博迪投资学第九版课件Chap009
博迪投资学答案chap0097thed.doc
CHAPTER 9: THE CAPITAL ASSET PRICING MODEL1. c.2. d. From CAPM, the fair expected return = 8 + 1.25(15 - 8) = 16.75%Actually expected return = 17%α = 17 - 16.75 = 0.25%3. Since the stock’s beta is equal to 1.2, its expected rate of return is:6 + [1.2 ⨯ (16 – 6)] = 18%011P P P D )r (E -+= 53$P 5050P 618.011=⇒+=-4. The series of $1,000 payments is a perpetuity. If beta is 0.5, the cash flow shouldbe discounted at the rate:6 + [0.5 ⨯ (16 – 6)] = 11%PV = $1,000/0.11 = $9,090.91If, however, beta is equal to 1, then the investment should yield 16%, and the price paid for the firm should be:PV = $1,000/0.16 = $6,250The difference, $2,840.91, is the amount you will overpay if you erroneouslyassume that beta is 0.5 rather than 1.5. Using the SML: 4 = 6 + β(16 – 6) ⇒ β = –2/10 = –0.26. a.7.E(r P ) = r f + β P [E(r M ) – r f ]18 = 6 + β P (14 – 6) ⇒ β P = 12/8 = 1.58.a. False. β = 0 implies E(r) = r f , not zero.b.False. Investors require a risk premium only for bearing systematic (undiversifiable or market) risk. Total volatility includes diversifiable risk. c. False. Your portfolio should be invested 75% in the market portfolio and25% in T-bills. Then:βP = (0.75 ⨯ 1) + (0.25 ⨯ 0) = 0.759. Not possible. Portfolio A has a higher beta than Portfolio B, but the expected returnfor Portfolio A is lower than the expected return for Portfolio B. Thus, these two portfolios cannot exist in equilibrium.10. Possible. If the CAPM is valid, the expected rate of return compensates only forsystematic (market) risk, represented by beta, rather than for the standard deviation, which includes nonsystematic risk. Thus, Portfolio A’s lower rate of return can be paired with a higher s tandard deviation, as long as A’s beta is less than B’s.11. Not possible. The reward-to-variability ratio for Portfolio A is better than that ofthe market. This scenario is impossible according to the CAPM because the CAPM predicts that the market is the most efficient portfolio. Using the numbers supplied:5.0121016S A =-= 33.0241018S M =-= Portfolio A provides a better risk-reward tradeoff than the market portfolio.12. Not possible. Portfolio A clearly dominates the market portfolio. Portfolio A hasboth a lower standard deviation and a higher expected return.13. Not possible. The SML for this scenario is: E(r) = 10 + β(18 – 10)Portfolios with beta equal to 1.5 have an expected return equal to:E(r) = 10 + [1.5 ⨯ (18 – 10)] = 22%The expected return for Portfolio A is 16%; that is, Portfolio A plots below the SML (α A = –6%), and hence, is an overpriced portfolio. This is inconsistent with the CAPM.14. Not possible. The SML is the same as in Problem 13. Here, Portfolio A’s requiredreturn is: 10 + (0.9 ⨯8) = 17.2%This is greater than 16%. Portfolio A is overpriced with a negative alpha:α A = –1.2%15. Possible. The CML is the same as in Problem 11. Portfolio A plots below theCML, as any asset is expected to. This scenario is not inconsistent with the CAPM.16. If the security’s correlation coefficient with the market portfolio doubles (with allother variables such as variances unchanged), then beta, and therefore the riskpremium, will also double. The current risk premium is: 14 – 6 = 8%The new risk premium would be 16%, and the new discount rate for the securitywould be: 16 + 6 = 22%If the stock pays a constant perpetual dividend, then we know from the original data that the dividend (D) must satisfy the equation for the present value of a perpetuity: Price = Dividend/Discount rate50 = D/0.14 ⇒ D = 50 ⨯ 0.14 = $7.00At the new discount rate of 22%, the stock would be worth: $7/0.22 = $31.82The increase in stock risk has lowered its value by 36.36%.17. d.18. a. Since the market portfolio, by definition, has a beta of 1, its expected rate ofreturn is 12%.b.