Question

Using the information in questions 13 and 14, what is your best estimate of the correlation between stocks A and B? Note that correlation is shown as a number rather than a percentage.

For reference:

The expected rate of return on the market portfolio is 13.25% and the risk–free rate of return is 3.00%. The standard deviation of the market portfolio is 18.75%.  

Stock A has a beta of 1.95 and a standard deviation of return of 42%. Stock B has a beta of 3.75 and a standard deviation of return of 70%. Assume that you form a portfolio that is 60% invested in Stock A and 40% invested in Stock B.

Answer 1

given data :-

Return of market portfolio(R_m) = 13.25%

Risk free rate of return (R_f) = 3%

Standard deviation of market portfolio (_m) = 18.75%

Beta of stock A (B_a) = 1.95

Beta of stock B (B_b) = 3.75

Lets calculate expected returns of stocks

formula :- E_r = R_f + (R_m - R_f) * Beta of stock

expected return for stock A (E_a)

E_a = 3% + (13.25% - 3%) * 1.95

E_a = 22.9875 %

Expected return for stock B (E_b)

E_b = 3% + (13.25% - 3% ) * 3.75

standard deviation of A (_a) = 42%

standard deviation of B (_b) = 70%

weight of A in portfolio (w_a) = 60%

weight of B in portfolio (w_b)= 40%

formula for variance of portfolio:-(²_p)

²_{p =} w²_a * ²_a + w²_b * ²_b + 2 * w_a * w_b * Covariance(a.b)

where covariance(a,b) = B_a * B_b * ²_m

So covariance(a,b) = 1.95 * 3.75 * (0.1875)²

covariance (a,b) = 0.257

There is another formula for covariance

Covariance(a,b) = r_ab * _a * _b

where r_ab = correlation between these stocks

putting values,

0.257 = r_ab * 0.42 * 0.70

On solving we get,

r_ab = 0.874 (answer)

Note:- Please upvote if you like the answer