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# CH6 - 1 3 E(rP =(0.5 15(0.4 10(0.10 6 = 12.1 a The mean...

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1. E(r P ) = (0.5 × 15) + (0.4 × 10) + (0.10 × 6) = 12.1% 3. a. The mean return should be equal to the value computed in the spreadsheet. The fund's return is 3% lower in a recession, but 3% higher in a boom. However, the variance of returns should be higher, reflecting the greater dispersion of outcomes in the three scenarios. b. Calculation of mean return and variance for the stock fund: (A) (B) (C) (D) (E) (F) (G) Scenario Probability Rate of Return Col. B × Col. C Deviation from Expected Return Squared Deviation Col. B × Col. G Recession 0.3 -14 -4.2 -24.0 576 172.8 Normal 0.4 13 5.2 3.0 9 3.6 Boom 0.3 30 9.0 20.0 400 120.0 Expected Return = 10.0 Variance = 296.4 Standard Deviation = 17.22 c. Calculation of covariance: (A) (B) (C) (D) (E) (F) Deviation from Mean Return Scenario Probability Stock Fund Bond Fund Col. C × Col. D Col. B × Col. E Recession 0.3 -24 10 -240.0 -72 Normal 0.4 3 0 0.0 0 Boom 0.3 20 -10 -200.0 -60 Covariance = -132 Covariance has increased because the stock returns are more extreme in the recession and boom periods. This makes the tendency for stock returns to be poor when bond returns are good (and vice versa) even more dramatic. 6. The parameters of the opportunity set are: E(r S ) = 15%, E(r B ) = 9%, σ S = 32%, σ B = 23%, ρ = 0.15, r f = 5.5% Use Rule 2 and Rule 3 (textbook page 169-170), we can calculate the portfolio expected returns and standard deviations for various portfolio weights.

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