β = 0 means no systematic risk. Hence, the stock’s expected rate of return inmarket equilibrium is the risk-free rate, 5%.ing the SML, the fair expected rate of return for a stock with β = –0.5 is:E(r) = 5 + [(–0.5)(12 – 5)] = 1.5%The actually expected rate of return, using the expected price and dividend fornext year is:E(r) = [($41 + $1)/40] – 1 = 0.10 = 10%Because the actually expected return exceeds the fair return, the stock isunderpriced.19. a. E(r P) = r f + β P [E(r M ) – r f ] = 5% + 0.8 (15% − 5%) = 13%α = 14% - 13% = 1%You should invest in this fund because alpha is positive.b. The passive portfolio with the same beta as the fund should be invested 80%in the market-index portfolio and 20% in the money market account. For thisportfolio:E(r P) = (0.8 × 15%) + (0.2 × 5%) = 13%14% − 13% = 1% = α20. d. [You need to know the risk-free rate]21. d. [You need to know the risk-free rate]22. a.Expected Return AlphaStock X 5% + 0.8(14% - 5%) = 12.2% 14.0% - 12.2% = 1.8%Stock Y 5% + 1.5(14% - 5%) = 18.5% 17.0% - 18.5% = -1.5%b.i. Kay should recommend Stock X because of its positive alpha, compared toStock Y, which has a negative alpha. In graphical terms, the expectedreturn/risk profile for Stock X plots above the security market line (SML),while the profile for Stock Y plots below the SML. Also, depending on theindividual risk preferences of Kay’s clients, the lower beta for Stock X mayhave a beneficial effect on overall portfolio risk.ii. Kay should recommend Stock Y because it has higher forecasted return andlower standard deviation than Stock X. The respective Sharpe ratios forStocks X and Y and the market index are:Stock X: (14% - 5%)/36% = 0.25Stock Y: (17% - 5%)/25% = 0.48Market index: (14% - 5%)/15% = 0.60The market index has an even more attractive Sharpe ratio than either of theindividual stocks, but, given the choice between Stock X and Stock Y, StockY is the superior alternative.When a stock is held as a single stock portfolio, standard deviation is the relevantrisk measure. For such a portfolio, beta as a risk measure is irrelevant. Althoughholding a single asset is not a typically recommended investment strategy, someinvestors may hold what is essentially a single-asset portfolio when they hold thestock of their employer company. For such investors, the relevance of standarddeviation versus beta is an important issue.23. The appropriate discount rate for the project is:r f + β[E(r M ) – r f ] = 8 + [1.8 ⨯ (16 – 8)] = 22.4% Using this discount rate:∑=+-=101t t 1.224150400NPV = −400 pesos + [150 pesos × Annuity factor (22.4%, 10 years) = 180.92 pesosThe internal rate of return (IRR) for the project is 35.73%. Recall from yourintroductory finance class that NPV is positive if IRR > discount rate (or,equivalently, hurdle rate). The highest value that beta can take before the hurdle rate exceeds the IRR is determined by:35.73 = 8 + β(16 – 8) ⇒ β = 27.73/8 = 3.4724. a. McKay should borrow funds and invest those funds proportionately inMurray’s existing portfolio (i.e., buy more risky assets on margin). In additionto increased expected return, the alternative portfolio on the capital marketline will also have increased risk, which is caused by the higher proportion ofrisky assets in the total portfolio.b. McKay should substitute low beta stocks for high beta stocks in order toreduce the overall beta of York’s portfolio. By reducing the overall portfoliobeta, McKay will reduce the systematic risk of the portfolio, and thereforereduce its volatility relative to the market. The security market line (SML)suggests such action (i.e., moving down the SML), even though reducing betamay result in a slight loss of portfolio efficiency unless full diversification ismaintained. York’s primary objective, however, is not to maintain efficiency,but to reduce risk exposure; reducing portfolio beta meets that objective.Because York does not want to engage in borrowing or lending, McKaycannot reduce risk by selling equities and using the proceeds to buy risk-freeassets (i.e., lending part of the portfolio). 