公司理财chap011

1、McGraw-Hill/IrwinCopyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved CHAPTER11An Alternative View of Risk and ReturnThe Arbitrage Pricing TheorySlide 2Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/IrwinKey Concepts and Skills Understand the decom

2、position of a securitys return into expected and unexpected components Discuss the relative importance of systematic and unsystematic risk in determining a portfolios return Compare and contrast the CAPM and Arbitrage Pricing TheorySlide 3Copyright 2008 by The McGraw-Hill Companies, Inc. All rights

3、reserved McGraw-Hill/IrwinChapter 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 Pricin

4、g Theory11.7 Empirical Approaches to Asset PricingSlide 4Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/IrwinArbitrage Pricing TheoryArbitrage arises if an investor can construct a zero investment portfolio with a sure profit. Since no investment is required, an in

5、vestor can create large positions to secure large levels of profit. In efficient markets, profitable arbitrage opportunities will quickly disappear.Slide 5Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin11.1 Factor Models: Announcements, Surprises, and Expected

6、 Returns The return on any security consists of two parts. First, the expected returns Second, the unexpected or risky returns A way to write the return on a stock in the coming month is:return theofpart unexpected theis return theofpart expected theis whereURURRSlide 6Copyright 2008 by The McGraw-H

7、ill Companies, Inc. All rights reserved McGraw-Hill/IrwinFactor 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 of

8、 any announcement is the 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.Slide 7Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin11.

9、2 Risk: Systematic and Unsystematic A systematic risk is any risk that affects a large number of assets, 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 system

10、atic risk include uncertainty about general economic conditions, such as GNP, interest rates or inflation. On the other hand, announcements specific to a single company are examples of unsystematic risk.Slide 8Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/IrwinRis

11、k: 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 Slide 9Copyright 2008 by The McGraw-Hill

12、 Companies, Inc. All rights reserved McGraw-Hill/Irwin11.3 Systematic Risk and Betas The beta coefficient, b, tells us the response of the stocks return to a systematic risk. In the CAPM, b measures the responsiveness of a securitys return to a specific risk factor, the return on the market portfoli

13、o.)()(2,MMiiRRRCovb We shall now consider other types of systematic risk.Slide 10Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/IrwinSystematic Risk and BetasFor example, suppose we have identified three systematic risks: inflation, GNP growth, and the dollar-euro

14、spot exchange rate, S($,).Our model is:risk icunsystemat theis beta rate exchangespot theis beta GNP theis betainflation theis FFFRRmRRSGNPISSGNPGNPIISlide 11Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/IrwinSystematic Risk and Betas: ExampleSuppose we have made

15、the following estimates:bI = -2.30bGNP = 1.50bS = 0.501. Finally, the firm was able to attract a “superstar” CEO, and this unanticipated development contributes 1% to the return.FFFRRSSGNPGNPII%1%150. 050. 130. 2SGNPIFFFRRSlide 12Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved

16、McGraw-Hill/IrwinSystematic Risk and Betas: ExampleWe 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%

17、150. 050. 130. 2SGNPIFFFRR%150. 050. 1%530. 2SGNPFFRRSlide 13Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/IrwinSystematic 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 th

18、e rate of GNP growth = actual expected = 1% 4% = 3%150. 050. 1%530. 2SGNPFFRR%150. 0%)3(50. 1%530. 2SFRRSlide 14Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/IrwinSystematic Risk and Betas: ExampleIf it were the case that the dollar-euro spot exchange rate, S($,),

19、 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 RRSlide 15Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-

20、Hill/IrwinSystematic 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%8RSlide 16Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin11.4 Portfol

21、ios and Factor Models Now 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 capture the systematic risk with a 1-factor model. The ith stock in the list has return:iiiiFRRSlide 17Copyrig

22、ht 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/IrwinRelationship Between the Return on the Common Factor & Excess ReturnExcess returnThe return on the factor FiiiiiFRRIf we assume that there is no unsystematic risk, then i = 0.Slide 18Copyright 2008 by The McGraw-Hill

23、 Companies, Inc. All rights reserved McGraw-Hill/IrwinRelationship 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.FRRiiiSlide 19Copyright 2008 by The McGraw-Hill Companies, Inc. All rights

24、reserved McGraw-Hill/IrwinRelationship Between the Return on the Common Factor & Excess ReturnExcess returnThe return on the factor FDifferent securities will have different betas.0 . 1B50. 0C5 . 1ASlide 20Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/IrwinPor

25、tfolios and Diversification We know that the portfolio return is the weighted average of the returns on the individual assets in the portfolio:NNiiPRXRXRXRXR2211)()()(22221111NNNNPFRXFRXFRXRNNNNNNPXFXRXXFXRXXFXRXR222222111111iiiiFRRSlide 21Copyright 2008 by The McGraw-Hill Companies, Inc. All rights

26、 reserved McGraw-Hill/IrwinPortfolios 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.NNPRXRXRXR2211The weighted average of expected returns.FXXXNN)(2

27、211The weighted average of the betas times the factor.NNXXX2211The weighted average of the unsystematic risks.Slide 22Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/IrwinPortfolios and DiversificationSo the return on a diversified portfolio is determined by two set

28、s of parameters: The weighted average of expected returns.1. 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.Slide 23Copyright 2008 by The McGraw-Hill Companies, Inc. All r

29、ights reserved McGraw-Hill/Irwin11.5 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.FXXRXRXRNNNNP)(1111FRRPPPNNPRXRXR11 that RecallNNPXX11 andPRPSlide 24Copyright 2008 by The McGraw-Hill Companies,

30、 Inc. All rights reserved McGraw-Hill/IrwinRelationship Between b & Expected Return If shareholders are ignoring unsystematic risk, only the systematic risk of a stock can be related to its expected return.FRRPPPSlide 25Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw

31、-Hill/IrwinRelationship Between b & Expected ReturnExpected returnb bFRABCDSML)(FPFRRRRSlide 26Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin11.6 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