复旦大学研究生投资学义CHPTTheCAPMtest

1、Chapter 14 The CAPM -Applications and testsFan LongzhenPredictions and applicationsCAPM: in market equilibrium, investors are only rewarded for bearing the market risk; APT: in the absence of arbitrage, investors are only rewarded for bearing the factor risk; Applications: -professional portfolio managers: evaluating security returns and fund performance -corporate manager: capital budgeting decisions.Early tests of CAPMCross-sectional test of the model: Douglas (1969); Miller and Scholes (1972)

2、; Black, Jensen and Scholes (1972); Fama and Macbeth (1973)fmfiiifmifiRRRnieRRRERRE=+=+=?1?010,.,2 , 1,)()(continuedDouglas (1969) Adds own-variance to regression significant; Linter adds to regression significant; Miller and Scholes (1972) Measurement error in s; Correlation between measurement error and Skewness of returns . Black, Jensen, and Scholes (1972) Time-series test Use portfolio to maximize dispersion of betas Low stocks positive High stocks negative )(2 iei)(2 ie0)(? =+=iitfmtiifite

3、RRRRsisiHypothesis testing Definition of size and power H true H false Accept correct Type II error Reject type I error correct Size=Pr(Type I error); Power=1-Pr(type II error); Tradeoff between size and power; Fix size, find most powerful test.CAPM test CAPM holds H: ftmtmtftitititmtiiit RRXRRXeXX+=,0=i)1 (222mme iTVVar+=), 0(VNiSome numbers for monthly U.s. data,1985-1989 S -expected returns are unobservable, and could be time- varying; -volatility is not directly observable, and is time-varyi

4、ng.An ideal test of the CAPMIn an idea situation, we have the following input: 1. Risk-free borrowing/lending rate ; 2. Expected returns on the market and on the risky asset ; 3. The exposure to market risk ; These input allow us to examine the relation between reward and risk : 1. More risk, more reward? 2. Do they line up? 3. What is the reward for a risk exposure of 1? 4. Zero risk, zero reward?fR)(MRE)(iRE)var(/ ),cov(MiM iRRR=)(fiRREiA linear relation between risk and reward)()(fM ifiRRERRE

5、=fR1=fMRRE)(Some practical compromiseThe market portfolio is unobservable:Use a proxy, e.g. the S Expected returns are unobservable:use sample average: Unobservable risk exposureUse sample estimates:MR)(),(iMRERE=ti ti tM tMRNmRNm1;1)var(/ ),cov(MiM iRRR=MiMiVC/ ,=()=tii tMM tiM tMM tMmRmRNCmRNV)(1,1,2Testing the linear relationPick a proxy for the market portfolio, and record N monthly returns:For the same sample period, collect a sample of I firms, each with N monthly returns: Construct sample

6、 estimates For , test the linear relation: NtRM t,.,2 , 1: =NtandIiRit,.,2 , 1,.,2 , 1:=iMimm,Ii,.,2 , 1=ifiRm10+=Implication of the CAPM and testingImplication of CAPM: with : zero exposure, zero reward; : one unit of exposure, the same reward as the market. With 43 industrial portfolios, the test tells us that this relation does not hold exactly. One possibility: our measures of the expected returns are contaminated by noises that are unrelated to the betas; What we still would like to know: -

7、on average, is reward related to risk at all? Or not? -On average, does zero risk results in zero reward? ? Or not? -on average, does one unit of risk exposure pay market return? or not ifiRm10+= 00=fMRm= 101= 00=%9 . 51=fMRmRegression in actionSet up a regression -the dependent variable: -the independent variable: -add noise. Feed beta to the regression package:iiieXY+=10fiiRmY= iiX=estimate tabdard errort-statisticR-square gamm06%1.80%3.50.02% gamm10.17%1.70%0.1A summary of the CAPM testsIn ge

8、neral, the test results depend on the sample data, sample periods, statistical approaches, proxy for the market portfolio, ect. But the following findings remain robust: the relation between risk and reward is much flatter than that predicted by the CAPM; The risk beta can not even to begin to explain the cross-sectional variation in the expected returns; Contrary to the prediction of the CAPM, the intercept is significant different from zero.Some possible explanations1. Is the stock market index a good proxy for the market portfolio? Only 1/3 non-governmental tangible assets are owned by the corporate sector; Among the corporate assets, only 1/3 are financed by equity What are about intangible assets, like human capital; What about international markets? 2. Measurement error in beta Except for the market portfolio, we never observe the true beta; To test CAPM, we use estimates for beta, which are measured with errors 3. Measurement error in e

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