Question

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.9%. The probability distributions of the risky funds are:   

	Expected Return		Standard Deviation
Stock fund (S)	20	%	49	%
Bond fund (B)	9	%	43	%

The correlation between the fund returns is .0721.

Suppose now that your portfolio must yield an expected return of 18% and be efficient, that is, on the best feasible CAL.

a. What is the standard deviation of your portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Standard deviation             %

b-1. What is the proportion invested in the T-bill fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Proportion invested in the T-bill fund             %

b-2. What is the proportion invested in each of the two risky funds? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

	Proportion Invested
Stocks	%
Bonds	%

Answer 1

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OPTIMAL RISKY POR VC AMORT SINKING JORDAN - Microsoft Excel (Product Activation Failed) File Home Insert Page Layout Formulas Data Review View Add-Ins E AutoSum - Cut AC Wrap Text Calibri 11 General E Copy Fill Merge & Center Paste B I U Conditional Format Cell Insert Delete Format Sort & Find & % Format Painter Clear Filter Select Formatting as Table Styles Alignment Clipboard Font Number Styles Cells Editing fox 196 Formula Bar A В C D F G Н K M 96 97 E(rS)= 98 opHma risky Port folio 20 E(rB) 99 rf = 100 5.9 a (S) 101 49 Ws E(A) E()-FCouCE,S) σ (Β) 102 43 103 rBS = 0.0721 Els)-A Ea)- 104 covCes 105 106 -ElA)- Afr E)-f aes) cov(B,S) = 107 151.91470 108 109 (L98-L100)*(L102^2) - (L99-L100)*(L107) |(L98-L100)*(L102^2) + (L99-L100)*(L101^2) - (L98-L100+L99-L100) *(L107) 110 Ws = 25599.96 30901.07 111 112 82.84% 113 Ws = 0.8284 WEIGHT OF STOCK FUND WB 0.1716 114 17.16% WEIGHT OF BOND FUND JORDAN Sheet2VC Sheet3 INSURANCE Sheet1 Sheet6 Sheet8 Sheet4 Sheet5 MIN VAR PORT BEST CAL BINOMIAL 2 TIME SINKING AMORTIZA greta 130 % erences WA 09:07 1ENG 30-11-2019

OPTIMAL RISKY POR VC AMORT SINKING JORDAN - Microsoft Excel (Product Activation Failed) Page Layout File Home Insert Formulas Data Review View Add-Ins E AutoSum - Cut AC Wrap Text Calibri 11 General Copy Fill Sort & Find & Filter Select в IU- Merge & Center Paste 000 Conditional Format Cell Insert Delete Format % Format Painter Clear Formatting as Table Styles Alignment Clipboard Font Number Styles Cells Editing fox 1134 В D Е G Н К M Expected return on portfolio 116 117 (wsCECas 118 EP) 119 120 E(rp) (E113*L98) (E114*L99) 121 18.1129 % Е(rp) - 122 18.11 % variance of portfolio 123 a) 124 2 2 P= w 125 126 127 +2.ww2 CovCB,s) 128 129 130 o2 p (E113^2)*(L101A2) +(E114^2)*(L102^2) +2*(E113)*(E114)*(L107) 131 1745.4698 % 132 133 41.7788 % STANDARD DEVIATION op 134 41.78 % op= Sheet2 VC JORDAN INSURANCE Sheet3 Sheet6 Sheet1 Sheet8 Sheet4 Sheet5 MIN VAR PORT BEST CAL BINOMIAL 2 TIME SINKING AMORTIZA greta 130 % erences WA XУ 09:07 1ENG 30-11-2019

VC AMORT SINKING JORDAN -Microsoft Excel (Product Activation Failed) OPTIMAL RISKY POR File Home Insert Page Layout Formulas Data Review View Add-Ins E AutoSum - Cut AC Wrap Text Calibri 11 General Copy Fill в IU- Merge & Center Sort & Find & Filter Select Paste 000 Conditional Format Cell Insert Delete Format % Format Painter Clear Formatting as Table Styles Alignment Clipboard Font Number Styles Cells Editing fx К151 В C D Е F G Н К M 135 Expected Retum en feasible Pofisho besr 136 CAL 137 138 Rehum - 139 140 y(18.1129%)(1-y) (5.9%) 18%= 141 142 y(18.1129%)+5.9% -(y)(5.9%) 18%= 12.1% y(12.2129%) 143 investment in risky fund 144 0.9908 99.08% У 3 145 Standardderiakn ts por fotio 146 147 EM) ECre2 148 149 150 |((18.1129% -5.9%)/(41.7788%))*(6c) 18%= 5.9%+ 151 12.2129%/(41.7788%) *(6c) 12.1%= 152 41.3925 % standard deviation of portfolio 153 ANS a 41.39 % OC Sheet2 VC JORDAN INSURANCE Sheet3 Sheet4 Sheet1 Sheet6 Sheet8 MIN VAR PORT Sheet5 4 BEST CAL BINOMIAL 2 TIME SINKING AMORTIZA greta 130 % erences WA 09:07 1ENG 30-11-2019

OPTIMAL RISKY PORTFOLIO VC AMORT SINKING JORDAN - Microsoft Excel (Product Activation Failed) File Home Insert Page Layout Formulas Data Review View Add-Ins E AutoSum - Cut AS Wrap Text Calibri 11 General Copy Fill Merge & Center Sort & Find & Filter Select Paste в IU* $ %, +.0 .00 .00 0 Conditional Format Cell Insert Delete Format Format Painter Clear Formatting as Table Styles Clipboard Font Alignment Number Styles Cells Editing fox K171 A В C D E F G Н K L M P standard deviation of portfolio 41.39 % 153 ANS a 41.3925 % OC 154 155 ANS b b-1 0.92% proportion in T-bill 100% 99.08% 99.08% x b-2 82.08% 156 82.84% proportion in stock proportion in bonds 99.08% X 17.16% 17.00% 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 SINKING AMORTIZA Sheet3 MIN VAR PORT Sheet2VCJORDAN Sheet1 Sheet5 Sheet6 Sheet4 Sheet8 BEST CAL BINOMIAL 2 TIME INSURANCE greta Rea erences 130% WA 09:07 1ENG 30-11-2019