Bodie2e-Chapter12-Portfolio-Opportunities-and-Choice-英文版-金融學(第二版)課件

1、Chapter 12: Portfolio Opportunities and ChoiceObjectiveTo understand the theory of personalportfolio selection in theory and in practice1Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallChapter 12: Portfolio OpChapter 12 Contents12.1 The process of personal portfolio selection12.2 T

2、he trade-off between expected return and risk12.3 Efficient diversification with many risky assets2Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallChapter 12 Contents12.1 The prObjectivesTo understand the process of personal portfolio selection in theory and practice3Copyright 2009

3、 Pearson Education, Inc. Publishing as Prentice HallObjectivesTo understand the prBodie2e_Chapter12-Portfolio-Opportunities-and-Choice-英文版-金融學(第二版)課件Bodie2e_Chapter12-Portfolio-Opportunities-and-Choice-英文版-金融學(第二版)課件12.1 The Process of Personal Portfolio SelectionPortfolio selectionthe study of how

4、people should invest their wealthprocess of trading off risk & expected return to find the best portfolio of assets & liabilitiesNarrower dfn: consider only securitiesWider dfn: house purchase, insurance, debtBroad dfn: human capital, education6Copyright 2009 Pearson Education, Inc. Publishing as Pr

5、entice Hall12.1 The Process of Personal PThe Life CycleThe risk exposure you should accept depends upon your ageConsider two investments (rho=0.2)Security 1 has a volatility of 20% and an expected return of 12%Security 2 has a volatility of 8% and an expected return of 5%7Copyright 2009 Pearson Educ

6、ation, Inc. Publishing as Prentice HallThe Life CycleThe risk exposurPrice TrajectoriesThe following graph show the the price of the two securities generated by a bivariate normal distribution for returnsThe more risky security may be thought of as a share of common stock or a stock mutual fundThe l

7、ess risky security may be thought of as a bond or a bond mutual fund8Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallPrice TrajectoriesThe followin9Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall9Copyright 2009 Pearson EduInterpretation of the GraphThe graph is p

8、lotted on a log scale in so that you can see the important featuresThe magenta bond trajectory is clearly less risky than the navy-blue stock trajectoryThe expected prices of the bond and the stock are straight lines on a log scale10Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallI

9、nterpretation of the GraphTheInterpretation of the GraphRecall the log scale: the volatility increases with the length of the investmentYou begin to form the conjecture that the chances of the stock price being less than the price bond is higher in earlier years11Copyright 2009 Pearson Education, In

10、c. Publishing as Prentice HallInterpretation of the GraphRecGenerating More TrajectoriesThis was just one of an infinite number of trajectories generated by the same 2 means, 2 volatilities, and the correlationI have not cheated you, this was indeed the first trajectory generated by the statisticsth

11、e following trajectories are not reordered nor editedInstructor: On slower computers there may be a delay12Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallGenerating More TrajectoriesTh13Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall13Copyright 2009 Pearson Ed14

12、Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall14Copyright 2009 Pearson Edand Lots More!15Copyright 2009 Pearson Education, Inc. Publishing as Prentice Halland Lots More!15Copyright 2From Conjecture to HypothesisYou are probably ready to make the hypothesis thatthe probability of

13、the high-risk, high-return security will out-perform the low-risk, low-return increases with time16Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallFrom Conjecture to HypothesisYBut:I promised to be perfectly frank and honest (pfah) with you about the ordering of the simulated traje

14、ctoriesThe next trajectory truly was the next trajectory in the sequence, honest!17Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallBut:I promised to be perfectly18Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall18Copyright 2009 Pearson EdExplanationThe bond and th

15、e stock end up at about the same price, when the expected prices are more than a magnitude apartThere is either a very good explanation for this, or there is a very high probability that I have been much less than perfectly frank and honest with you19Copyright 2009 Pearson Education, Inc. Publishing

16、 as Prentice HallExplanationThe bond and the stAnother View of the ModelA little mathematics, and we are able to generate the following price distributions for the stock and the bond for 2, 5, 10, and 40 years into the future20Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallAnother

17、 View of the ModelA lit21Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall21Copyright 2009 Pearson EdThere is a lot going on here, so we will further constrain our viewFirst look at stock prices over a period of 10 yearsThe prices are distributed according to the lognormal distribut

18、ion22Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallThere is a lot going on here, 23Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall23Copyright 2009 Pearson EdNotethe scale is $0 to $800the distribution diffuses and drifts towards higher prices with timethe diffu

19、sion is more pronounced in the earlier years than in the later yearsyou may see that the mode, median, and mean appear to drift apart with time24Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallNotethe scale is $0 to $80024CBond in TimeYou will recall that if you invest in a 5-year

20、default-free pure discount bond for 5 years, the return is known with certaintyTo avoid this effect, assume we invest in short term bonds, and roll them over as they mature25Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallBond in TimeYou will recall th26Copyright 2009 Pearson Educa

