第十一章-套利定价理论课件.ppt

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1、第十一章第十一章 套利定价理论套利定价理论2023/1/8第十一章 套利定价理论Arbitrage 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,profitable arbitra

2、ge opportunities will quickly disappear.第十一章 套利定价理论11.1 Factor Models:Announcements,Surprises,and Expected ReturnsThe return on any security consists of two parts.First the expected returnsSecond is the unexpected or risky returns.A way to write the return on a stock in the coming month is:第十一章 套利定价

3、理论11.1 Factor Models:Announcements,Surprises,and Expected ReturnsAny 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 of any announcement is part of the information the market uses to

4、form the expectation,R of the return on the stock.The surprise is the news that influences the unanticipated return on the stock,U.第十一章 套利定价理论11.2 Risk:Systematic and UnsystematicA systematic risk is any risk that affects a large number of assets,each to a greater or lesser degree.An unsystematic ri

5、sk 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.On the other hand,announcements specific to a company,suc

6、h as a gold mining company striking gold,are examples of unsystematic risk.第十一章 套利定价理论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 risk and unsystematic risk:第十一章 套利定价理论11.3 Syst

7、ematic Risk and BetasThe 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,the return on the market portfolio.We shall now consider many types of systematic risk.第十一章 套利定价理论11.3

8、 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:第十一章 套利定价理论Systematic Risk and Betas:ExampleSuppose we have made the following estimates:1.bI=-2.302.bGDP=1.

9、503.bS=0.50.Finally,the firm was able to attract a“superstar”CEO and this unanticipated development contributes 1%to the return.第十一章 套利定价理论Systematic 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

10、 by 3%,but in fact was 8%during the time period,then FI =Surprise in the inflation rate=actual expected=8%-3%=5%第十一章 套利定价理论Systematic 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 exp

11、ected=1%-4%=-3%第十一章 套利定价理论Systematic 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%第十一章 套利定价理论Systematic Risk and B

12、etas:ExampleFinally,if it was the case that the expected return on the stock was 8%,then第十一章 套利定价理论11.4 Portfolios and Factor ModelsNow let us consider what happens to portfolios of stocks when each of the stocks follows a one-factor model.We will create portfolios from a list of N stocks and will c

13、apture the systematic risk with a 1-factor model.The ith stock in the list have returns:第十一章 套利定价理论Relationship Between the Return on the Common Factor&Excess ReturnExcess returnThe return on the factor FIf we assume that there is no unsystematic risk,then ei=0第十一章 套利定价理论Relationship Between the Ret

14、urn on the Common Factor&Excess ReturnExcess returnThe return on the factor FIf we assume that there is no unsystematic risk,then ei=0第十一章 套利定价理论Relationship Between the Return on the Common Factor&Excess ReturnExcess returnThe return on the factor FDifferent securities will have different betas第十一章

15、 套利定价理论Portfolios and DiversificationWe know that the portfolio return is the weighted average of the returns on the individual assets in the portfolio:第十一章 套利定价理论Portfolios and DiversificationThe return on any portfolio is determined by three sets of parameters:In a large portfolio,the third row of

16、 this equation disappears as the unsystematic risk is diversified away.1.The weighed average of expected returns.2.The weighted average of the betas times the factor.3.The weighted average of the unsystematic risks.第十一章 套利定价理论Portfolios and DiversificationSo the return on a diversified portfolio is

17、determined by two sets of parameters:1.The weighed average of expected returns.2.The weighted average of the betas times the factor F.In a large portfolio,the only source of uncertainty is the portfolios sensitivity to the factor.第十一章 套利定价理论11.5 Betas and Expected ReturnsThe return on a diversified

18、portfolio is the sum of the expected return plus the sensitivity of the portfolio to the factor.第十一章 套利定价理论Relationship Between b&Expected ReturnIf shareholders are ignoring unsystematic risk,only the systematic risk of a stock can be related to its expected return.第十一章 套利定价理论Relationship Between b&

19、Expected ReturnExpected returnb bABCDSML第十一章 套利定价理论11.6 The Capital Asset Pricing Model and the Arbitrage Pricing TheoryAPT 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 mor

20、e general in that it gets to an expected return and beta relationship without the assumption of the market portfolio.APT can be extended to multifactor models.第十一章 套利定价理论11.7 Empirical Approaches to Asset PricingBoth the CAPM and APT are risk-based models.There are alternatives.Empirical methods are

21、 based less on theory and more on looking for some regularities 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 portfolioGrowth portfolio第十一章 套利定价理论演讲完毕，谢谢听讲!再见，see you again3rew3rew2023/1/8第十一章 套利定价理论