Portfolio consists of assets which have different rates as well as different risk associated with the assets, a risk free asset and asset that contains risk, both have a certain percentage of return. To calculate: the utility levels of each portfolio for an investor with A=2. Utility of portfolio can be calculated by the formula provided below: U = E ( r ) − 1 2 A σ 2 U = Utility E ( r ) = Expected Return A = Risk Aversion Coefficient σ = Standard Deviation Calculating utility for each investment taking A=2 Return of portfolio (Return × Weight of bills Standard deviation of portfolio (Standard deviation × weight of bills) Variance of Portfolio Weight of bills Weight of Index U(A=2) 0.130 0.20 0.0400 0.0 1.0 U = 0.13 − 1 2 × 2 × ( 0.20 ) 2 = 0.090 0.114 0.16 0.0256 0.2 0.8 U = 0.114 − 1 2 × 2 × ( 0.16 ) 2 = 0.0884 0.098 0.12 0.0144 0.4 0.6 U = 0.098 − 1 2 × 2 × ( 0.12 ) 2 = 0.0836 0.082 0.08 0.0064 0.6 0.4 U = 0.082 − 1 2 × 2 × ( 0.08 ) 2 = 0.0756 0.066 0.04 0.0016 0.8 0.2 U = 0.066 − 1 2 × 2 × ( 0.04 ) 2 = 0.0644 0.050 0.00 0.0000 1.0 0.0 U = 0.050 − 1 2 × 2 × ( 0.0 ) 2 = 0.050

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Answer 1

Question

Chapter 6, Problem 11PS

Summary Introduction

Introduction: Portfolio consists of assets which have different rates as well as different risk associated with the assets, a risk free asset and asset that contains risk, both have a certain percentage of return.

To calculate: the utility levels of each portfolio for an investor with A=2.

Utility of portfolio can be calculated by the formula provided below:

U=E(r)−12Aσ2U= UtilityE(r)=Expected ReturnA=Risk Aversion Coefficientσ= Standard Deviation

Calculating utility for each investment taking A=2

Return of portfolio (Return ×
Weight of bills Standard deviation of portfolio (Standard deviation ×
weight of bills) Variance of Portfolio Weight of bills Weight of Index U(A=2)
0.130 0.20 0.0400 0.0 1.0 U=0.13−12×2×(0.20)2=0.090
0.114 0.16 0.0256 0.2 0.8 U=0.114−12×2×(0.16)2=0.0884
0.098 0.12 0.0144 0.4 0.6 U=0.098−12×2×(0.12)2=0.0836
0.082 0.08 0.0064 0.6 0.4 U=0.082−12×2×(0.08)2=0.0756
0.066 0.04 0.0016 0.8 0.2 U=0.066−12×2×(0.04)2=0.0644
0.050 0.00 0.0000 1.0 0.0 U=0.050−12×2×(0.0)2=0.050

Expert Solution & Answer

Explanation of Solution

Utility of portfolio can be calculated by the formula provided below:

U=E(r)−12Aσ2U= UtilityE(r)=Expected ReturnA=Risk Aversion Coefficientσ= Standard Deviation

Calculating utility for each investment taking A=2

Return of portfolio (Return × Weight of bills	Standard deviation of portfolio (Standard deviation × weight of bills)	Variance of Portfolio	Weight of bills	Weight of Index	U(A=2)
0.130	0.20	0.0400	0.0	1.0	U=0.13−12×2×(0.20)2=0.090
0.114	0.16	0.0256	0.2	0.8	U=0.114−12×2×(0.16)2=0.0884
0.098	0.12	0.0144	0.4	0.6	U=0.098−12×2×(0.12)2=0.0836
0.082	0.08	0.0064	0.6	0.4	U=0.082−12×2×(0.08)2=0.0756
0.066	0.04	0.0016	0.8	0.2	U=0.066−12×2×(0.04)2=0.0644
0.050	0.00	0.0000	1.0	0.0	U=0.050−12×2×(0.0)2=0.050

