Question

Problem 7-23 Greta, an elderly investor, has a degree of risk aversion of A 3 when applied to return on wealth over a one-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of 1-year strategies. (All rates are annual and continuously compounded.) The S&P 500 risk premium is estimated at 8% per year, with a SD of 23%. The hedge fund risk premium is estimated at 10% with a SD of 40%. The returns on both of these portfolios in any particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual returns on the S&P 500 and the hedge fund in the same year is zero, but Greta is not fully convinced by this claim. a-1. Assuming the correlation between the annual returns on the two portfolios is indeed zero, what would be the optimal asset allocation? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.) S&P Hedge a-2. What is the expected risk premium on the portfolio? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.) Expected risk premium

Answer 1

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OPTIMAL RISKY PORTFOLIO VC AMORT SINKING JORDAN - Microsoft Excel (Product Activation Failed) Data Review View Add-Ins Formulas - 2x 11 A = = = V General A A AutoSum - A Fill 2 Sort & Wrap Text FMerce Merge & Center Center m Find & E E E File Home Insert Page Layout % Cut Calibri E Copy Paste Format Painter B I U - D Clipboard Font K24 - fi A B s $ - % % 4.0 .00 8. Insert Delete Format Conditional Format Formatting as Table Styles Cell Styles 2 Clear Filter Editing Select Alignment Number Cells D E F G H I J K | L M N O Wo - E(RD) .E - ERRED.R.SE. GD E(RD). 6 + E(RE). ER(E) + E(RD)). r. 5E. D 11 12 17 18 19 20 21 22 23 24 25 WD = weight of s&p WE= weighs of Hedge E(RD) = Risk premium sto E(RE) = Risk premium Hedge DE Standard deviation Str SE= Standard deviation Hedge K M BEST CALBINOMIAL 2 TIME SINKING AMORTIZA Sheet2 VC JORDAN INSURANCE Sheet1 Sheet3 Sheet4 Sheets Sheeth greta I > MIN VAR PORT ferences Sheet8 I BOU 120% Red _ D. . . * ENG NO 24-11-2019

OPTIMAL RISKY PORTFOLIO VC AMORT SINKING JORDAN - Microsoft Excel (Product Activation Failed) Data Review View Add-Ins File Home Insert Page Layout Formulas - 2x % Cut General $ 4.0 .00 :.: Insert Delete Format % % , Number Conditional Format Formatting as Table Styles Cell Styles AutoSum - A Fill Sort & 2 Clear Filter Editing Find & Select Cells H I J K L M N O Calibri 11 A A = = = V Wrap Text E Copy Paste BI U D- DA E E E s Format Painter FMerce Merge & Center - Center Clipboard Font Alignment K28 A B C D E F G 26 27 28 29 SD VARIANCE 30 O (D) 23.00 (o (D))^2 529.00 31 o(E) 40.00 (o (E))^2 1600.00 32 r= 0.0000 33 34 35 W(D) = [=(130)*(G31) - (131)*((G32)*(D30)*(D31))] 36 (=(J30)*(G31)+(131)*(G30)-(130+J31)*((G32)*(D30)*(D31))] 37 38 WEIGHTS W(D )= 0.7076 70.76% 39 W(E) = 0.2924 29.24% E(RD) = R(RE) = 8 10 12800 18090.0 s&p hedge 40 E(RD) = R(RE) = 10 41 42 43 44 45 46 EXPECTED RISK PREMIUM = E(Rp) = W(D)*R(D) + W(E)*R(E ) = (70.76%)*(8%) + (29.24%)*(10%) = 8.5849% K M BEST CALBINOMIAL 2 TIME SINKING AMORTIZA Sheet2 VC JORDAN INSURANCE Sheet1 Sheet3 Sheet4 Sheets Sheeth greta I > MIN VAR PORT ferences Sheet8 I BOU 120% Rea _ 2. 9 * ENG 24-11-2019