Question

Suppose the expected returns and standard deviations of stocks A and B are E( R_A ) = 0.15, E( R_B ) = 0.21, σ _A = 0.48, and σ _B = 0.72, respectively.

Required:

(a)	Calculate the expected return and standard deviation of a portfolio that is composed of 42 percent A and 58 percent B when the correlation between the returns on A and B is 0.46. (Round your answers to 2 decimal places. (e.g., 32.16))
	Expected return	%
	Standard deviation	%
(b)	Calculate the standard deviation of a portfolio that is composed of 37 percent A and 63 percent B when the correlation coefficient between the returns on A and B is −0.46. (Round your answer to 2 decimal places. (e.g., 32.16))
	Standard deviation	%

Answer 1

a) Expected Return = weight of A * return of A + weight of B * return of B = 42%*0.15+58%*0.21 = 18.48%

Standard Deviation = ((Weight of A * Standard Deviation of A)² + (weight of B* stand =ard Deviation of B)² + 2* Weight of A * Standard Deviation of A * weight of B * standard Deviation of B * correlation)^0.5 = ((42% * 0.48)² + (58%* 0.72)² + 2* 42% * 0.48 **52% * .72 * 0.46)^0.5 = 54.08%

b) Standard Deviation = ((Weight of A * Standard Deviation of A)² + (weight of B* stand =ard Deviation of B)² + 2* Weight of A * Standard Deviation of A * weight of B * standard Deviation of B * correlation)^0.5 = ((37% * 0.48)² + (63%* 0.72)² + 2* 37% * 0.48 *63% * .72 * -0.46)^0.5 = 40.40%

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