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,1/9/2014,Hafiz Hoque,6-,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Copyright 2011 by The McGraw-Hill Companies,Inc.All rights reserved.,McGraw-Hill/Irwin,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,1/9/2014,Hafiz Hoque,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,1/9/2014,Hafiz Hoque,6-,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Hafiz Hoque,1/9/2014,6-,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,1/9/2014,Hafiz Hoque,6-,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,1/9/2014,Hafiz Hoque,6-,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,1/9/2014,Hafiz Hoque,6-,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,1/9/2014,Hafiz Hoque,6-,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,6-,*,1/9/2014,Hafiz Hoque,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,6-,*,1/9/2014,Hafiz Hoque,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,1/9/2014,Hafiz Hoque,6-,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,6-,*,1/9/2014,Hafiz Hoque,RISK AVERSION AND CAPITAL ALLOCATION TO RISKY ASSETS,Lecture 3,Allocation to Risky Assets,Investors will avoid risk unless there is a reward.,The utility model gives the optimal allocation between a risky portfolio and a risk-free asset.,Risk and Risk Aversion,Speculation,Taking considerable risk for a commensurate gain,Parties have heterogeneous expectations,Risk and Risk Aversion,Gamble,Bet or wager on an uncertain outcome for enjoyment,Parties assign the same probabilities to the possible outcomes,Risk Aversion and Utility Values,Investors are willing to consider:,risk-free assets,speculative positions with positive risk premiums,Portfolio attractiveness increases with expected return and decreases with risk.,What happens when return increases with risk?,Table 6.1 Available Risky Portfolios(Risk-free Rate=5%),Each portfolio receives a utility score to assess the investors risk/return trade off,Utility Function,U,=utility,E(r),=expected return on the asset or portfolio,A,=coefficient of risk aversion,s,2,=variance of returns,=a scaling factor,Table 6.2 Utility Scores of Alternative Portfolios for Investors with Varying Degree of Risk Aversion,Mean-Variance(M-V)Criterion,Portfolio A dominates portfolio B if:,And,Estimating Risk Aversion,Use questionnaires,Observe individuals decisions when confronted with risk,Observe how much people are willing to pay to avoid risk,Capital Allocation Across Risky and Risk-Free Portfolios,Asset Allocation:,Is a very important part of portfolio construction.,Refers to the choice among broad asset classes.,Controlling Risk:,Simplest way:Manipulate the fraction of the portfolio invested in risk-free assets versus the portion invested in the risky assets,Basic Asset Allocation,Total Market Value,$300,000,Risk-free money market fund,$90,000,Equities,$113,400,Bonds(long-term),$96,600,Total risk assets,$210,000,Basic Asset Allocation,Let,y,=weight of the risky portfolio,P,in the,complete portfolio;(1-,y,)=weight of risk-free assets:,The Risk-Free Asset,Only the government can issue default-free bonds.,Risk-free in real terms only if price indexed and maturity equal to investors holding period.,T-bills viewed as“the risk-free asset,Money market funds also considered risk-free in practice,Figure 6.3 Spread Between 3-Month CD and T-bill Rates,Its possible to create a complete portfolio by splitting investment funds between safe and risky assets.,Let y=portion allocated to the risky portfolio,P,(1-y)=portion to be invested in risk-free asset,F.,Portfolios of One Risky Asset and a Risk-Free Asset,Example Using Chapter 6.4 Numbers,r,f,=7%,rf,=0%,E(r,p,),=15%,p,=22%,y,=%in,p,(,1-y,)=%in,r,f,Example(Ctd.),The expected return on the complete portfolio is the risk-free rate plus the weight of P times the risk premium of P,Example(Ctd.),The risk of the complete portfolio is the weight of P times the risk of P:,Example(Ctd.),Rearrange and substitute y=,s,C,/,s,P,:,Figure 6.4 The Investment Opportunity Set,Lend at r,f,=7%and borrow at r,f,=9%,Lending range slope=8/22=0.36,Borrowing range slope=6/22=0.27,CAL kinks at P,Capital Allocation Line with Leverage,Figure 6.5 The Opportunity Set with Differential Borrowing and Lending Rates,Risk To
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