## Answers

1 stock fund 2 expected return 3 standard deviation 4 variance 5 correlation 6 covariance 7 T-bill rate bond fund 0.14 0.07 0.43 0.37 0.1849 0.1369 0.0459 0.00730269 0.053 8 portfolio stock fund 9 a) 10 expected return 11 12 weights in portfolio 13 variance of portfolio 14 expected return of portfolio 15 standard deviation of portfolio 0.12 bond fund 0.7143 0.2857 0.108492935 0.1200 32.94% 16 stock fund stock fund 17 18 optimal risky portfolio 19 excess return 20 21 Portfolio weights 22 expected return 23 variance 24 standard deviation Bond fund 0.087 0.017 Bond fund 0.8245 0.1755 0.1277 0.1320 0.3634 25 optimal risky portfolio T-bill 0.896702621 0.10329738 26 27 % invested 28 b-1 29 % invested in T-bill 30 b-2 31 32 % invested 10.33% stock fund Bond fund 15.73% 73.94% 22

1 stock fund 0.14 0.43 =B3*B3 0.0459 =B5*B3*C3 0.053 bond fund 0.07 0.37 =C3*C3 2 expected return 3 standard deviation 4 variance 5 correlation 6 covariance 7 T-bill rate portfolio 0.12 stock fund =(B10-C2)/(B2-C2) =(B12*B12* B4)+(C12*C12* C4)+(2*B12*C12*B6) =(B12*B2)+(C12*C2) =SQRT(B13) bond fund =1-B12 15 9 a) 10 expected return 11 12 weights in portfolio 13 variance of portfolio 14 expected return of portfolio standard deviation of portfolio 16 17 18 optimal risky portfolio 19 excess return 20 21 Portfolio weights 22 expected return 23 variance 24 standard deviation 25 stock fund =B2-$B$ 7 stock fund =((B19*C4)-(C19*B6)/((B19*C4)+(C19*B4)-((B19+C19)* B6)) =(B21*B2)+(C21*C2) =(B21*B21*B4)+(C21*C21*C4)+(2*B21*C21*B6) =SQRT(B23) Bond fund =C2-$B$7 Bond fund =1-B21 26 optimal risky portfolio = (B10-B7)/(B22-B7) T-bill =1-B27 27 % invested 28 b-1 29 % invested in T-bill 30 b-2 =C27 31 stock fund =$B$27*B21 Bond fund =$B$27*C21 32 % invested 33

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