Suppose the expected returns and standard deviations of Stocks A and B are E( R

Question

Suppose the expected returns and standard deviations of Stocks A and B are E(RA) = .088, E(RB) = .148, A = .358, and B = .618.

Calculate the expected return of a portfolio that is composed of 33 percent A and 67 percent B when the correlation between the returns on A and B is .48. (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Calculate the standard deviation of a portfolio that is composed of 33 percent A and 67 percent Bwhen the correlation between the returns on A and B is .48. (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Calculate the standard deviation of a portfolio with the same portfolio weights as in part (a) when the correlation coefficient between the returns on A and B is .48. (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Suppose the expected returns and standard deviations of Stocks A and B are E(RA) = .088, E(RB) = .148, A = .358, and B = .618.

Explanation / Answer

1 a.

XA=.33

XB=.67

Corr(AB)=.48

E(RP)=XA×E(RA)+XB×E(RB)

=.33×.088+.67×.148

=.1282 OR 12.82%

2.(a)

VARIANCE (P)=XA×S.D (A)

+XB×S.D(B)+2(XA)(XB)(S.D (A))(S.D(B))(Corr(AB))

=.33×.358+.67×.618+2(.33)(.67)(.358)(.618)(.48)

=.11814+.41406+.04696

=.57916

S.D(P)=(.57916)^1/2

=.7610

2.(b)

VARIANCE (P)=XA×S.D (A)

+XB×S.D(B)+2(XA)(XB)(S.D (A))(S.D(B))(Corr(AB))

=.33×.358+.67×.618+2(.33)(.67)(.358)(.618)(-.48)

=.11814+.41406-.04696

=.48524

S.D(P)=(.48524)^1/2

=.6966

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