we can say that as the correlation coefficient decreases the standard deviation too decreases.