25. d.26. r 1 = 19%; r 2 = 16%; β1 = 1.5; β2 = 1a. To determine which investor was a better selector of individual stocks we lookat abnormal return, which is the ex-post alpha; that is, the abnormal return isthe difference between the actual return and that predicted by the SML.Without information about the parameters of this equation (risk-free rate andmarket rate of return) we cannot determine which investor was more accurate.b. If r f = 6% and r M = 14%, then (using the notation alpha for the abnormal return):α 1 = 19 – [6 + 1.5(14 – 6)] = 19 – 18 = 1%α 2 = 16 – [6 + 1(14 – 6)] =16 – 14 = 2%Here, the second investor has the larger abnormal return and thus appears tobe the superior stock selector. By making better predictions, the secondinvestor appears to have tilted his portfolio toward underpriced stocks.c. If r f = 3% and r M = 15%, then:α 1 =19 – [3 + 1.5(15 – 3)] = 19 – 21 = –2%α 2 = 16 – [3+ 1(15 – 3)] = 16 – 15 = 1%Here, not only does the second investor appear to be the superior stockselector, b ut the first investor’s predictions appear valueless (or worse).27. In the zero-beta CAPM the zero-beta portfolio replaces the risk-free rate, and thus: E(r) = 8 + 0.6(17 – 8) = 13.4%28. a. Call the aggressive stock A and the defensive stock D. Beta is the sensitivityof the stock’s return to the market return, i.e., the cha nge in the stock returnper unit change in the market return. Therefore, we compute each stock’s betaby calculating the difference in its return across the two scenarios divided by the difference in the market return:00.2255382A =---=β 30.0255126D =--=βb. With the two scenarios equally likely, the expected return is an average of thetwo possible outcomes:E(r A ) = 0.5 ⨯ (–2 + 38) = 18%E(r D ) = 0.5 ⨯ (6 + 12) = 9%c. The SML is determined by the market expected return of [0.5(25 + 5)] = 15%,with a beta of 1, and the T-bill return of 6% with a beta of zero. See thefollowing graph.The equation for the security market line is:E(r) = 6 + β(15 – 6)d.Based on its risk, the aggressive stock has a required expected return of:E(r A ) = 6 + 2.0(15 – 6) = 24%The analyst’s forecast of expected return is only 18%. Thus the stock’s alpha is:α A = actually expected return – required return (given risk)= 18% – 24% = –6%Similarly, the required return for the defensive stock is:E(r D) = 6 + 0.3(15 – 6) = 8.7%The analyst’s forecast of expected return for D is 9%, and hence, the stock hasa positive alpha:α D = actually expected return – required return (given risk)= 9 – 8.7 = +0.3%The points for each stock plot on the graph as indicated above.e. The hurdle rate is determined by the project beta (0.3), not the firm’s beta.The correct discount rate is 8.7%, the fair rate of return for stock D.29. a. Agree; Regan’s conclusion is correct. By definition, the market portfol io lies onthe capital market line (CML). Under the assumptions of capital market theory,all portfolios on the CML dominate, in a risk-return sense, portfolios that lie onthe Markowitz efficient frontier because, given that leverage is allowed, the CMLcreates a portfolio possibility line that is higher than all points on the efficientfrontier except for the market portfolio, which is Rainbow’s portfolio. BecauseEagle’s portfolio lies on the Markowitz efficient frontier at a point other than themarke t portfolio, Rainbow’s portfolio dominates Eagle’s portfolio.b. Unsystematic risk is the unique risk of individual stocks in a portfolio that isdiversified away by holding a well-diversified portfolio. Total risk is composedof systematic (market) risk and unsystematic (firm-specific) risk.Disagree; Wilson’s remark is incorrect. Because both portfolios lie on theMarkowitz efficient frontier, neither Eagle nor Rainbow has any unsystematic risk.Therefore, unsystematic risk does not explain the different expected returns. Thedetermining factor is that Rainbow lies on the (straight) line (the CML)connecting the risk-free asset and the market portfolio (Rainbow), at the point oftangency to the Markowitz efficient frontier having the highest return per unit ofrisk. Wilson’s remark is also countered by the fact that, since unsystematic riskcan be eliminated by diversification, the expected return for bearing