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1、Foundations of Financial Analysis and InvestmentsLecture 3: Capital Asset Pricing Model (CAPM)Dr Ekaterina SvetlovaTodays lecture1.Brief revision: Lecture 22.Mean-variance optimization with unlimited borrowing and lending at a risk-free rate3.MPT and CAPM: Preliminary remarks 4.The Capital Asset Pri
2、cing Model (CAPM)5.First considerations about the limitations of CAPMDr Ekaterina SvetlovaThe portfolio consists of two risky assets D (debt) and E (equity)Their weights in the portfolio are We construct risky portfolios varying to provide the lowest possible risk for any given level of expected ret
3、urnE(rp) = wD E(rD) + wEE(rE) Dr Ekaterina Svetlovax xD D and x xE E(xD + xE = 1; xD 0, xE 0)x xD D and x xE E222222Cov,pDDEEDEDEwww wrrCov(rD,rE) = DEDESuccess of diversification depends on the correlation coefficientBodie et al. 2014, Ch. 71. Brief revision: Lecture 2Dr Ekaterina SvetlovaDebtEquit
4、yExpected return E(r)8%13%Standard deviation 12%20%Bodie et al. (2014), Table 7.1, p. 208Bodie et al. (2014), Table 7.3, p. 211ABBodie et al. (2014), p. 2141. Brief revision: Lecture 2Dr Ekaterina SvetlovaDebtEquityExpected return E(r)8%13%Standard deviation 12%20%Bodie et al. (2014), Table 7.1, p.
5、208Bodie et al. (2014), Table 7.3, p. 211When DE = -1,DEDDEww1When DE = 0,1. Brief revision: Lecture 21. Brief revision: Lecture 2Source: Bodie et al. 2014: p. 220Dr Ekaterina SvetlovaDr Ekaterina SvetlovaDiversifiable (non systematic) risk vs undiversifiable (systematic) risk 1. Brief revision: Lec
6、ture 2Bodie et al. (2014), p. 207Dr Ekaterina SvetlovaHow does diversification matter?Dr Ekaterina SvetlovaSponsorsTrusteesThe Investment Management FirmInvestment consultantsthe Tampa firefighters and police officers pension fundCity of Tampa, FloridaHarold J. Bowen III How does diversification mat
7、ter?As for being diversified, which is the mantra of nearly all institutional money managers and consultants, the Tampa fund isnt. The funds assets are concentrated in a relatively small number of stocks and fixed-income investments.In short, the Tampa pension fund pretty much breaks all the convent
8、ional rules of fund management.2. Mean-variance optimization with unlimited borrowing and lending at a risk-free rateDr Ekaterina SvetlovaUnlimited borrowing and lending at a risk-free rate: - Riskless asset is an asset with a certain return for the given time horizon. - For example: US Treasury bon
9、ds that automatically adjust for inflation (TIPS: Treasury inflation protected securities) or short term US Treasury bills (US T-bills)- Standard deviation of the return: = 0 Dr Ekaterina Svetlova2. Mean-variance optimization with unlimited borrowing and lending at a risk-free rateIf you invest in a
10、sset H and riskless asset: xH and xf = 1 - xHErErp p = (1 - xH) Rf + xH RH = R Rf f + x + xH H(Er(ErH H - R Rf f) )p = (1 - xH)2 f + xH2 H2 + 2xH (1 - xH) fH f HAs f = 0, we obtain: p p = x = xH H H H2. Mean-variance optimization with unlimited borrowing and lending at a risk-free rateDr Ekaterina S
11、vetlovaSource: Perold 2004Dr Ekaterina SvetlovaCombining equations for portfolio return and risk, we obtain : ErH - RfErp = Rf + p H2. Mean-variance optimization with unlimited borrowing and lending at a risk-free rateSource: Perold 2004 ErH - Rf HThe slope: Sharpe ratio(Er(ErH H - R - Rf f) )Risk p
12、remium2. Mean-variance optimization with unlimited borrowing and lending at a risk-free rateDr Ekaterina SvetlovaSource: Perold 2004Sharpe ratio of asset H:(12% - 5%)/ 40% = 0.175Important: all combinations of asset H with risk-free borrowing and lending have the same Sharpe ratio: it is the slope o
13、f a straight lineSharpe ratio of asset M:(10% - 5%)/ 20% = 0.252. Mean-variance optimization with unlimited borrowing and lending at a risk-free rateDr Ekaterina SvetlovaSource: Perold 2004Use of Sharpe ratio in practice:Shape ratio is used to measure the performance of a portfolioAdvantage: the ris
14、k adjusted performance measurement2. Mean-variance optimization with unlimited borrowing and lending at a risk-free rateDr Ekaterina SvetlovaSharpe ratio of H 1, it indicates that the securitys price will be more volatile than the marketExample: a beta equals to 1.3 means that the security is 30% mo
15、re volatile than the marketDr Ekaterina SvetlovaUse of beta in practice:Beta as a measure of risk of a mutual fundExample: The BlackRock Global Small Cap Fund (factsheet)4. The Capital Asset Pricing Model (CAPM)Dr Ekaterina SvetlovaThe security market line provides abenchmark for the evaluation of i
16、nvestment performance Asset plots above the SML offer a greater expected returns than indicated by the CAPM (underpriced assets)Asset plots below the SML offer a lower expected returns than indicated by the CAPM (overpriced assets)4. The Capital Asset Pricing Model (CAPM)Dr Ekaterina SvetlovaExample
17、: Market return is expected to be 14%, the stock beta is 1.2, the T-bill rate is 6%.The expected return on the stock is:6 + 1.2(14 6) = 15.6%If you expect 17% return for the stock, the implied alpha is 1.4%4. The Capital Asset Pricing Model (CAPM)Dr Ekaterina SvetlovaImplications of the CAPM:1.The e
