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Using the information in questions 13 and 14, what is your best estimate of the correlation...

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.

Solutions

Expert Solution

given data :-

Return of market portfolio(Rm) = 13.25%

Risk free rate of return (Rf) = 3%

Standard deviation of market portfolio (m) = 18.75%

Beta of stock A (Ba) = 1.95

Beta of stock B (Bb) = 3.75

Lets calculate expected returns of stocks

formula :- Er = Rf + (Rm - Rf) * Beta of stock

expected return for stock A (Ea)

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

Ea = 22.9875 %

Expected return for stock B (Eb)

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

standard deviation of A (a) = 42%

standard deviation of B (b) = 70%

weight of A in portfolio (wa) = 60%

weight of B in portfolio (wb)= 40%

formula for variance of portfolio:-(2p)

2p = w2a * 2a + w2b * 2b + 2 * wa * wb * Covariance(a.b)

where covariance(a,b) = Ba * Bb * 2m

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) = rab * a * b

where rab = correlation between these stocks

putting values,

0.257 = rab * 0.42 * 0.70

On solving we get,

rab = 0.874 (answer)

Note:- Please upvote if you like the answer


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