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1、Chapter Outline11.1 Factor Models:Announcements,Surprises,and Expected Returns11.2 Risk:Systematic and Unsystematic11.3 Systematic Risk and Betas11.4 Portfolios and Factor Models11.5 Betas and Expected Returns11.6 The Capital Asset Pricing Model and the Arbitrage Pricing Theory11.7 Parametric Approa
2、ches to Asset Pricing11.8 Summary and ConclusionsArbitrage Pricing TheoryArbitrage-arises if an investor can construct a zero investment portfolio with a sure profit.Since no investment is required,an investor can create large positions to secure large levels of profit.In efficient markets,profitabl
3、e arbitrage opportunities will quickly disappear.11.1 Factor Models:Announcements,Surprises,and Expected Returns The return on any security consists of two parts.First the expected returns Second is the unexpected or risky returns.A way to write the return on a stock in the coming month is:return th
4、eofpart unexpected theis return theofpart expected theis whereURURR11.1 Factor Models:Announcements,Surprises,and Expected Returns Any announcement can be broken down into two parts,the anticipated or expected part and the surprise or innovation:Announcement=Expected part+Surprise.The expected part
5、of any announcement is part of the information the market uses to form the expectation,R of the return on the stock.The surprise is the news that influences the unanticipated return on the stock,U.11.2 Risk:Systematic and Unsystematic A systematic risk is any risk that affects a large number of asse
6、ts,each to a greater or lesser degree.An unsystematic risk is a risk that specifically affects a single asset or small group of assets.Unsystematic risk can be diversified away.Examples of systematic risk include uncertainty about general economic conditions,such as GNP,interest rates or inflation.O
7、n the other hand,announcements specific to a company,such as a gold mining company striking gold,are examples of unsystematic risk.11.2 Risk:Systematic and UnsystematicSystematic Risk;m Nonsystematic Risk;n Total risk;UWe can break down the risk,U,of holding a stock into two components:systematic ri
8、sk and unsystematic risk:risk icunsystemat theis risk systematic theis wherebecomesmmRRURR 11.3 Systematic Risk and Betas The beta coefficient,b,tells us the response of the stocks return to a systematic risk.In the CAPM,b measured the responsiveness of a securitys return to a specific risk factor,t
9、he return on the market portfolio.)()(2,MMiiRRRCovb We shall now consider many types of systematic risk.11.3 Systematic Risk and BetasFor example,suppose we have identified three systematic risks on which we want to focus:1.Inflation2.GDP growth3.The dollar-euro spot exchange rate,S($,)Our model is:
10、risk icunsystemat theis beta rate exchangespot theis beta GDP theis betainflation theis FFFRRmRRSGDPISSGDPGDPIISystematic Risk and Betas:ExampleSuppose we have made the following estimates:1.bI=-2.302.bGDP=1.503.bS=0.50.Finally,the firm was able to attract a“superstar”CEO and this unanticipated deve
11、lopment contributes 1%to the return.FFFRRSSGDPGDPII%1%150.050.130.2SGDPIFFFRRSystematic Risk and Betas:ExampleWe must decide what surprises took place in the systematic factors.If it was the case that the inflation rate was expected to be by 3%,but in fact was 8%during the time period,then FI =Surpr
12、ise in the inflation rate=actual expected=8%-3%=5%150.050.130.2SGDPIFFFRR%150.050.1%530.2SGDPFFRRSystematic Risk and Betas:ExampleIf it was the case that the rate of GDP growth was expected to be 4%,but in fact was 1%,then FGDP=Surprise in the rate of GDP growth =actual expected=1%-4%=-3%150.050.1%5
13、30.2SGDPFFRR%150.0%)3(50.1%530.2SFRRSystematic Risk and Betas:ExampleIf it was the case that dollar-euro spot exchange rate,S($,),was expected to increase by 10%,but in fact remained stable during the time period,then FS=Surprise in the exchange rate=actual expected=0%-10%=-10%150.0%)3(50.1%530.2SFR
14、R%1%)10(50.0%)3(50.1%530.2 RRSystematic Risk and Betas:ExampleFinally,if it was the case that the expected return on the stock was 8%,then%150.0%)3(50.1%530.2SFRR%12%1%)10(50.0%)3(50.1%530.2%8RR%8R11.4 Portfolios and Factor Models Now let us consider what happens to portfolios of stocks when each of
15、 the stocks follows a one-factor model.We will create portfolios from a list of N stocks and will capture the systematic risk with a 1-factor model.The ith stock in the list have returns:iiiiFRRRelationship Between the Return on the Common Factor&Excess ReturnExcess returnThe return on the factor Fi
16、iiiiFRRIf we assume that there is no unsystematic risk,then i=0Relationship Between the Return on the Common Factor&Excess ReturnExcess returnThe return on the factor FIf we assume that there is no unsystematic risk,then i=0FRRiiiRelationship Between the Return on the Common Factor&Excess ReturnExce
17、ss returnThe return on the factor FDifferent securities will have different betas0.1B50.0C5.1APortfolios and Diversification We know that the portfolio return is the weighted average of the returns on the individual assets in the portfolio:NNiiPRXRXRXRXR2211)()()(22221111NNNNPFRXFRXFRXRNNNNNNPXFXRXX
18、FXRXXFXRXR222222111111iiiiFRRPortfolios and DiversificationThe return on any portfolio is determined by three sets of parameters:In a large portfolio,the third row of this equation disappears as the unsystematic risk is diversified away.NNPRXRXRXR22111.The weighed average of expected returns.FXXXNN)
19、(22112.The weighted average of the betas times the factor.NNXXX22113.The weighted average of the unsystematic risks.Portfolios and DiversificationSo the return on a diversified portfolio is determined by two sets of parameters:1.The weighed average of expected returns.2.The weighted average of the b
20、etas times the factor F.FXXXRXRXRXRNNNNP)(22112211In a large portfolio,the only source of uncertainty is the portfolios sensitivity to the factor.11.5 Betas and Expected ReturnsThe return on a diversified portfolio is the sum of the expected return plus the sensitivity of the portfolio to the factor
21、.FXXRXRXRNNNNP)(1111FRRPPPNNPRXRXR11 that RecallNNPXX11 andPRPRelationship Between b&Expected Return If shareholders are ignoring unsystematic risk,only the systematic risk of a stock can be related to its expected return.FRRPPPRelationship Between b&Expected ReturnExpected returnb bFRABCDSML)(FPFRR
22、RR11.6 The Capital Asset Pricing Model and the Arbitrage Pricing Theory APT applies to well diversified portfolios and not necessarily to individual stocks.With APT it is possible for some individual stocks to be mispriced-not lie on the SML.APT is more general in that it gets to an expected return
23、and beta relationship without the assumption of the market portfolio.APT can be extended to multifactor models.11.7 Empirical Approaches to Asset Pricing Both the CAPM and APT are risk-based models.There are alternatives.Empirical methods are based less on theory and more on looking for some regular
24、ities in the historical record.Be aware that correlation does not imply causality.Related to empirical methods is the practice of classifying portfolios by style e.g.Value portfolio Growth portfolio11.8 Summary and Conclusions The APT assumes that stock returns are generated according to factor mode
25、ls such as:FFFRRSSGDPGDPIIAs securities are added to the portfolio,the unsystematic risks of the individual securities offset each other.A fully diversified portfolio has no unsystematic risk.The CAPM can be viewed as a special case of the APT.Empirical models try to capture the relations between re
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第十一章 套利定價(jià)理論
