Question

Week 3.CH7 6 Saved Help Save&Exit Check my Problem 7-7 25 points 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 rate of 8% The probability distribution of the risky funds is as follows: Expected standard Deviation Return Stock fund (s Bond fund (8) 14 The correlation between the fund returns is 012 of each asset and for the expected return and standard deviation of the optimal risky portfolio. ermediate calculations. Enter your answers as decimals rounded to 4 places.) Portfolio invested in the stock Portfoio invested in the bond Expected retun Standard deviation

Answer 1

Solution :-

Given data ,

Expected return on stock fund $E[r_{s}]$ = 23%

Standard deviation on stock fund  $\sigma _{_{s}}$ = 29%

Expected return on bond fund $E[r_{B}]$ = 14

Standard deviation on bond fund  $\sigma _{_{B}}$ = 17

Fund returns $r_{SB}$ = 0.12

Rate on fund $r_{f}$ = 8

$\rightarrow$ Now , we are finding the correlation on bond and stock .

$Cor (B,S)=\sigma _{s} * \sigma _{b} * r_{SB}$

= 29 * 17 * 0.12

= 59.16

$Cor (B,S)=59.16$

$\Rightarrow$Portfolio invested in the stock :-

Portfolio invested in the stock  $[ W_{s}] = \frac{\left | E(r_{s}) - r_{f}\right |*\sigma _{B}^{2} - \left |E(r_{B}) - r_{f} \right |* Cor ( B,S)}{\left | E(r_{s}) - r_{f}\right |*\sigma _{B}^{2} +\left |E(r_{B}) - r_{f} \right |*\sigma _{S}^{2} - \left | E(r_{s}) - r_{f} + E(r_{B}) - r_{f} \right |* Cor (B,S)}$

$[ W_{s}] = \frac{\left | 23 - 8\right |*17^{2} - \left |14 - 8 \right |* 59.16}{\left | 23 - 8\right |*17^{2} +\left |14 - 8 \right |*29^{2} - \left | 23 - 8+14 - 8 \right |*59.16}$

$[ W_{s}] = \frac{\left | 15\right |*289 - \left |6 \right |* 59.16}{\left | 15\right |*289 +\left |6 \right |*841-\left | 21 \right |*59.16 }$

$[ W_{s}] = \frac{4,335 -354.96}{4,335 +5046 - 1,242.36}$

$[ W_{s}] = \frac{3,980.04}{8,138.64 }$

$[ W_{s}] =0.4890$

$[ W_{s}] =48.90$%

Portfolio invested in the stock = 48.90%

$\therefore$Portfolio invested in the stock = 48.90%

$\Rightarrow$Portfolio invested in the bond :-

Portfolio invested in the bond  $[W_{B}] = 1-W_{s}$

$[W_{B}] = 1-0.4890$

$[W_{B}] = 0.5110$

$[W_{B}] = 51.10$%

Portfolio invested in the bond = 51.10%

$\therefore$Portfolio invested in the bond = 51.10%

$\Rightarrow$Expected return :-

Expected return $[E(r_{p})] = [ W_{s}*E(r_{s})] + [ W_{B}*E(r_{B})]$

$[E(r_{p})] = [ 0.4890*0.23] + [ 0. 5110*0.14]$

$[E(r_{p})] =0.11247 + 0.07154$

$[E(r_{p})] =0.18401$

$[E(r_{p})] =18.40$%

Expected return = 18.40%

Expected return = 18.40%

$\Rightarrow$Standard deviation :-

Standard deviation $\sigma _{p} = \sqrt{[(W_{s})^{2}*\sigma _{s}^{2}]+[(W_{B})^{2}*\sigma _{B}^{2}]+[2 * W_{s}*W_{B}*cor(B,S)]}$

$\sigma _{p} = \sqrt{[0.4890^{2}*0.29^{2}]+[(0.5110^{2}*\0.17^{2}]+[2 * 0.4890*0.5110*0.5916]}$$\sigma _{p} = \sqrt{[0.2391*0.0841]+[0.2611*0.0289]+0.2956$

$\sigma _{p} = \sqrt{0.0201+0.0075+0.2956}$

$\sigma _{p} = \sqrt{0.3232}$

$\sigma _{p} = 0.5685$

$\sigma _{p} = 56.85$%

Note :-

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