公司理財原版英文課件Chap

1、An Alternative View of Risk and Return: The Arbitrage Pricing TheoryChapter 12Copyright 2010 by the McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin12-1Key Concepts and SkillsoDiscuss the relative importance of systematic and unsystematic risk in determining a portfolios returnoComp

2、are and contrast the CAPM and Arbitrage Pricing Theory12-2Chapter Outline12.1 Introduction12.2 Systematic Risk and Betas12.3 Portfolios and Factor Models12.4 Betas and Expected Returns12.5 The Capital Asset Pricing Model and the Arbitrage Pricing Theory12.6 Empirical Approaches to Asset Pricing12-3A

3、rbitrage Pricing TheoryArbitrage arises if an investor can construct a zero investment portfolio with a sure profit.nSince no investment is required, an investor can create large positions to secure large levels of profit.nIn efficient markets, profitable arbitrage opportunities will quickly disappe

4、ar.12-4Total RiskoTotal risk = systematic risk + unsystematic riskoThe standard deviation of returns is a measure of total risk.oFor well-diversified portfolios, unsystematic risk is very small.oConsequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk

5、.12-5Risk: Systematic and UnsystematicSystematic Risk: m Nonsystematic Risk: n 2Total risk We can break down the total risk of holding a stock into two components: systematic risk and unsystematic risk:risk icunsystemat theis risk systematic theis wherebecomesmmRRURR 12-612.2 Systematic Risk and Bet

6、asoThe beta coefficient, b, tells us the response of the stocks return to a systematic risk.oIn the CAPM, b measures the responsiveness of a securitys return to a specific risk factor, the return on the market portfolio.)()(2,MMiiRRRCovb We shall now consider other types of systematic risk.12-7Syste

7、matic Risk and BetasoFor example, suppose we have identified three systematic risks: inflation, GNP growth, and the dollar-euro spot exchange rate, S($,).oOur model is:risk icunsystemat theis beta rate exchangespot theis beta GNP theis betainflation theis FFFRRmRRSGNPISSGNPGNPII12-8Systematic Risk a

8、nd Betas: ExampleoSuppose we have made the following estimates:1.bI = -2.302.bGNP = 1.503.bS = 0.50oFinally, the firm was able to attract a “superstar” CEO, and this unanticipated development contributes 1% to the return.FFFRRSSGNPGNPII%1%150. 050. 130. 2SGNPIFFFRR12-9Systematic Risk and Betas: Exam

9、pleWe must decide what surprises took place in the systematic factors. If it were the case that the inflation rate was expected to be 3%, but in fact was 8% during the time period, then: FI = Surprise in the inflation rate = actual expected= 8% 3% = 5%150. 050. 130. 2SGNPIFFFRR%150. 050. 1%530. 2SGN

10、PFFRR12-10Systematic Risk and Betas: ExampleIf it were the case that the rate of GNP growth was expected to be 4%, but in fact was 1%, then: FGNP = Surprise in the rate of GNP growth = actual expected = 1% 4% = 3%150. 050. 1%530. 2SGNPFFRR%150. 0%)3(50. 1%530. 2SFRR12-11Systematic Risk and Betas: Ex

11、ampleIf it were the case that the 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. 2SFRR%1%)10(50. 0%)3(50. 1%530. 2 RR12-12Systemat

12、ic Risk and Betas: ExampleFinally, if it were the case that the expected return on the stock was 8%, then:%1%)10(50. 0%)3(50. 1%530. 2 RR%12%1%)10(50. 0%)3(50. 1%530. 2%8RR%8R12-1312.3 Portfolios and Factor ModelsoNow let us consider what happens to portfolios of stocks when each of the stocks follo

13、ws a one-factor model.oWe will create portfolios from a list of N stocks and will capture the systematic risk with a 1-factor model.oThe ith stock in the list has return:iiiiFRR12-14Relationship Between the Return on the Common Factor & Excess ReturnExcess returnThe return on the factor FiiiiiFR

14、RIf we assume that there is no unsystematic risk, then i = 0.12-15Relationship 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 = 0.FRRiii12-16Relationship Between the Return on the Common Factor

15、 & Excess ReturnExcess returnThe return on the factor FDifferent securities will have different betas.0 . 1B50. 0C5 . 1A12-17Portfolios and DiversificationoWe know that the portfolio return is the weighted average of the returns on the individual assets in the portfolio:NNiiPRXRXRXRXR2211)()()(2

16、2221111NNNNPFRXFRXFRXRNNNNNNPXFXRXXFXRXXFXRXR222222111111iiiiFRR12-18Portfolios 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 w

17、eighted average of expected returns.FXXXNN)(22112. The weighted average of the betas times the factor.NNXXX22113. The weighted average of the unsystematic risks.12-19Portfolios and DiversificationSo the return on a diversified portfolio is determined by two sets of parameters:1.The weighted average

18、of expected returns.2.The weighted average of the betas times the factor F.FXXXRXRXRXRNNNNP)(22112211In a large portfolio, the only source of uncertainty is the portfolios sensitivity to the factor.12-2012.4 Betas and Expected ReturnsThe return on a diversified portfolio is the sum of the expected r

19、eturn plus the sensitivity of the portfolio to the factor.FXXRXRXRNNNNP)(1111FRRPPPNNPRXRXR11 that RecallNNPXX11 andPRP12-21Relationship Between b & Expected ReturnoIf shareholders are ignoring unsystematic risk, only the systematic risk of a stock can be related to its expected return.FRRPPP12-

20、22Relationship Between b & Expected ReturnExpected returnb bFRABCDSML)(FPFRRRR12-2312.5 The Capital Asset Pricing Model and the Arbitrage Pricing TheoryoAPT applies to well diversified portfolios and not necessarily to individual stocks.oWith APT it is possible for some individual stocks to be mispriced - not lie on the SML.oAPT is more general in that it gets to an expected return and beta relationship without the assumption