GEN COMBO LOOSELEAF INVESTMENTS; CONNECT ACCESS CARD
GEN COMBO LOOSELEAF INVESTMENTS; CONNECT ACCESS CARD
11th Edition
ISBN: 9781260201550
Author: Bodie
Publisher: MCG
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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 PortfolioWeight of billsWeight of IndexU(A=2)
    0.1300.200.04000.01.0U=0.1312×2×(0.20)2=0.090
    0.1140.160.02560.20.8U=0.11412×2×(0.16)2=0.0884
    0.0980.120.01440.40.6U=0.09812×2×(0.12)2=0.0836
    0.0820.080.00640.60.4U=0.08212×2×(0.08)2=0.0756
    0.0660.040.00160.80.2U=0.06612×2×(0.04)2=0.0644
    0.0500.000.00001.00.0U=0.05012×2×(0.0)2=0.050

Expert Solution & Answer
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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 PortfolioWeight of billsWeight of IndexU(A=2)
    0.1300.200.04000.01.0U=0.1312×2×(0.20)2=0.090
    0.1140.160.02560.20.8U=0.11412×2×(0.16)2=0.0884
    0.0980.120.01440.40.6U=0.09812×2×(0.12)2=0.0836
    0.0820.080.00640.60.4U=0.08212×2×(0.08)2=0.0756
    0.0660.040.00160.80.2U=0.06612×2×(0.04)2=0.0644
    0.0500.000.00001.00.0U=0.05012×2×(0.0)2=0.050

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