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Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 38% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 5%. Calculate the expected return and variance of portfolios invested in T-bills and the S&P 500 index with weights as shown below. (Enter your answers as decimals rounded to 4 places. Leave no cells blank - be certain to enter "0" wherever required.) WBills: WIndex: Expected Return: Variance: 0.0 1.0 0.1300 0.1444 Example 0.2 0.8 0.4 0.6 0.6 0.4 0.8 0.2 1.0 0.0

Assuming the below annual rates of return: Annual Rates of Return: Wamart - 12.36% Coca Cola - 25.51% Pfizer - 14% CVS - 32.99% Berkshire Hathaway - 29.66% Assume that you initially invested $1,000,000 in the portfolio and that the distribution of the annual rate of return of the portfolio is normal. What is the distribution of the return of the portfolio 20 years after its formation? Provide the graph of the distribution of the return of the portfolio.

Consider a portfolio consisting of $ 10 million invested in the S&P 500 and $ 7.5 million invested in U.S treasury bonds. The S&P 500 has an expected return of 14% and a standard deviation of 16%. The treasury bonds have an expected return of 9% and a standard deviation of 8%. The correlation between the S&P 500 and Bonds is 0.35. All figures are stated on an annual basis. Find the VAR for one year at a probability of 5%. Identify and use the most appropriate method given the information you have. Using the information, you obtained in part a, find VAR for one day.

Answer 2

Question

Chapter 6, Problem 11PS

Summary Introduction

Introduction: Portfolio consists of assets which have different rates as well as different risk associated with the assets, a risk free asset and asset that contains risk, both have a certain percentage of return.

To calculate: the utility levels of each portfolio for an investor with A=2.

Utility of portfolio can be calculated by the formula provided below:

U=E(r)−12Aσ2U= UtilityE(r)=Expected ReturnA=Risk Aversion Coefficientσ= Standard Deviation

Calculating utility for each investment taking A=2

Return of portfolio (Return ×
Weight of bills Standard deviation of portfolio (Standard deviation ×
weight of bills) Variance of Portfolio Weight of bills Weight of Index U(A=2)
0.130 0.20 0.0400 0.0 1.0 U=0.13−12×2×(0.20)2=0.090
0.114 0.16 0.0256 0.2 0.8 U=0.114−12×2×(0.16)2=0.0884
0.098 0.12 0.0144 0.4 0.6 U=0.098−12×2×(0.12)2=0.0836
0.082 0.08 0.0064 0.6 0.4 U=0.082−12×2×(0.08)2=0.0756
0.066 0.04 0.0016 0.8 0.2 U=0.066−12×2×(0.04)2=0.0644
0.050 0.00 0.0000 1.0 0.0 U=0.050−12×2×(0.0)2=0.050

Expert Solution & Answer

Explanation of Solution

Utility of portfolio can be calculated by the formula provided below:

U=E(r)−12Aσ2U= UtilityE(r)=Expected ReturnA=Risk Aversion Coefficientσ= Standard Deviation

Calculating utility for each investment taking A=2

Return of portfolio (Return × Weight of bills	Standard deviation of portfolio (Standard deviation × weight of bills)	Variance of Portfolio	Weight of bills	Weight of Index	U(A=2)
0.130	0.20	0.0400	0.0	1.0	U=0.13−12×2×(0.20)2=0.090
0.114	0.16	0.0256	0.2	0.8	U=0.114−12×2×(0.16)2=0.0884
0.098	0.12	0.0144	0.4	0.6	U=0.098−12×2×(0.12)2=0.0836
0.082	0.08	0.0064	0.6	0.4	U=0.082−12×2×(0.08)2=0.0756
0.066	0.04	0.0016	0.8	0.2	U=0.066−12×2×(0.04)2=0.0644
0.050	0.00	0.0000	1.0	0.0	U=0.050−12×2×(0.0)2=0.050

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Answer 3

Question

Chapter 6, Problem 11PS

Summary Introduction

Introduction: Portfolio consists of assets which have different rates as well as different risk associated with the assets, a risk free asset and asset that contains risk, both have a certain percentage of return.

To calculate: the utility levels of each portfolio for an investor with A=2.