21、tion, Inc. Publishing as Prentice Hall26Copyright 2009 Pearson EdNotethe scale is now $0 to $400 (not $0 to $800 as in the case of the stock)we observe the same kind of diffusion and drift behavior, and there is less of each(remember to adjust for the scale)27Copyright 2009 Pearson Education, Inc. P

22、ublishing as Prentice HallNotethe scale is now $0 to $40Contrast of Trajectories and DistributionsThe price distributions and the trajectories were generated from the same distribution. ButThey do not seem to agreeThe distributions appear to produce much lower averages (expected returns) than the tr

23、ajectories28Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallContrast of Trajectories and DMeaty TailsThe resolution is that the distributions have much meatier tails than your intuition allows, pushing the median and mean further and further from the mode with timeThe region where

24、the left tail appears to have drifted into insignificance has a profound affect on the mean29Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallMeaty TailsThe resolution is tStock and Bonds Distributions Compared at the Same TimesThe next sequence of slides contrasts the distribution

25、of stock and bond prices at 1, 2, 5, 10, and 40 into the futureSome of the slides have different measures of central tendency indicatedNote the behavior of these statistics as time increases30Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallStock and Bonds Distributions Mode =104Mod

26、e =106Median=104Mean =104Median=111Mean = 11331Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallMode =104Mode =106Median=104Me32Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall32Copyright 2009 Pearson EdMode = 122 Mode = 135 Median= 126Mean = 128Median= 165Mean = 1

27、8233Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallMode = 122 Mode = 135 Median= 34Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall34Copyright 2009 Pearson EdMode =503 Mode =1,102 Median=650Mean =739Median=5,460Mean =12,15135Copyright 2009 Pearson Education, Inc.

28、 Publishing as Prentice HallMode =503 Mode =1,102 Median=6Slide Sequence SummaryThe next table summarizes the drifts of the measures of central tendencyNote that the means do in fact tie back to the trajectoriesThe last (anomalous?) trajectory not an uncommon occurrence, and I was pfah with you36Cop

29、yright 2009 Pearson Education, Inc. Publishing as Prentice HallSlide Sequence SummaryThe next37Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall37Copyright 2009 Pearson EdImplication for InvestorsIf you are older, the average remaining life of the investment is relatively short, and

30、 there is a larger probability that an investment in the risky security will result in a lossThis is not serious if you have substantial assets, in which case you can afford to take the risk, and enjoy higher expected returns38Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallImplica

31、tion for InvestorsIf yoImplication for InvestorsIf you are younger, the average remaining life of retirement investment is longer, and there is only a small probability that an investment in the risky security will be less than the “safer” oneInvesting in the less risky security will almost always r

32、esult in a significantly smaller retirement income39Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallImplication for InvestorsIf yoImplication for InvestorsRelatively early during a typical life cycle, there may be a need to liquidate some invested funds, perhaps for a house deposit

33、, a childs education, or an uninsured medical emergencyIn the case where liquidating an investment early may damage long-term goals, some precautionary funds should be kept in lower-risk securities40Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallImplication for InvestorsRelatTime

34、HorizonsPlanning horizonThe total length of time for which one plansDecision horizonThe length of time between decisions to revise a portfolioTrading horizonThe shortest possible time interval over which investors may revise their portfolios41Copyright 2009 Pearson Education, Inc. Publishing as Pren

35、tice HallTime HorizonsPlanning horizon4Computing Life ExpectancyMortality tables may be organized as three columns: actuary age, deaths/year per 1000 live births, and remaining life expectation. Note:if you survive from 60 to 65, for example, the expected date of your death advances by 3 to 4 yearsy

36、oung women have a higher life expectation than men, but this is lost with advancing age42Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallComputing Life ExpectancyMortaUseful Internet AddressThe Society of Actuaries maintain a web site that provides detailed mortality tables, intera

37、ctive computer models, mortgage experiences, career information, and current research papers43Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallUseful Internet AddressThe Soc44Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall44Copyright 2009 Pearson Ed45Copyright 200

38、9 Pearson Education, Inc. Publishing as Prentice Hall45Copyright 2009 Pearson EdLife Expectancy05101520256065707580859095AgeRemaining Expected LifeMExLifeFExLife46Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallLife Expectancy051015202560657Risk ToleranceYour tolerance for bearing

39、risk is a major determinant of portfolio choicesIt is the mirror image of risk aversionWhatever its cause, we do not distinguish between capacity to bear risk and attitude towards risk47Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallRisk ToleranceYour tolerance fRole of Profession

40、al Asset ManagersMost people have neither the time nor the skill necessary to optimize a portfolio for risk and returnProfessional fund managers provide this service asindividually designed solutions to the precise needs of a customer ($)a set of financial products which may be used together to sati

41、sfy most customer goals ($)48Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallRole of Professional Asset Man12.2 Trade-Off between Expected Return and RiskAssume a world with a single risky asset and a single riskless assetThe risky asset is, in the real world, a portfolio of risky

42、assetsThe risk-free asset is a default-free bond with the same maturity as the investors decision (or possibly the trading) horizon49Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall12.2 Trade-Off between ExpecteTrade-Off between Expected Return and RiskThe assumption of a risky and

