Question

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 one-year strategies. All rates are annual and continuously compounded.) The S&P 500 risk premium is estimated at 6.6% per year, with a SD of 21.6%. The hedge fund risk premium is estimated at 11.6% with a SD of 36.6%. 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. Calculate Greta's capital allocation using an annual correlation of 0.3. (Do not round your intermediate calculations. Round your answers to 2 decimal places.) S&P Hedge Risk-free asset

Answer 1

OPTIMAL RISKY PORTFOLIO VC AMORT SINKING JORDAN - Microsoft Excel (Product Activation Failed) File Home Insert Page Layout Formulas Data Review View Add-Ins * Cut Calibri 11 AA = D. Wrap Text General Ea Copy Paste BI U. - E A Merge & Center - $ -% , Conditional Format Cell Format Painter Insert Delete Format Formatting as Table Styles Clipboard Font Alignment Number Styles Cells 16 AB Σ AutoSum Fill Sort & 2 Clear Filter Editing Find & Select L MNO C Wo - D E F G H I J K ElRD). E- ELRE).E.GE 6D ERD). 6 + E(RE). -ERO+E(R)). 2.06.09 WD = weight of s&e WE= weight of Hedge E(RD) = Risk premium sto E(RE) = Risk premium Hedge DE Standard deviation S4P. TE = Standard deviation Hedge 25 26 K M BEST CALBINOMIAL 2 TIME SINKING AMORTIZA Sheet2 VC JORDAN INSURANCE Sheet1 Sheet3 Sheet4 Sheets Sheeto greta MIN VAR PORT ferences Rea Sheet8 D DOO 120% 0 + m * NG 12:00 TENO 21-11-2019 10 ENG S EX 9

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 Calibri A = = = V General 11 B- A A Wrap Text FMerce Merge & Center - Center AutoSum - A Fill 2 Sort & m Find & B I U E E E s $ -% % 4.0 .00 . Insert Delete Format Conditional Format Formatting as Table Styles Cell Styles 2 Clear Filter Editing Select E Copy Paste Format Painter Clipboard 126 A B Font Alignment Number Cells C D E F G H I J K L M N O 26 27 28 SD (D) o(E) 21.6000 36.6000 VARIANCE (0 (D))^2 (o (E))^2 466.56 1339.56 0.3000 E(RD) = R(RE) = 6.6 11.6 29 30 31 32 33 34 35 W(D) = 36 37 38 39 [=(130)*(G31) - (131)*((G32)*(D30)*(D31))] [=(J30)*(G31)+(131)*(G30)-(130+J31)*((G32)*(D30)*(D31))] 6089.947 9936.7 WEIGHTS W(D )= W(E) = 0.6129 0.3871 61.29% 38.71% s&p hedge 40 E(RD) = R(RE) = 6.6 11.6 41 42 43 44 45 46 HEM Rea EXPECTED RISK PREMIUM = E(Rp) = W(D)*R(D) + W(E)*R(E ) = (61.29%)*(6.6%) + (38.71%)*(11.6%) = 8.5356% M IN VAR PORT ferences BEST CALBINOMIAL 2 TIME SINKING AMORTIZA Sheet2 VC JORDAN INSURANCE Sheet1 Sheet3 Sheet4 Sheets Sheeto greta Sheet8 | 0 203 120% 1 + * * OENG 21-11-2019 ODOB 9

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 Calibri A = = = V General 11 B- A A Wrap Text Merge Merge & Center - Center B I U SF $ -% % 4:0 .00 . Insert Delete Format Conditional Format Formatting as Table Styles Cell Styles AutoSum - A Fill Sort & 2 Clear Filter Editing Find & Select Font Alignment Number Cells C D E F G H I J K L M N O E Copy Paste Format Painter Clipboard 165 A B 46 47 48 49 50 51 52 53 54 55 0 (D) 0 (E) 21.6 36.6 0.3000 PORTFOLIO VARIANCE = (W(D))^2* (SD(D))^2 + (W(E))^2*(SD(E))^2 + 2 W(D)*W(E)* SD(D)*SD(E)* PORTFOLIO VARIANCE = [(0.6129)^2* (21.6)^2 + (0.3871)^2*(36.6)^2 + 2*(0.6129)*(0.3871)*(21.6)*(36.6)*(0.3)] PORTFOLIO VARIANCE = 488.527765 STANDARD DEVIATION = 22.1027 % [SQRT(variance)] 56 58 57 (E(rp))/(A*(62)) (8.5356%)/3(22.1027%) = 0.58240562 59 60 INVESTMENT PROPORTION y = 58.24% 61 62 ANSWER INVESTMENT IN S&P = 0.6129 X 58.24% 63 INVESTMENT IN HEDGE= 0.3871 X 58.24% 64 INVESTMENT IN I BILL = 100%- 58.24% IN % 35.69% 22.55% 41.76% 65 66 HEM Rea M IN VAR PORT ferences BEST CALBINOMIAL 2 TIME SINKING AMORTIZA Sheet2 VC JORDAN INSURANCE Sheet1 Sheet3 Sheet4 Sheets Sheeto greta Sheet8 | 0 203 120% 1 + * * OENG 21-11-2019 ODOB 9