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 3.0%. The probability distributions of the risky funds are:   

	Expected Return		Standard Deviation
Stock fund (S)	12	%	41	%
Bond fund (B)	5	%	30	%

The correlation between the fund returns is .0667.

Suppose now that your portfolio must yield an expected return of 9% 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 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	%

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 3.0%. The probability distributions of the risky funds are Standard Deviation Stack Fund (5) Expected Return 12% Bond fund (3) The correlation between the fund returns is .0667 Suppose now that your portfolio must yield an expected return of 9% 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.) Answer is not complete. 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-bil fund %

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 Wrap Text Merge Merge & Center Center m Find & SF $ - % % 4:0 .00 8. Insert Delete Format Conditional Format Formatting as Table Styles Cell Styles AutoSum - A Fill 2 Sort & 2 Clear Filter Editing Select Alignment Number Cells File Home Insert Page Layout % Cut Calibri Ea Copy Paste Format Painter B I U - D Clipboard Font M110 А в 97 98 99 K L M N O P Optimal risky Portfolio 100 E(rs) = E(rB) = rf = O(S) 0 (B) rBS = 41 101 102 30 0.0667 103 104 105 Ws. 1E(Ms) – ef 15 - E(Mos) - ef | CouC B,s), Elrs)-if | 8 + 8(26)-26.8 - Elns) - nf + 6(23) -rf.cov 8,5) CONCB,s) = ros. Iss 106 107 COV(B,S) = 82.04100 108 109 110 111 Ws = (L98-L100) *(L102^2) - (L99-L100)*(L107) (L98-L100)*(L10242) + (L99-L100)*(L101^2) - (L98-L100+L99-L100)*(L107) 7935.918 10559.55 112 113 Ws = WB = 0.7515 0.2485 75.15% 24.85% WEIGHT OF STOCK FUND WEIGHT OF BOND FUND 114 115 HEM Red MIN VAR PORT BEST CAL BINOMIAL 2 TIME SINKING AMORTIZA Sheet2 VC JORDAN INSURANCE Sheet1 Sheet3 Sheet4 Sheets Sheeto greta Sheets I THE TW 130% 6 0 +) 4 * 4 OENG 03-11-2019 DO

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 = = = V General Wrap Text FMerce Merge & Center Center E E E s $ - % % 4.0 .00 8. Insert Delete Format Conditional Format Formatting as Table Styles Cell Styles AutoSum - A Fill Sort & 2 Clear Filter Editing Find & Select Alignment Number Cells E F G H L M N O P Emp) = (ws) Cerrs)) + (ws) (Elnas) Calibri 11 A A E Copy Paste Format Painter B I U - D A Clipboard Font M134 Α B C D 116 Expected return on portfolio: 117 118 119 120 121 E(rp) = 10.2608 % E(rp) = 10.26 % 123 variance of portfolio: 124 125 126 127 128 129 130 131 o? p = 1035.6463 % (E113*L98) + (E114*L99) 0.1026 122 888 = (ws}(053² (W3) Coor +2.0, W2 CovC3,5) (E113^2)*(L101^2)+(E114^2)*(L102^2)+2*(E113)*(E114)*(L107) 132 133 134 op = op = MIN VAR PORT 32.1815 % 32.18 % BEST CAL BINOMIAL 2 TIME STANDARD DEVIATION 0.3218 SINKING AMORTIZA Sheet2 VC JORDAN INSURANCE Sheet1 Sheet3 Sheet4 Sheets Sheeto HEM Red greta Sheets I | THE I7 130% 0 +) 4 * 4 OENG 03-11-2019 DO

- 2x Σ AutoSum : A Fill Sort & 2 Clear Filter Editing Find & Select M N O P ? 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 A A = = = V Wrap Text General E Copy Paste BI U D- DA E E E s FMerce Merge & Center - Center Format Painter $ % % , 4.0 .00 :.: Conditional Format Cell Insert Delete Format Formatting as Table Styles Clipboard Font Alignment Number Styles Cells L135 A J K L 135 136 137 138 139 140 141 9% = y(10.2608%) + (1-y)(3%) 142 9% = y(10.2608%) + 3%-(y)(3%) 143 6% = y(7.2608%) 144 y = 0.8264 82.64% investment in risky fund B C D E F G H Expected Reteen on Portfolio on best feasible CAL Rehen (E6rp)) + (1-y) (af) 145 Standard deviation of this portfolio rf Elrp) - rf Elrc = 146 147 148 149 150 151 9% = 6% = 153 ANS a OC = HEM MIN VAR PORT Red 152 3% + (10.2608% -3%)/(32.1815%))*(62) 7.2608%/32.1815%)*(60) 26.5934 % 26.59 % standard deviation of portfolio BEST CAL BINOMIAL 2 TIME SINKING AMORTIZA Sheet2 VC JORDAN INSURANCE Sheet1 Sheet3 Sheet4 Sheets Sheeto 0 + greta Sheets I BOI 130% 4 * 4 OENG DO 03-11-2019

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 AutoSum - A 11 A = = = V General A A Wrap Text Merge Merge & Center Center U - D SF $ - % % 4:0 .00 8.9 Insert Delete Format . Conditional Format Formatting as Table Styles Cell Styles Fill 2 Clear Sort & Filter Editing Find & Select Font Alignment Number Cells L M N O P 26.5934 % 26.59 % standard deviation of portfolio Calibri E Copy Paste Format Painter B I Clipboard 1162 A B 153 ANS a oC = 154 155 ANS b b-1 156 b-2 157 158 159 160 161 162 163 proportion in T-bill proportion in stock proportion in bonds 100% 82.64% 82.64% - x X 82.64% 75.15% 24.85% = 17.36% 62.10% 20.54% 164 165 166 167 168 169 170 K 171 M Red MIN VAR PORT BEST CAL BINOMIAL 2 TIME SINKING AMORTIZA Sheet2 VC JORDAN INSURANCE Sheet1 Sheet3 Sheet4 Sheets Sheeto greta Sheet8 I THE TW 130% 6 0 +) * 4 OENG 03-11-2019 DO 4