资本资产定价模型(CAPM

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?Source: http:/ 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

8、all the conventional 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

9、 Treasury bonds 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

10、 invest in asset 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

11、 Ekaterina SvetlovaSource: 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 - R

12、f f) )Risk premium2. 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

13、 the slope of 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 portfolioAdvant

14、age: the risk 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 securi

15、ty is 30% more 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)Source: https:/ The Capital Asset Pricing Model (CAPM)Dr Ekaterina SvetlovaThe security market line provides abenchmar

16、k for the evaluation of investment 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

17、Ekaterina SvetlovaExample: 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 SvetlovaImplica

18、tions of the CAPM:1.The expected 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=Systema

19、tic riskCompany specific 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 speci

20、fic to each particular asset = 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

21、 this riskSystematic risk 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 Ekaterin

22、a SvetlovaQuick check:Are 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 i

23、nvestment budget in T-bills 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

24、 in the corporation warehousec. 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 investors-will always combine a risk free asset with the market portfolio-

25、will have the same portfolio of risky assets (the market portfolio)-agree on the expected return and on the expected variance of the market portfolio and of every asset-agree on the market risk premium and on the beta of every asset-agree on the market portfolio being on the minimum variance frontie

26、r and being mean-variance efficient -expect returns from their investments according to the betas-Trading 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 = equil

27、ibrium model (“snapshot” of the 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 mat

28、ter?CAPM has not been confirmed 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

29、legendary investor:Beta is a more 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

30、 price in relation to the general 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)?Montier (2007): “Institutional money