An investor has a $200,000 portfolio of which $120,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are shown in the accompanying table. Stock A Stock BE(RA ) = μA = 8.4% E(RB ) = μB = 6.5%σA = 11.82% σB = 7.19%Cov(RA,RB ) = σAB = 17.10% The correlation coefficient between the returns on Stocks A and B is _____.Multiple Choice0.80−0.174.970.20
Question
An investor has a 120,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are shown in the accompanying table. Stock A Stock BE(RA ) = μA = 8.4% E(RB ) = μB = 6.5%σA = 11.82% σB = 7.19%Cov(RA,RB ) = σAB = 17.10% The correlation coefficient between the returns on Stocks A and B is _____.Multiple Choice0.80−0.174.970.20
Solution
The correlation coefficient (ρ) between the returns on Stocks A and B can be calculated using the formula:
ρ = Cov(RA, RB) / (σA * σB)
where: Cov(RA, RB) is the covariance between the returns on Stocks A and B, σA is the standard deviation of the returns on Stock A, and σB is the standard deviation of the returns on Stock B.
Given that Cov(RA, RB) = 17.10%, σA = 11.82%, and σB = 7.19%, we can substitute these values into the formula to find the correlation coefficient:
ρ = 17.10% / (11.82% * 7.19%)
After calculating the above expression, we will get the correlation coefficient between the returns on Stocks A and B.
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