18、xpected return of a stock does not depend on its idiosyncratic risk2.In the CAPM, a stocks expected return does not depend on the growth rate of its expected future cash flows3.Beta measures the risk of an asset that cannot be diversified away Overall riskof an asset=Systematic riskCompany specific
19、risk+ 4. The Capital Asset Pricing Model (CAPM)Dr Ekaterina Svetlova Implications of the CAPM for diversificationDiversification reduces risks but does not eliminate themThe type of risk that diversification reduces is the company specific = idiosyncratic risk = a risk specific to each particular as
20、set = it is not correlated across assetsWhen we increase a number of assets in a portfolio, we expect that on average the idiosyncratic risks cancel each other and that the actual return gets closer to the expected return there is no reason to expect compensation for bearing this riskSystematic risk
21、 is common across assets you cannot reduce this risk through diversificationSources of systematic risk: the overall economy or financial markets risk-avers investors require compensation for bearing this riskFullenkamp 20124. The Capital Asset Pricing Model (CAPM)Dr Ekaterina SvetlovaQuick check:Are
22、 the following true or false? Explain.a.Stocks with a beta of zero offer an expected rate of return of zero.b.The CAPM implies that investors require a higher return to hold highly volatile securitiesc.You can construct a portfolio with beta of 0.75 by investing 75% of the investment budget in T-bil
23、ls and the remainder in the market portfolio.Source: Bodie et al. 2014: 317Dr Ekaterina Svetlova4. The Capital Asset Pricing Model (CAPM)Quick check:Which of the following factors reflect pure market risk for a given corporation?a. Increased short-term interest rates.b. Fire in the corporation wareh
24、ousec. Increased insurance costsd. Death of the CEOe. Increased labour costs.Source: Bodie et al. 2014: 235Dr Ekaterina Svetlova4. The Capital Asset Pricing Model (CAPM)Main predictions of the CAPMAll investorswill always combine a risk free asset with the market portfoliowill have the same portfoli
25、o of risky assets (the market portfolio)agree on the expected return and on the expected variance of the market portfolio and of every assetagree on the market risk premium and on the beta of every assetagree on the market portfolio being on the minimum variance frontier and being mean-variance effi
26、cient expect returns from their investments according to the betasTrading volume of financial markets will be very small4. The Capital Asset Pricing Model (CAPM)Dr Ekaterina Svetlova5. First considerations about the limitations of CAPMDr Ekaterina SvetlovaCAPM = equilibrium model (“snapshot” of the
27、market at one point in time)What is “market portfolio”? Indices, national vs. internationalRisk premiums depend on invesment climate and business cycleWarren Buffett: “Risk comes from not knowing what youre doing.”Does the fundamental cash flow analysis really not matter?CAPM has not been confirmed
28、empirically (next lecture)Dr Ekaterina Svetlova doesnt explain the variance of returns: Basu (1977): earning-price-ratio effectBanz (1981): size effectBhandari (1988): high debt-equity-ratio effectStatman et al. (1980): book-to-market-ratio effectBenjamin Graham, the legendary investor:Beta is a mor
29、e or less useful measure of past price fluctuations of common stocks. What bothers me is that authorities now equate the beta idea with the concept of risk. Price variability yes; risk no. Real investment risk is measured not by the percent that a stock may decline in price in relation to the genera
30、l market in a given period, but the danger of a loss of quality and earning power through economic changes or deterioration of management.Is beta the real source of risk? 5. First considerations about the limitations of CAPMDr Ekaterina SvetlovaIs CAPM just CRAP (completely redundant asset pricing)?
31、Montier (2007): “Institutional money managers dont think in terms of variance as a description of risk. Never yet have I met a long only investor who cares about up-side standard deviation; this gets lumped into return.” “An entire industry appears to have arisen obsessed with and .“Fama/French (200
32、4): The CAPM, like Markowitz (1952, 1959) portfolio model on which it is built, is nevertheless a theoretical tour de force. We continue to teach the CAPM as an introduction to the fundamental concepts of portfolio theory and asset pricing, to be built on by more complicated models like Mertons (197
33、3) ICAPM. But we also warn students that despite its seductive simplicity, the CAPMs empirical problems probably invalidate its use in applications.”5. First considerations about the limitations of CAPMDr Ekaterina SvetlovaReferencesBodie, Kane and Markus (2014), Investments, McGrauw Hill, section 7.3 and chapter 9Perold, Andre (2004), The Capital Asset Pricing Model, Journal of Economic Perspectives 18(3), pp. 773-806.Dr Ekaterina Svetlova