Question

4-) (20 points) Rf=2%, Rm= 10%

According to the CAPM model

Expected Return X= 10

Expected Return Y= 6

Portfolios:

A portfolio of stock X and rf with a 50% equal weighted investment yielded a STANDARD DEVIATION of 3.

A portfolio of stock Y and rf with a 25% investment in stock Y yielded a STANDARD DEVIATION of 1.

A portfolio of the market and rf with a 50% investment in the market yielded a STANDARD DEVIATION of 1.

An equally weighted portfolio of stock X and Y yielded a variance of 1.

Find the variance of the portfolio that invests EQUALLY WEIGHTED in X, Y, and Rf.

Find the BETA of the portfolio that invests EQUALLY WEIGHTED in X, Y, and Rf.

Answer 1

A B с DE F G н K L M N 1 Answer to Part a. 2 3 4 5 6 7 Standard Deviation Rf^2 Standard Deviation X^2 36.00 Standard Deviation Y^2 16.00 Weight Rf^2 11.11% Weight X^2 11.11% Weight Y^2 11.11% Correlation Cofficient xrf Correlation Cofficient xrf Correlation Cofficient xy -1.00 Variance of Portfolio 0.44 =(N2*N5)+(N3*N6)+(N4*N7)+(2*D19*D20*N10*J17* J18) 8 9 10 Risk Free Return = Rf 2.00%|Using CAPM Model E{R} = Rf + B* (Rm-Rf) Standard Deviation Rf Market Return = Rm 10.00% Expected Return Y E{R} = Rf + By *(Rm-Rf) Correlation Cofficient xrf Expected Return X = E{R} X 10.00% Beta of Stock Y By = (E{R} - Rf)/(Rm-Rf) Standard Deviation X SDxrf = WX * SDX Expected Return Y E{R} Y 6.00% Beta of Stock Y 0.50 Standard Deviation X SDx = SDxrf / Wx Standard Deviation = SDxrf 3.00% =(D5-D2)/(D3-D2) Standard Deviation X 6.00% =D6/D7 Weight x = Pxrf 50.00% Weight rf = Pxrf 50.00% Standard Deviation Rf Standard Deviation = SDmrf 1.00% Using CAPM Model E{R} = Rf +B*(Rm-Rf) Correlation Cofficient xrf Weight y = Pyrf 25.00%|Expected Return X E{R} = Rf + Bx *(Rm-Rf) Standard Deviation Y SDyrf = Wy * Sdy Weight rf = Pyrf 75.00% Beta of Stock X Bx = (E{R} - Rf)/(Rm-Rf) Standard Deviation Y SDy = SDyrf / Wy Standard Deviation = SDmrf 1.00% Beta of Stock X 1.00 Standard Deviation Y 4.00% =D9/010 Weight m = Pmrf 50.00% =(D4-D2)/(D3-D2) Weight rf = Pmrf 50.00% Variance 1.00 Variance = Pxy 0.01 Weight X^2 0.25 Weight X = Pxy 50.00%|Expected Return X 10.00% Weight Y^2 0.25 Weight Y = Pxy 50.00%| Expected Return Y 6.00% Standard Deviation X 6.00 Weight Rf = Prfxy 33.33% Risk Free Return 2.00% Standard Deviation Y 4.00 Weight x = Prfxy 33.33% Portfolio Return 6.00% Correlation Cofficient xy -1.00 Weight Y = Prfxy 33.33% =G16*D18+G17*D19+G18*D20 =(J14-(((J15)*((11742)))+((J16)*(J18^2))))/(2*D16*D17*J17*J18) 11 12 Answer to Part b. 13 14 15 16 17 18 19 20 21 Using CAPM Model Beta of Portfolio Beta of Portfolio Beta of Portfolio E{R} = Rf +B*(Rm-Rf) E{R} = Rf + Bp *(Rm-Rf) Bp = (E{R} - Rf)/(Rm-Rf) 0.50 =(G19-D2)/(D3-D2)