unsystematicis zero. This is a result of the fact that well-diversified investors bid up the priceof every asset to the point where only systematic risk earns a positive return(unsystematic risk earns no return).30. E(r) = r f+ β × [E(r M) − r f]Fuhrman Labs: E(r) = 5 + 1.5 × [11.5 − 5.0] = 14.75%Garten Testing: E(r) = 5 + 0.8 × [11.5 − 5.0] = 10.20%If the forecast rate of return is less than (greater than) the required rate of return,then the security is overvalued (undervalued).Fuhrman Labs: Forecast return –Required return = 13.25% − 14.75% = −1.50%Garten Testing: Forecast return –Required return = 11.25% − 10.20% = 1.05%Therefore, Fuhrman Labs is overvalued and Garten Testing is undervalued.31. Under the CAPM, the only risk that investors are compensated for bearing is therisk that cannot be diversified away (systematic risk). Because systematic risk(measured by beta) is equal to 1.0 for both portfolios, an investor would expect thesame rate of return from both portfolios A and B. Moreover, since both portfoliosare well diversified, it doesn’t matter if the specific risk of the individual securitiesis high or low. The firm-specific risk has been diversified away for both portfolios.。
博迪投资学英文课件 (9)
23-6
Text Pricing Example
rus = 4% ruk = 5% E0 = $2.00 per pound
T = 1 yr
F0
$2.001.04 1 1.05
$1.981
If the futures price varies from $1.981 per pound, covered interest arbitrage is possible.
A US exporter wants to protect against a decline in profit that would result from depreciation of the pound. The current futures price is $2/£1. Suppose FT = $1.90? •The exporter anticipates a profit loss of $200,000 if the pound declines by $.10 •Short or sell pounds for future delivery to avoid the exposure.
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Creating Synthetic Positions with Futures
• Speculators on broad market moves are major players in the index futures market. – Strategy: Buy and hold T-bills and vary the position in market-index futures contracts. – If bullish, then long futures – If bearish, then short futures
兹维博迪-投资学-第九版-中文PPT课件
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系统性风险的上升
银行资产和负债的到期日和流动性之间并不匹配。
负债是短期的、流动的 资产是长期的、非流动的 需要不断再融资改善资产组合
高杠杆比率使得银行几乎没有保证金来确保其安全。
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系统性风险的上升
投资者过分依赖结构化产品，如信用违约掉期来实现信 用升级。
信用违约掉期合约通常是场外交易，缺少公开披露，没 有要求保证金。
为什么会低估信用风险?
没有人会预料到房地产市场的价格会一直下跌 跨地区来分散风险的愿望并未实现 代理问题和评级机构 信用违约掉期并未像预计那样降低风险
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信用违约掉期 (CDS)
信用违约掉期实质上是一种针对借款者违约的保险合同。 投资者购买次级贷款使用信用违约掉期来保证其安全性。
投资银行
• 同意买下新发行的股票 和债券
• 在一级市场上向公众销 售新证券
• 投资者在二级市场上买 卖一级市场发行的证券
商业银行
• 吸收存款、发放贷款
1-14
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2008年的金融危机
金融危机的前情:
“大稳健”: 美国经历了一个低利率和经济稳定的时期，只有一 些温和的经济衰退，经济周期似乎已被驯服。
第一章
1
投资环境
McGraw-Hill/Irwin
Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved.
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实物资产与金融资产
实物资产 取决于该社会经济的生产能力，为经济创 造净利润。 如土地、建筑物、机器以及可用于生产产 品和提供服务的知识。
《投资学》博迪第九版课件Chap009
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Extensions of the CAPM
• Zero-Beta Model – Helps to explain positive alphas on low beta stocks and negative alphas on high beta stocks • Consideration of labor income and non-traded assets
Figure 9.3 The SML and a Positive-Alpha Stock
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The Index Model and Realized Returns
• To move from expected to realized returns, use the index model in excess return form:
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Is the CAPM Practical?
• We must use a proxy for the market portfolio.
• CAPM is still considered the best available description of security pricing and is widely accepted.
• Reward-to-risk ratios of GE and the market portfolio should be equal:
CovrGE , rM
研究生考试博迪《投资学》(第9版)笔记和课后习题详解 第五部分 共七部分
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博迪投资学第九版ppt
27-11
Table 27.4 The Optimal Risky Portfolio with Constraint on the Active Portfolio (wA ≤1)
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• How accurate is your forecast?