Utility of portfolio can be calculated by the formula provided below:

U=E(r)−12Aσ2U= UtilityE(r)=Expected ReturnA=Risk Aversion Coefficientσ= Standard Deviation

Calculating utility for each investment taking A=2

Return of portfolio (Return ×
Weight of bills Standard deviation of portfolio (Standard deviation ×
weight of bills) Variance of Portfolio Weight of bills Weight of Index U(A=2)
0.130 0.20 0.0400 0.0 1.0 U=0.13−12×2×(0.20)2=0.090
0.114 0.16 0.0256 0.2 0.8 U=0.114−12×2×(0.16)2=0.0884
0.098 0.12 0.0144 0.4 0.6 U=0.098−12×2×(0.12)2=0.0836
0.082 0.08 0.0064 0.6 0.4 U=0.082−12×2×(0.08)2=0.0756
0.066 0.04 0.0016 0.8 0.2 U=0.066−12×2×(0.04)2=0.0644
0.050 0.00 0.0000 1.0 0.0 U=0.050−12×2×(0.0)2=0.050

Expert Solution & Answer

Explanation of Solution

Utility of portfolio can be calculated by the formula provided below:

U=E(r)−12Aσ2U= UtilityE(r)=Expected ReturnA=Risk Aversion Coefficientσ= Standard Deviation

Calculating utility for each investment taking A=2

Return of portfolio (Return × Weight of bills	Standard deviation of portfolio (Standard deviation × weight of bills)	Variance of Portfolio	Weight of bills	Weight of Index	U(A=2)
0.130	0.20	0.0400	0.0	1.0	U=0.13−12×2×(0.20)2=0.090
0.114	0.16	0.0256	0.2	0.8	U=0.114−12×2×(0.16)2=0.0884
0.098	0.12	0.0144	0.4	0.6	U=0.098−12×2×(0.12)2=0.0836
0.082	0.08	0.0064	0.6	0.4	U=0.082−12×2×(0.08)2=0.0756
0.066	0.04	0.0016	0.8	0.2	U=0.066−12×2×(0.04)2=0.0644
0.050	0.00	0.0000	1.0	0.0	U=0.050−12×2×(0.0)2=0.050

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Answer 4

Question

Chapter 6, Problem 11PS

Summary Introduction

Introduction: Portfolio consists of assets which have different rates as well as different risk associated with the assets, a risk free asset and asset that contains risk, both have a certain percentage of return.

To calculate: the utility levels of each portfolio for an investor with A=2.

Utility of portfolio can be calculated by the formula provided below:

U=E(r)−12Aσ2U= UtilityE(r)=Expected ReturnA=Risk Aversion Coefficientσ= Standard Deviation

Calculating utility for each investment taking A=2

Return of portfolio (Return ×
Weight of bills Standard deviation of portfolio (Standard deviation ×
weight of bills) Variance of Portfolio Weight of bills Weight of Index U(A=2)
0.130 0.20 0.0400 0.0 1.0 U=0.13−12×2×(0.20)2=0.090
0.114 0.16 0.0256 0.2 0.8 U=0.114−12×2×(0.16)2=0.0884
0.098 0.12 0.0144 0.4 0.6 U=0.098−12×2×(0.12)2=0.0836
0.082 0.08 0.0064 0.6 0.4 U=0.082−12×2×(0.08)2=0.0756
0.066 0.04 0.0016 0.8 0.2 U=0.066−12×2×(0.04)2=0.0644
0.050 0.00 0.0000 1.0 0.0 U=0.050−12×2×(0.0)2=0.050

Expert Solution & Answer

Explanation of Solution

Utility of portfolio can be calculated by the formula provided below:

U=E(r)−12Aσ2U= UtilityE(r)=Expected ReturnA=Risk Aversion Coefficientσ= Standard Deviation

Calculating utility for each investment taking A=2

Return of portfolio (Return × Weight of bills	Standard deviation of portfolio (Standard deviation × weight of bills)	Variance of Portfolio	Weight of bills	Weight of Index	U(A=2)
0.130	0.20	0.0400	0.0	1.0	U=0.13−12×2×(0.20)2=0.090
0.114	0.16	0.0256	0.2	0.8	U=0.114−12×2×(0.16)2=0.0884
0.098	0.12	0.0144	0.4	0.6	U=0.098−12×2×(0.12)2=0.0836
0.082	0.08	0.0064	0.6	0.4	U=0.082−12×2×(0.08)2=0.0756
0.066	0.04	0.0016	0.8	0.2	U=0.066−12×2×(0.04)2=0.0644
0.050	0.00	0.0000	1.0	0.0	U=0.050−12×2×(0.0)2=0.050

