兹维 博迪投资学英文课件 Chap006

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Figure 6.6 Utility as a Function of Allocation to the Risky Asset, y
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Table 6.6 Spreadsheet Calculations of Indifference Curves
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Figure 6.7 Indifference Curves for U = .05 and U = .09 with A = 2 and A = 4
CHAPTER 6
Risk Aversion and Capital Allocation to Risky Assets
Investments, 8th edition
Bodie, Kane and Marcus
Slides by Susan Hine
McGraw-Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved.
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Figure 6.2 The Indifference Curve
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Table 6.3 Utility Values of Possible Portfolios for an Investor with Risk Aversion, A = 4
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Table 6.4 Investor’s Willingness to Pay for Catastrophe Insurance
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Example Using Chapter 6.4 Numbers
rf = 7% E(rp) = 15%
y = % in p
srf = 0%
sp = 22%
(1-y) = % in rf
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Expected Returns for Combinations
E (rc ) yE (rp ) (1 y )rf
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Risk Aversion and Utility Values
• Risk averse investors reject investment portfolios that are fair games or worse • These investors are willing to consider only risk-free or speculative prospects with positive risk premiums • Intuitively one would rank those portfolios as more attractive with higher expected returns
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Figure 6.3 Spread Between 3-Month CD and T-bill Rates
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Portfolios of One Risky Asset and a Risk-Free Asset
• It’s possible to split investment funds between safe and risky assets. • Risk free asset: proxy; T-bills • Risky asset: stock (or a portfolio)
rc = complete or combined portfolio For example, y = .75 E(rc) = .75(.15) + .25(.07) = .13 ithout Leverage
If y = .75, then
sc s
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Capital Allocation Across Risky and Risk-Free Portfolios
• Control risk – Asset allocation choice • Fraction of the portfolio invested in Treasury bills or other safe money market securities
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Passive Strategies: The Capital Market Line
• Passive strategy involves a decision that avoids any direct or indirect security analysis • Supply and demand forces may make such a strategy a reasonable choice for many investors
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Figure 6.5 The Opportunity Set with Differential Borrowing and Lending Rates
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Risk Tolerance and Asset Allocation
• The investor must choose one optimal portfolio, C, from the set of feasible choices – Trade-off between risk and return – Expected return of the complete portfolio is given by: – Variance is:
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Estimating Risk Aversion
• Observe individuals’ decisions when confronted with risk • Observe how much people are willing to pay to avoid risk
– Insurance against large losses
E (rc ) rf y E (rP ) rf
s ys
2 C 2
2 P
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Table 6.5 Utility Levels for Various Positions in Risky Assets (y) for an Investor with Risk Aversion A = 4
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Figure 6.8 Finding the Optimal Complete Portfolio Using Indifference Curves
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Table 6.7 Expected Returns on Four Indifference Curves and the CAL
sc = (1.5) (.22) = .33
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Figure 6.4 The Investment Opportunity Set with a Risky Asset and a Risk-free Asset in the Expected Return-Standard Deviation Plane
1 2 U E (r ) As 2
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Table 6.2 Utility Scores of Alternative Portfolios for Investors with Varying Degree of Risk Aversion
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Figure 6.1 The Trade-off Between Risk and Returns of a Potential Investment Portfolio, P
Risk and Risk Aversion
• Speculation
– Considerable risk
• Sufficient to affect the decision
– Commensurate gain
• Gamble
– Bet or wager on an uncertain outcome
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The Risky Asset Example
Total portfolio value = $300,000 Risk-free value = 90,000 Risky (Vanguard & Fidelity) = 210,000 Vanguard (V) = 54% Fidelity (F) = 46%
Portfolio C
90,000/300,000 = 0.300
300,000/300,000 = 1.000
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The Risk-Free Asset
• Only the government can issue default-free bonds – Guaranteed real rate only if the duration of the bond is identical to the investor’s desire holding period • T-bills viewed as the risk-free asset – Less sensitive to interest rate fluctuations
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Table 6.1 Available Risky Portfolios (Risk-free Rate = 5%)
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Utility Function
Where U = utility E ( r ) = expected return on the asset or portfolio A = coefficient of risk aversion s2 = variance of returns
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Table 6.8 Average Annual Return on Stocks and 1-Month T-bills; Standard Deviation and Rewardto-Variability Ratio of Stocks Over Time