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/TSX Composite Index and a hedge fund, as well as a number of one-year strategies. (All rates are annual and continuously compounded.) The S&P/TSX Composite risk premium is estimated at 6% per year, with a SD of 21%. The hedge fund risk premium is estimated at 9% with a SD of 38%. 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 return on the S&P/TSX Composite and the hedge fund return in the same year is zero, but Greta is not fully convinced by this claim.

Assuming the correlation between the annual returns on the two portfolios is 0.3, What should be Greta’s capital allocation? (Do not round intermediate calculations. Enter your answer as percentage rounded to 2 decimals.)

Greta’s capital allocation            

Answer 1

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VC AMORT SINKING JORDAN -Microsoft Excel (Product Activation Failed) OPTIMAL RISK Page Layout File Home Insert Formulas Data Review View Add-Ins Cut E AutoSum - A A Wrap Text Calibri 11 General Copy Fill Merge & Center Conditional Format Formatting as Table Styles Insert Delete Format Paste B I U Cell Sort & Find & % Format Painter Clear Filter Select Alignment Number Clipboard Font Styles Cells Editing F6 Formula Bar D C. G J K L 6 6D E(RE 7 8 9 10 11 EKEE . 12 13 14 15 WDweight of s&p WEE E(RD) E RE) 16 weigntof Hedze Risk premium S4p Risk pemiym Hedse Stan dard deviahon Stendand deviahin Hedgge 17 18 19 20 21 22 23 24 25 26 SINKING AMORTIZA Sheet2VC Sheet3 Sheet4 Sheet5 Sheet8 MIN VAR PORT BEST CAL INSURANCE Sheet1 Sheet6 BINOMIAL 2 TIME JORDAN greta Rea 120% ferences WA 08:16 TENG 18-11-2019

OPTIMAL RISKY PORTFOLIO VC AMORT SINKING JORDAN - Microsoft Excel (Product Activation Failed) File Home Insert Page Layout Formulas Data Review View Add-Ins Σ AutoSum - Cut A A Wrap Text Calibri 11 General ECopy Fill Merge & Center Paste в IU* +.0 .00 .00 0 Conditional Format Cell Insert Delete Format Sort & Find & % Format Painter Clear Filter Select Formatting as Table Styles Number Editing Clipboard Font Alignment Styles Cells fox F26 Formula Bar D A В C F G K L 26 27 28 29 SD VARIANCE (o (D) )A2 (a (E) )A2 441.00 E(RD)= 30 a (D) 21.0000 6 R(RE)= a (E) 31 38.0000 1444.00 9 0.3000 32 r = 33 34 E(30) * (G31)- (J31)*((G32)*(D30)* (D31)] 35 W(D) 6509.4 [=(U30)* (G31)+(J31)* (G30)-(130+J31)*((G32)*(D30)*(D31)] 36 9042.0 37 WEIGHTS W(D )= W(E) = s&p 38 0.7199 71.99% 28.01% hedge 39 0.2801 40 41 E(RD) = 42 6 R(RE)= 43 9 44 EXPECTED RISK PREMIUM = E(Rp) W(D) R(D) + W(E)*R(E ) = (71.99%) * (6%) + (28.01%) * (9%) = 6.8403% 45 46 MIN VAR PORT ΒΙΝΟΜΑΙ ΤΙΜΕ SINKING AMORTIZA Sheet3 Sheet2 VCJORDAN Sheet1 Sheet4 Sheet5 Sheet6 Sheet8 BEST CAL INSURANCE greta 120% Rea erences WA 08:16 TENG 18-11-2019

OPTIMAL RISKY PORTFOLIO VC AMORT SINKING JORDAN - Microsoft Excel (Product Activation Failed) File Home Insert Page Layout Formulas Data Review View Add-Ins Cut Σ AutoSum - A A Wrap Text Calibri 11 General Copy Fill Merge & Center Insert Delete Format Paste B I U +.0 .00 .00 0 Conditional Format Cell Sort & Find & % Format Painter Clear Filter Select Formatting as Table Styles Editing Clipboard Font Alignment Number Styles Cells fx F46 Formula Bar D A В C F G H K L 46 a (D) 47 21 σ (Ε) 48 38 0.3000 49 r= 50 PORTFOLIO VARIANCE = (W(D))^2*(SD(D))^2 + (W(E))^2*(SD(E))^2 + 2 W(D)*W(E)* SD(D)*SD(E)* r 51 PORTFOLIO VARIANCE = [(0.7199)^2*(21)^2 + (0.2801)^2*(38)^2 +2*(0.7199)* (0.2801)*(21)*(38)* (0.3) 52 438.388521 53 PORTFOLIO VARIANCE = [SQRT(variance)] 20.9377 % 54 STANDARD DEVIATION = 55 56 (E(rp))/ (A*(62)) 57 y = (6.8403%)/3(20.9377%) = 58 0.5201078 59 52.01% 60 INVESTMENT PROPORTION y = IN % 61 62 ANSWER INVESTMENT IN S&P 0.7199 x 52.01% 37.44% 0.2801 x 52.01% 63 INVESTMENT IN HEDGE= 14.57% 100% 52.01% 64 INVESTMENT IN T BILL = 47.99% 65 66 MIN VAR PORT BEST CAL SINKING AMORTIZA Sheet3 Sheet2VCJORDAN Sheet1 Sheet5 Sheet6 Sheet8 Sheet4 BINOMIAL 2 TIME INSURANCE greta 120% Rea erences WA 08:16 TENG 18-11-2019