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…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 4GP

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

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%

Definition Definition Relationship between two independent variables. A correlation tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

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