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Answer 5

Chapter 6, Problem 11PS

Summary Introduction

Introduction: Portfolio consists of assets which have different rates as well as different risk associated with the assets, a risk free asset and asset that contains risk, both have a certain percentage of return.

To calculate: the utility levels of each portfolio for an investor with A=2.

Utility of portfolio can be calculated by the formula provided below:

U=E(r)−12Aσ2U= UtilityE(r)=Expected ReturnA=Risk Aversion Coefficientσ= Standard Deviation

Calculating utility for each investment taking A=2

Return of portfolio (Return ×
Weight of bills Standard deviation of portfolio (Standard deviation ×
weight of bills) Variance of Portfolio Weight of bills Weight of Index U(A=2)
0.130 0.20 0.0400 0.0 1.0 U=0.13−12×2×(0.20)2=0.090
0.114 0.16 0.0256 0.2 0.8 U=0.114−12×2×(0.16)2=0.0884
0.098 0.12 0.0144 0.4 0.6 U=0.098−12×2×(0.12)2=0.0836
0.082 0.08 0.0064 0.6 0.4 U=0.082−12×2×(0.08)2=0.0756
0.066 0.04 0.0016 0.8 0.2 U=0.066−12×2×(0.04)2=0.0644
0.050 0.00 0.0000 1.0 0.0 U=0.050−12×2×(0.0)2=0.050

Expert Solution & Answer

Explanation of Solution

Utility of portfolio can be calculated by the formula provided below:

U=E(r)−12Aσ2U= UtilityE(r)=Expected ReturnA=Risk Aversion Coefficientσ= Standard Deviation

Calculating utility for each investment taking A=2

Return of portfolio (Return × Weight of bills	Standard deviation of portfolio (Standard deviation × weight of bills)	Variance of Portfolio	Weight of bills	Weight of Index	U(A=2)
0.130	0.20	0.0400	0.0	1.0	U=0.13−12×2×(0.20)2=0.090
0.114	0.16	0.0256	0.2	0.8	U=0.114−12×2×(0.16)2=0.0884
0.098	0.12	0.0144	0.4	0.6	U=0.098−12×2×(0.12)2=0.0836
0.082	0.08	0.0064	0.6	0.4	U=0.082−12×2×(0.08)2=0.0756
0.066	0.04	0.0016	0.8	0.2	U=0.066−12×2×(0.04)2=0.0644
0.050	0.00	0.0000	1.0	0.0	U=0.050−12×2×(0.0)2=0.050

Answer 6

Chapter 6, Problem 11PS

Summary Introduction

Introduction: Portfolio consists of assets which have different rates as well as different risk associated with the assets, a risk free asset and asset that contains risk, both have a certain percentage of return.

To calculate: the utility levels of each portfolio for an investor with A=2.

Utility of portfolio can be calculated by the formula provided below:

U=E(r)−12Aσ2U= UtilityE(r)=Expected ReturnA=Risk Aversion Coefficientσ= Standard Deviation

Calculating utility for each investment taking A=2

Return of portfolio (Return ×
Weight of bills Standard deviation of portfolio (Standard deviation ×
weight of bills) Variance of Portfolio Weight of bills Weight of Index U(A=2)
0.130 0.20 0.0400 0.0 1.0 U=0.13−12×2×(0.20)2=0.090
0.114 0.16 0.0256 0.2 0.8 U=0.114−12×2×(0.16)2=0.0884
0.098 0.12 0.0144 0.4 0.6 U=0.098−12×2×(0.12)2=0.0836
0.082 0.08 0.0064 0.6 0.4 U=0.082−12×2×(0.08)2=0.0756
0.066 0.04 0.0016 0.8 0.2 U=0.066−12×2×(0.04)2=0.0644
0.050 0.00 0.0000 1.0 0.0 U=0.050−12×2×(0.0)2=0.050