• Regress forecast alphas on actual, realized alphas to adjust alpha for the accuracy of the analysts’ previous forecasts.
• The BL model is a generalization of the TB model that allows you to have views about relative performance that cannot be used in the TB model.
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Table 27.5 The Optimal Risky Portfolio with the Analysts’ New Forecasts
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Adjusting Forecasts for the Precision of Alpha
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Steps in the Black-Litterman Model
《投资学博迪Cha》PPT课件
投资者为什么喜欢凸性?
• 曲率大的债券价格在收益下降时的价格上升大于在收益上涨时的价格下降。 • 收益率越不稳定，这种不对称性的吸引力就越大。 • 对于凸性较大的债券而言，投资者必须付出更高的价格并接受更低的到期收
益率。
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可赎回债券
• 当利率下降时，债券的市场价格有一个上限，债券价格不会超过其赎 回价格。
$1,000/1.053.7704 = $831.6717。价格下降 了0.0359%。
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久期法则
法则 1 零息债券的久期等于它的到期时间。 法债则券2 久到期期较时短间。不变时，当息票率较高时， 法限则增3 加票而面增利加率。不变时，债券久期会随期
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久期法则
法收则益4 率保较持低其时他，因息素票都债不券变的，久当期债会券较到长期。
5. 利率风险与债券票面利率成反比。 6. 债券价格对其收益变化的敏感性与当期
出售债券的到期收益率成反比。
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图 16.1 作为到期收益率变化的函数的债券 价格变化
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表 16.1 票面利率为8%的债券价格(半年付 息一次)
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表 16.2 零息债券的价格(半年计一次复利)
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积极债券管理：互换策略
• 替代互换 • 市场价差价互换 • 利率预期互换 • 纯收益获得互换 • 税收互换
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水平分析
• 选择特定的持有期并预测该期末的收益 率曲线。
• 给定持有到期时债券的到期时间， – 它的收益可以从预测的收益率曲线和 计算的期末价格中得出
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感谢下 载
• 负凸性 • 使用有效久期:
有效久期 P / P r
博迪投资学第九版课件
p
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Risk Adjusted Performance: Treynor
2) Treynor Measure
(rP rf )
P
rp = Average return on the portfolio
rf = Average risk free rate ßp = Weighted average beta for portfolio
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Introduction
• Two common ways to measure average portfolio return: 1. Time-weighted returns 2. Dollar-weighted returns • Returns must be adjusted for risk.
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Time-Weighted Return
53 50 2 r1 10% 50 54 53 2 r2 5.66% 53
rG = [ (1.1) (1.0566) ]1/2 – 1 = 7.81% The dollar-weighted average is less than the time-weighted average in this example because more money is invested in year two, when the return was lower.
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M Measure
• Developed by Modigliani and Modigliani • Create an adjusted portfolio (P*)that has the same standard deviation as the market index. • Because the market index and P* have the same standard deviation, their returns are comparable:
Chap009 资本资产定价模型兹维 博迪 《投资学 》第九版课件PPT
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图9.3 证券市场线和一只α值为正的股票
股票的实际期望 收益与正常期望收 益之间的差，称为 股票的阿尔法，。 被低估的股票期 望收益值将高于证 券市场线给出的正 常收益值。
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9.4 计量经济学与期望收益—贝塔关系
9.3.2 实证检验不支持CAPM
• 实证拒绝了假设：α等于0。 • 统计偏差的引进。 • 米勒和斯科尔斯的论文证明了计量问题可 能会导致拒绝资本资产定价模型，即使该 模型是非常有效的。 • 但也可能是模型本身的问题。
E r r
M f
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• 变换一下，我们可以得到：
ErGE rf GE ErM rf
– 风险溢价取决于两个因素：
• 一是市场组合风险报酬[E(r )－rf]； • 二是资产对市场组合的风险暴露程度β；
M
注意：预测的是收益
9-8
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E (rM ) rf M E ( r ) r M f
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9.1.5 证券市场线★
均衡市场中，所有证券 都必须在证券市场线上。 证券市场线：期望收益 -贝塔关系。斜率为市 场投资组合的风险溢价 ：【E(rM)-rf 】。
• βi为个股对市场组合方差的贡献。
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博迪投资学第九版课件
Security D and Security E
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Two-Security Portfolio: Risk
• Another way to express variance of the portfolio:
2 P wD wDCov(rD , rD ) wE wE Cov(rE , rE ) 2wD wE Cov(rD , rE )
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Figure 7.6 The Opportunity Set of the Debt and Equity Funds and Two Feasible CALs
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Figure 7.3 Portfolio Expected Return as a Function of Investment Proportions
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Figure 7.4 Portfolio Standard Deviation as a Function of Investment Proportions
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Figure 7.2 Portfolio Diversification
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Covariance and Correlation
• Portfolio risk depends on the correlation between the returns of the assets in the portfolio
《投资学》(博迪)ppt课件
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表25.6 综合评分与单项评分
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表 25.7 综合风险与政治风险预测
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表25.7 的解释
该表通过情景分析了解国家风险。 风险稳定度就是最好情况的风险值减去最
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熊市中国际分散化投资还会带来好处吗?
