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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?

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?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 4GP
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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)
Transcribed Image Text: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%
Transcribed Image Text: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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