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 28% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 6%. Calculate the utility levels of each portfolio for an investor with A-2. Assume the utility function is U = E(r) - 0.5 x Ao². (Do not round intermediate calculations. Round your answers to 4 decimal places. Negative amounts should be indicated by a minus sign.) WBills 0.0 0.2 0.4 0.6 0.8 1.0 Windex 1.0 0.8 0.6 0.4 0.2 0.0 U(A=2)

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 31% per year. Assume these values are representative of Investors' expectations for future performance and that the current T-bill rate is 3%. Calculate the utility levels of each portfolio for an Investor with A = 2. Assume the utility function is u = E(r) - 8.5 x Ao². Note: Do not round Intermediate calculations. Round your answers to 4 decimal places. Negative amounts should be Indicated by a minus sign. W Bills 0.0 0.2 0.4 0.6 0.8 1.0 Windex 1.0 0.8 0.6 0.4 Oo 0.2 0.0 U(A = 2)

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 25% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 4%. Calculate the utility levels of each portfolio for an investor with A = 3. Assume the utility function is U = E(r) 0.5 x Ao2. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 4 decimal places.) WBills 0.0 0.2 0.4 0.6 0.8 1.0 Windex 1.0 0.8 0.6 0.4 0.2 0.0 U(A = 3) -

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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