在资本市场动荡时 期，国家组合投资 收益之间的相关性 将增大。
罗尔模型揭示了全 球股价变动背后一 个广泛的因素。
预测：
分散化只能减轻各 国特殊事件的影响。
在1987年发生了什 么? 2008年呢?
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和外币。
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国际化投资的风险因素
风险变化的两 个来源:
1. 以当地货币计量的收益 率
2. 当地货币调整为本国货 币后的收益率
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例 25.1 汇率风险
假设英国无风险利率为10% 现在的汇率是 1英镑兑2美元 。
一个投资者有20,000 美元，即可以购买 10,000 英镑，一年后投资可得11,000英镑。
如果汇率下跌为1英镑兑1.80美元那么最终 只能得到19, 800美元, 损失了200美元。
对美国投资者而言，这项投资并不是无风 险的。
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Zvi Bodie《投资学》 (第9版中文)第二章金融工具(一)
注意：有报价风险。 非竞争性：是无条件的，以成功的竞争性报价 的平均价格为国库券的成交价，最大购买额为 每一定单不能超过100万美元。
按照投资者报价的高低排序，依次向竞争 性与非竞争性投资者出售国库券，直至国 库券全部售完为止。
投资学 第2章
短期国债的收益率计算方法——银行 折现收益率
期限为182天（26周）的票面价值为10000美元的 国库券，售价为9600美元 半年的收益率为：400/9600=0.0417 年收益率r=(1+0.0417)2-1=8.51% 银行折现（bank discount method）收益率为
投资学 第2章
2.2.1 中、长期国债
中期国债（T-Notes）：一年以上10年以下 长期国债（T-Bonds） ：10年～30年。 国债的收益（资本利得和利息）可以免税。 美国：两者都是以1000美元的面值发行， 每半年付息一次，属于息票（Coupon）债 券。
投资学 第2章
货币市场工具
金 融 工 具
资本市场工具பைடு நூலகம்
固定收益证券 股票 衍生金融工具
投资学 第2章
Historical Returns
Investment U.S. Treasury Bills Intermediate-term T-bonds Long term T-bonds U.S. Corporate bonds (AAA) Non-U.S. bonds (AAA) U.S. common stocks (S&P 500) U.S. common stocks (small cap) Non-U.S. common stocks (in $ terms) U.S. real estate U.S. inflation rate (annual rate) Total Return, Total Return, 1929-1993 1984-1993 3.7% 5.3% 5.0% 5.6% n/a 9.5% 12.0% n/a n/a 3.2%
博迪投资学第九版课件
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Intrinsic Value and Market Price
• The intrinsic value (IV) is the “true” value, according to a model. • The market value (MV) is the consensus value of all market participants Trading Signal: IV > MV Buy IV < MV Sell or Short Sell IV = MV Hold or Fairly Priced
2013
kg
kg
0.111 0.077
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Honda Example
18-18
Example 18.4 Growth Opportunities
• Firm reinvests 60% of its earnings in projects with ROE of 10%, capitalization rate is 15%. Expected year-end dividend is $2/share, paid out of earnings of $5/share. • g=ROE x b = 10% x .6 = 6%
$5 PVGO $22.22 $11.11 .15
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Life Cycles and Multistage Growth Models • Expected dividends for Honda: 2010 $.50 2012 $ .83 2011 $.66 2013 $1.00 • Since the dividend payout ratio is 30% and ROE is 11%, the “steadystate” growth rate is 7.7%.