43、 riskless security simplifies the analysis50Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallTrade-Off between Expected RetThe Risk-Reward Trade-Off Line51Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallThe Risk-Reward Trade-Off LineCombining the Riskless Asset and

44、 a Single Risky AssetAssume that you invest W1 proportion of your wealth in security 1 and proportion W2 of your wealth in security 2You must invest in either 1 or 2, so W1+W2 = 1Let 2 be the riskless asset, and 1 be the risky asset (portfolio)52Copyright 2009 Pearson Education, Inc. Publishing as P

45、rentice HallCombining the Riskless Asset aCombining the Riskless Asset and a Single Risky AssetYour statistics background tells you how to determine the expected return and volatility of any two-security portfolio1. Form a new random variable, the return of the portfolio,RP, from the two given rando

46、m variables, R1 and R2RP = W1*R1 + W2*R253Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallCombining the Riskless Asset aCombining the Riskless Asset and a Single Risky AssetThe expected return of the portfolio is the weighted average of the component returnsmp = W1*m1 + W2*m2 mp =

47、W1*m1 + (1- W1)*m2 54Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallCombining the Riskless Asset aCombining the Riskless Asset and a Single Risky AssetThe volatility of the portfolio is not quite as simple:sp = (W1* s1)2 + 2W1* s1* W2* s2 + (W2* s2)2)1/255Copyright 2009 Pearson Ed

48、ucation, Inc. Publishing as Prentice HallCombining the Riskless Asset aCombining the Riskless Asset and a Single Risky AssetWe know something special about the portfolio, namely that security 2 is riskless, so s2 = 0, and sp becomes:sp = (W1* s1)2 + 2W1* s1* W2* 0 + (W2* 0)2)1/2sp = |W1| * s156Copyr

49、ight 2009 Pearson Education, Inc. Publishing as Prentice HallCombining the Riskless Asset aCombining the Riskless Asset and a Single Risky AssetIn summarysp = |W1| * s1, And:mp = W1*m1 + (1- W1)*rf , So:If W10, mp = (rf -m1)/ s1*sp + rf Else mp = (m1-rf )/ s1*sp + rf 57Copyright 2009 Pearson Educati

50、on, Inc. Publishing as Prentice HallCombining the Riskless Asset aReflectionThe risk-free rate, rf, the risky securitys expected rate of return, m1, and volatility, s1, are constants, so we have a “ray” that “reflects” from the expected return axes at mp = rf58Copyright 2009 Pearson Education, Inc.

51、Publishing as Prentice HallReflectionThe risk-free rate, IllustrationConsider the set of all portfolios that may be formed by investing (long and or short) in a risky security with a volatility of 20% and an expected return of 15%a riskless security with a volatility of 0% and a known return of 5%59

52、Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallIllustrationConsider the set o60Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall60Copyright 2009 Pearson EdSub-Optimal InvestmentsInvestments on the higher part of the line are always preferred (by normal folk) to in

53、vestments on the lower part of the line, so for our current purposes we may ignore the lower lineThat is, we will not sell the risky asset short and invest the proceeds in the riskless security61Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallSub-Optimal InvestmentsInvestmLong risk

54、y and short risk-free Long both risky and risk-free100% Risky100% Risk-less62Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallLong risky and short risk-freeObservationsAn investor with a low risk tolerance may invest in a portfolio containing a small % of risky securities, and a cor

55、respondingly higher % of riskless securitiesAn investor with a high tolerance for risk may sell risk-free securities he does not own, and invest the proceeding in the risky investmentThey both use the same two securities63Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallObservations

56、An investor with aObservationsThe graph has been labeled the “capital market line” a little prematurelyWe will soon discover that ifthe risky security is the market portfolio of risky securities investors have similar expectations and time horizonsAll investors will invest (long or short) in the mar

57、ket portfolio and risk-free securityThe line joins the capital markets for risky and risk-less securities64Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallObservationsThe graph has beenAchieving a Target Expected Return (1)Your boss has just read an ad that included the data for th

58、e Janus Twenty Fund (Scientific American, Sept 1998, page 6)“You beat them, or Ill find another portfolio manager”, she quips“Wrong way to compute return?” you venture, as you rush for the door65Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallAchieving a Target Expected ReMutual Fu

59、nd Average % Total Returns66Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallMutual Fund Average % Total ReTo obtain a 20% ReturnYou settle on a 20% return, and decide not to pursue on the computational issueRecall: mp = W1*m1 + (1- W1)*rf Your portfolio: s = 20%, m = 15%, rf = 5%So

60、: W1 = (mp - rf)/(m1 - rf) = (0.20 - 0.05)/(0.15 - 0.05) = 150%67Copyright 2009 Pearson Education, Inc. Publishing as Prentice HallTo obtain a 20% ReturnYou settTo obtain a 20% ReturnAssume that you manage a $50,000,000 portfolioA W1 of 1.5 or 150% means you invest (go long) $75,000,000, and borrow