投資學(xué)英文版課件：Chap006 Risk Aversion and Capital Allocation to Risky Assets

1、CHAPTER 6Risk Aversion and Capital Allocation to Risky Assets6-1Allocation to Risky AssetsInvestors will avoid risk unless there is a reward.The utility model gives the optimal allocation between a risky portfolio and a risk-free asset.6-2Risk and Risk AversionSpeculationTaking considerable risk for

2、 a commensurate gainParties have heterogeneous expectations6-3Risk and Risk AversionGamble Bet or wager on an uncertain outcome for enjoymentParties assign the same probabilities to the possible outcomes6-4Risk Aversion and Utility ValuesInvestors are willing to consider:risk-free assetsspeculative

3、positions with positive risk premiumsPortfolio attractiveness increases with expected return and decreases with risk.What happens when return increases with risk?6-5Table 6.1 Available Risky Portfolios (Risk-free Rate = 5%)Each portfolio receives a utility score to assess the investors risk/return t

4、rade off6-6Utility FunctionU = utilityE ( r ) = expected return on the asset or portfolioA = coefficient of risk aversions2 = variance of returns = a scaling factor 6-7Table 6.2 Utility Scores of Alternative Portfolios for Investors with Varying Degree of Risk Aversion6-8Mean-Variance (M-V) Criterio

5、nPortfolio A dominates portfolio B if:And6-9Estimating Risk AversionUse questionnairesObserve individuals decisions when confronted with riskObserve how much people are willing to pay to avoid risk6-10Capital Allocation Across Risky and Risk-Free Portfolios Asset Allocation:Is a very important part

6、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 assets6-11Basic Asset AllocationTotal Market Value$300,000Risk-free money market fund

7、$90,000Equities$113,400Bonds (long-term)$96,600Total risk assets$210,0006-12Basic Asset AllocationLet y = weight of the risky portfolio, P, in the complete portfolio; (1-y) = weight of risk-free assets:6-13The Risk-Free AssetOnly the government can issue default-free bonds.Risk-free in real terms on

8、ly if price indexed and maturity equal to investors holding period.T-bills viewed as “the” risk-free assetMoney market funds also considered risk-free in practice6-14Figure 6.3 Spread Between 3-Month CD and T-bill Rates 6-15Its possible to create a complete portfolio by splitting investment funds be

9、tween 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 Asset6-16rf = 7%rf = 0%E(rp) = 15%p = 22%y = % in p(1-y) = % in rfExample Using Chapter 6.4 Numbers6-17Example (Ctd.)The expec

10、ted return on the complete portfolio is the risk-free rate plus the weight of P times the risk premium of P6-18Example (Ctd.)The risk of the complete portfolio is the weight of P times the risk of P:6-19Example (Ctd.)Rearrange and substitute y=sC/sP:6-20Figure 6.4 The Investment Opportunity Set 6-21

11、Lend at rf=7% and borrow at rf=9%Lending range slope = 8/22 = 0.36Borrowing range slope = 6/22 = 0.27CAL kinks at PCapital Allocation Line with Leverage6-22Figure 6.5 The Opportunity Set with Differential Borrowing and Lending Rates6-23Risk Tolerance and Asset AllocationThe investor must choose one

12、optimal portfolio, C, from the set of feasible choicesExpected return of the complete portfolio:Variance:6-24Table 6.4 Utility Levels for Various Positions in Risky Assets (y) for an Investor with Risk Aversion A = 46-25Figure 6.6 Utility as a Function of Allocation to the Risky Asset, y6-26Table 6.

13、5 Spreadsheet Calculations of Indifference Curves6-27Figure 6.7 Indifference Curves for U = .05 and U = .09 with A = 2 and A = 4 6-28Figure 6.8 Finding the Optimal Complete Portfolio Using Indifference Curves 6-29Table 6.6 Expected Returns on Four Indifference Curves and the CAL6-30Passive Strategie

14、s: The Capital Market LineThe passive strategy avoids any direct or indirect security analysisSupply and demand forces may make such a strategy a reasonable choice for many investors6-31Passive Strategies: The Capital Market LineA natural candidate for a passively held risky asset would be a well-di

15、versified portfolio of common stocks such as the S&P 500.The capital market line (CML) is the capital allocation line formed from 1-month T-bills and a broad index of common stocks (e.g. the S&P 500).6-32Passive Strategies: The Capital Market LineThe CML is given by a strategy that involves investment in two passive portfolios: virtually risk-free short-term T-bills (or a money market fund) a fund of common stocks that mimics a