EBK INVESTMENTS
EBK INVESTMENTS
11th Edition
ISBN: 9781259357480
Author: Bodie
Publisher: MCGRAW HILL BOOK COMPANY
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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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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) -
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Portfolio return, variance, standard deviation; Author: MyFinanceTeacher;https://www.youtube.com/watch?v=RWT0kx36vZE;License: Standard YouTube License, CC-BY