A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the third is a money market fund that provides a safe return of 5.5%. The characteristics of the risky funds are as follows:Expected Return Standard DeviationStock fund (S) 15% 32%Bond fund (B) 9 23The correlation between the fund returns is .1512.) if you were to use only the two risky funds and still require an expected return of 12% what would be the investment proportions of your portfolio? Compare its standard deviation to that of the optimal portfolio in the previous problem. What do you conclude? B21=B10*(12%-B4)'(B11-B4)AВ1Expected returnStandard deviation2 Stock fund3 Bond fund4 Money market fund0.32|0.230.150.0910.055lo56 Correlation (S,B)7 Covariance (S,B)0.15=B6*C2*C389 Proportion of stock10 Proportion of bond11 Mean of portfolio12 Standard deviation of portfolio|=(B2-B4)*(C3^2))-(B3-B4)*B7))/(B2-B4)*C3^2)+((B3-B4)*C2^2)-((B2-B4+B3-B4)*B7))I=1-B9l=(B9*B2)+(B10*B3)|=SQRT((B9^2*(C2^2))+(B10^2*(C3^2))+(2*B9*B10*B7))|=B11-B4)/B1213 Reward to variability ratio1415 Part a:16 Standard deviation of optimal portfolio =(12%-B4)/B131718 Part b:19 Proportion of money market fund20 Proportion of stock fund21 Proportion of bond fund=1-((12%-B4)/(B11-B4))|=B9*(12%-B4)/(Bl1-B4)=B10*(12%-B4)/(B11-B4) В21=B10*(12%-B4)/(B11-B4)ABExpected return Standard deviation15%9%5.50%12 Stock fund32%23%3 Bond fund4 Money market fund56 Correlation (S.B)7 Covariance (S,B)0.150.011048.9 Proportion of stock10 Proportion of bond11 Mean of portfolio12 Standard deviation of portfolio13 Reward to variability ratio64.66%35.34%12.88%23.34%31.62%1415 Part a:| 16 Standard deviation of optimal portfolio20.56%1718 Part b:11.92%19 Proportion of money market fund20 Proportion of stock fund21 Proportion of bond fund56.95%31.12%

Given money market fund that provides a safe return = 5.5% Expected Return Standard…

Answered: A pension fund manager is considering…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the third is a money market fund that provides a safe return of 5.5%. The characteristics of the risky funds are as follows:

Expected Return Standard Deviation

Stock fund (S) 15% 32%

Bond fund (B) 9 23

The correlation between the fund returns is .15

12.) if you were to use only the two risky funds and still require an expected return of 12% what would be the investment proportions of your portfolio? Compare its standard deviation to that of the optimal portfolio in the previous problem. What do you conclude?

B21
=B10*(12%-B4)'(B11-B4)
A
В
1
Expected return
Standard deviation
2 Stock fund
3 Bond fund
4 Money market fund
0.32
|0.23
0.15
0.09
10.055
lo
5
6 Correlation (S,B)
7 Covariance (S,B)
0.15
=B6*C2*C3
8
9 Proportion of stock
10 Proportion of bond
11 Mean of portfolio
12 Standard deviation of portfolio
|=(B2-B4)*(C3^2))-(B3-B4)*B7))/(B2-B4)*C3^2)+((B3-B4)*C2^2)-((B2-B4+B3-B4)*B7))
I=1-B9
l=(B9*B2)+(B10*B3)
|=SQRT((B9^2*(C2^2))+(B10^2*(C3^2))+(2*B9*B10*B7))
|=B11-B4)/B12
13 Reward to variability ratio
14
15 Part a:
16 Standard deviation of optimal portfolio =(12%-B4)/B13
17
18 Part b:
19 Proportion of money market fund
20 Proportion of stock fund
21 Proportion of bond fund
=1-((12%-B4)/(B11-B4))
|=B9*(12%-B4)/(Bl1-B4)
=B10*(12%-B4)/(B11-B4)

В21
=B10*(12%-B4)/(B11-B4)
A
B
Expected return Standard deviation
15%
9%
5.50%
1
2 Stock fund
32%
23%
3 Bond fund
4 Money market fund
5
6 Correlation (S.B)
7 Covariance (S,B)
0.15
0.01104
8.
9 Proportion of stock
10 Proportion of bond
11 Mean of portfolio
12 Standard deviation of portfolio
13 Reward to variability ratio
64.66%
35.34%
12.88%
23.34%
31.62%
14
15 Part a:
| 16 Standard deviation of optimal portfolio
20.56%
17
18 Part b:
11.92%
19 Proportion of money market fund
20 Proportion of stock fund
21 Proportion of bond fund
56.95%
31.12%

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