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# Expected return and standard deviation for a portfolio

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4.

Asset 1 Asset 2
E(R1) = .12 E(R2) = .16
E(s1) = .04 E(s2) = .06

a. Calculate the expected return and expected standard deviation of a two stock portfolio when r1,2 = - .60 and w1 = .75.

b. Calculate the expected returns and expected standard deviations of a two stock portfolio when r1,2 = .80 and w1 = .60.

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See the attached file.

Asset 1 Asset 2
E(R1) = .12 E(R2) = .16
E(s1) = .04 E(s2) = .06

a. Calculate the expected return and expected standard deviation of a two stock portfolio when r1,2 = - .60 and w1 = .75.

Stock Portfolio Share (w) Expected return ( r ) Standard deviation (s) Correlation (rho)
A (Asset 1) 0.75 0.12 0.04 -0.6
B (Asset 2) 0.25 0.16 0.06
1.00

Expected return = wA rA + wB rB= 0.1300 =0.75*0.12+0.25*0.16
Expected Standard deviation =square root of (wA^2sA^2 + wB^2sB^2+ 2 wAwBrhosAsB)= 0.0242 =square root of (0.75^2*0.04^2+0.25^2*0.06^2+2*0.75*0.25*-0.6*0.04*0.06)

(* means multiplication; ^2 means squared)

Expected return= 0.1300
Expected Standard deviation= 0.0242

b. Calculate the expected returns and expected standard deviations of a two stock portfolio when r1,2 = .80 and w1 = .60.

Stock Portfolio Share (w) Expected return ( r ) Standard deviation (s) Correlation (rho)
A (Asset 1) 0.6 0.12 0.04 0.8
B (Asset 2) 0.4 0.16 0.06
1.00

Expected return = wA rA + wB rB= 0.1360 =0.6*0.12+0.4*0.16
Expected Standard deviation =square root of (wA^2sA^2 + wB^2sB^2+ 2 wAwBrhosAsB)= 0.0455 =square root of (0.6^2*0.04^2+0.4^2*0.06^2+2*0.6*0.4*0.8*0.04*0.06)

(* means multiplication; ^2 means squared)