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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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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