Question

True or False? -- Stock A has an expected return of 7% and a standard deviation of 8%. Stock B has an expected return of 9% and a standard deviation of 10%. If the portfolio that consists of 50% stock A and 50% stock B has a standard deviation of 8%, the correlation coefficient of stocks A and B must be 0.88.

Answer 1

Standard Deviation of Portfolio = [(Standard Deviation A)^2(Weight A)^2 + (Standard Deviation B)^2(Weight B)^2 + 2(Standard Deviation A)(Standard Deviation B)(Weight A)(Weight B)(Correlation Coefficient)'^1/2

Standard Deviation when correlation coefficient is 0.88 = [(8%)^2(0.5)^2 + (10%)^2(0.5)^2 + 2(8)(10)(0.5)(0.5)(0.88)]^1/2

= 8.7293%

Hence, the given statement is FALSE as Standard Deviation of portfolio given is different from Standard Deviation with Correlation coefficient at 0.88