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1 1 - 11
Active or Passive Management
• Active Management
– An expensive strategy – Suitable only for very large portfolios
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Resource Allocation
• I f markets were i n e f f i c i e n t , resources would be s y s t e m a t i c a l l y misallocated.
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Types of Stock Analysis
• Fundamental Analysis - using economic and accounting information to predict stock prices
• How do we explain random stock p r i c e changes?
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E f f i c i e n t Market Hypothesis (EMH)
• EMHsays stock p r i c e s already r e f l e c t a l l available information
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Assumptions
• Individual investors are price takers • Single-period investment horizon • Investments are limited to traded financial assets • No taxes and transaction costs
• Information is costless and available to all investors • Investors are rational mean-variance optimizers • There are homogeneous expectations
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9-19
Econometrics and the Expected ReturnBeta Relationship
• Statistical bias is easily introduced. • Miller and Scholes paper demonstrated how econometric problems could lead one to reject the CAPM even if it were perfectly valid.
Figure 9.3 The SML and a Positive-Alpha Stock
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The Index Model and Realized Returns
• To move from expected to realized returns, use the index model in excess return form:
9-16
Figure 9.4 Estimates of Individual Mutual Fund Alphas, 1972-1991
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Is the CAPM Practical?
• CAPM is the best model to explain returns on risky assets. This means: – Without security analysis, α is assumed to be zero. – Positive and negative alphas are revealed only by superior security analysis.
Ri i i RM ei
• The index model beta coefficient is the same as the beta of the CAPM expected return-beta relationship.
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Extensions of the CAPM
• Merton’s Multiperiod • Consumption-based Model and hedge CAPM portfolios • Rubinstein, Lucas, • Incorporation of the and Breeden effects of changes in • Investors allocate the real rate of wealth between interest and inflation consumption today and investment for the future
• Therefore, the reward-to-risk ratio for investments in GE would be:
GE's contribution to risk premium wGE E (rGE ) rf E (rGE ) rf GE's contribution to variance wGE Cov(rGE , rM ) Cov(rGE , rM )
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GE Example
• Reward-to-risk ratio for investment in market portfolio:
Market risk premium E (rM ) rf 2 Market variance M
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9-9
GE Example
• Covariance of GE return with the market portfolio:
n n Cov(rGE , rM ) Cov rGE , wk rk wk Cov(rk , rGE ) k 1 k 1
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Figure 9.1 The Efficient Frontier and the Capital Market Line
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Market Risk Premium
•The risk premium on the market portfolio will be proportional to its risk and the degree of risk aversion of the investor:
2 E (rM ) rf A M 2 where M is the variance of the market portolio and
A is the average degree of risk aversion across investors
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Return and Risk For Individual Securities
• The risk premium on individual securities is a function of the individual security’s contribution to the risk of the market portfolio. • An individual security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio.
9-11
GE Example
• The risk premium for GE:
E rGE rf COV rGE , rM
2
Er r
M f
M
• Restating, we obtain:
E rGE rf GE E rM rf
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• Reward-to-risk ratios of GE and the market portfolio should be equal: E rGE rf E rM rf 2 CovrGE , rM M
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Resulting Equilibrium Conditions
• All investors will hold the same portfolio for risky assets – market portfolio • Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value
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Liquidity and the CAPM
•Liquidity: The ease and speed with which an asset can be sold at fair market value • Illiquidity Premium: Discount from fair market value the seller must accept to obtain a quick sale. – Measured partly by bid-asked spread – As trading costs are higher, the illiquidity discount will be greater.
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Expected Return-Beta Relationship
• CAPM holds for the overall portfolio because:
E (rP ) wk E (rk ) and
P wk k
k
k
• This also holds for the market portfolio:
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