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Stock JAY has an expected return of 13 percent and a standard deviation of 75 percent....

Stock JAY has an expected return of 13 percent and a standard deviation of 75 percent. Stock ELIZABETH has an expected return of 9 percent and a standard deviation of 42 percent. The covariancr between the two stocks is .07. you invest 1/3 of your money in JAY and the rest in ELIZABETH. What is the variance of the portfolios returns?

Expert Solution

Let expected return of jay is X = 13%

& expected return of elizabeth is Y = 9%

Other given data:

Standard deviation of X (jay) _x= 0.75

Standard deviation of Y (elizabeth) _y = 0.42

covariance between x(jay) and y (elizabeth) i.e., cov(x,y)= 0.7

There is a portfolio (p) consist of X (jay) with weight 1 / 3 and Y (elizabeth) with weight 2 / 3

so, w_x= 1 / 3 and w_y= 2 / 3

Calculation of variance of portfolio (p):-

formula:-

²_p
= w²_x * ²_x + w²_y * ²_y + 2 * w_x * w_y * Covariance(x,y)

Lets put value in the above formula

²_p = (1 / 3)² * (0.75)² + (2 / 3)² * (0.42)² + 2 * (1 /3 ) * (2 / 3) * 0.7

on solving we get,

variance of portfolio i.e ²_p = 0.0625 + 0.0784 + 0.3111

So variance of portfolio i.e., ²_p = 0.452

jeff jeffy answered 1 year ago

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