Expert Solution & Answer

Explanation of Solution

Utility of portfolio can be calculated by the formula provided below:

U=E(r)−12Aσ2U= UtilityE(r)=Expected ReturnA=Risk Aversion Coefficientσ= Standard Deviation

Calculating utility for each investment taking A=2

Return of portfolio (Return × Weight of bills	Standard deviation of portfolio (Standard deviation × weight of bills)	Variance of Portfolio	Weight of bills	Weight of Index	U(A=2)
0.130	0.20	0.0400	0.0	1.0	U=0.13−12×2×(0.20)2=0.090
0.114	0.16	0.0256	0.2	0.8	U=0.114−12×2×(0.16)2=0.0884
0.098	0.12	0.0144	0.4	0.6	U=0.098−12×2×(0.12)2=0.0836
0.082	0.08	0.0064	0.6	0.4	U=0.082−12×2×(0.08)2=0.0756
0.066	0.04	0.0016	0.8	0.2	U=0.066−12×2×(0.04)2=0.0644
0.050	0.00	0.0000	1.0	0.0	U=0.050−12×2×(0.0)2=0.050

Answer 7

Chapter 6, Problem 11PS

Summary Introduction

Introduction: Portfolio consists of assets which have different rates as well as different risk associated with the assets, a risk free asset and asset that contains risk, both have a certain percentage of return.

To calculate: the utility levels of each portfolio for an investor with A=2.

Utility of portfolio can be calculated by the formula provided below:

U=E(r)−12Aσ2U= UtilityE(r)=Expected ReturnA=Risk Aversion Coefficientσ= Standard Deviation

Calculating utility for each investment taking A=2

Return of portfolio (Return ×
Weight of bills Standard deviation of portfolio (Standard deviation ×
weight of bills) Variance of Portfolio Weight of bills Weight of Index U(A=2)
0.130 0.20 0.0400 0.0 1.0 U=0.13−12×2×(0.20)2=0.090
0.114 0.16 0.0256 0.2 0.8 U=0.114−12×2×(0.16)2=0.0884
0.098 0.12 0.0144 0.4 0.6 U=0.098−12×2×(0.12)2=0.0836
0.082 0.08 0.0064 0.6 0.4 U=0.082−12×2×(0.08)2=0.0756
0.066 0.04 0.0016 0.8 0.2 U=0.066−12×2×(0.04)2=0.0644
0.050 0.00 0.0000 1.0 0.0 U=0.050−12×2×(0.0)2=0.050

Answer 8

Expert Solution & Answer

Explanation of Solution

Utility of portfolio can be calculated by the formula provided below:

U=E(r)−12Aσ2U= UtilityE(r)=Expected ReturnA=Risk Aversion Coefficientσ= Standard Deviation

Calculating utility for each investment taking A=2

Return of portfolio (Return × Weight of bills	Standard deviation of portfolio (Standard deviation × weight of bills)	Variance of Portfolio	Weight of bills	Weight of Index	U(A=2)
0.130	0.20	0.0400	0.0	1.0	U=0.13−12×2×(0.20)2=0.090
0.114	0.16	0.0256	0.2	0.8	U=0.114−12×2×(0.16)2=0.0884
0.098	0.12	0.0144	0.4	0.6	U=0.098−12×2×(0.12)2=0.0836
0.082	0.08	0.0064	0.6	0.4	U=0.082−12×2×(0.08)2=0.0756
0.066	0.04	0.0016	0.8	0.2	U=0.066−12×2×(0.04)2=0.0644
0.050	0.00	0.0000	1.0	0.0	U=0.050−12×2×(0.0)2=0.050

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Ch. 6.A - Prob. 1P Ch. 6.A - Prob. 2P Ch. 6 - Prob. 1PS Ch. 6 - Prob. 2PS Ch. 6 - Prob. 3PS Ch. 6 - Prob. 4PS Ch. 6 - Prob. 5PS Ch. 6 - Prob. 6PS Ch. 6 - Prob. 7PS Ch. 6 - Prob. 8PS

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