第五章CAPM的應(yīng)用ppt課件

1、第五章 CAPM的運(yùn)用.利用Markowitz 模型進(jìn)展積極證券組合管理市場(chǎng)模型在消極證券組合管理中的運(yùn)用利用Beta去得到好的協(xié)方差估計(jì)利用Beta去得到好的期望報(bào)答率估計(jì)CAPM在消極證券組合管理中的運(yùn)用Black-Litterman 方法例子：Global Portfolio Optimization.1. 利用Markowitz 模型進(jìn)展積極證券組合管理經(jīng)典Markowitz 模型的缺陷待估計(jì)的期望值、協(xié)方差參數(shù)數(shù)量大利用歷史數(shù)據(jù)得到的最優(yōu)證券組合權(quán)重不合理When investors impose no constraints, the models almost always or

2、dain large short positions in many assets. When constraints rule out short positions, the models often prescribe corner solutions with zero weights in many assets, as well as unreasonably large weights in the assets of markets with small capitalizations.These unreasonable results stem from two well

3、recognized problems:由歷史數(shù)據(jù)得到的期望值估計(jì)對(duì)未來報(bào)答率預(yù)測(cè)才干很差最優(yōu)證券組合權(quán)重對(duì)于期望報(bào)答率假設(shè)非常敏感.例：100種證券構(gòu)成的證券組合.例： let us look at the sort of portfolio allocation we get if we use historical returns and volatilities as inputs:.Historical correlations:.If you use our procedures and calculate and optimal portfolio, with , you wil

4、l get portfolio weights of: .We can make a number of points about these optimal portfolios.They illustrate what we mean when we claim that standard mean-variance optimization models often generate unreasonable portfolios.The use of past excess returns to represent a neutral set of views is equivalen

5、t to assuming that the constant portfolio weights that would have performed best historically are in some sense neutral. In reality, of course, they are not neutral at all, but rather are a very special set of weights that go short assets that have done poorly and go long assets that have done well

6、in the particular historical period.A remedy for both of these problems is to use(1) market model to calculate asset covariance, (2) and use the CAPM to determine what market expectation must be, and then combine your “view with the CAPM derived estimates to get portfolio weights.The key input we wi

7、ll need for both of these is the set of asset betas, so, first, we must consider the problem of estimating betas .2. Beta值的估計(jì).利用市場(chǎng)模型估計(jì)An approach to estimating and is to assume that a market model ( and the CAPM) describes returnsThe market modelTo get expected returns use:To get covariances /correl

8、ations, use:For standard deviations:.待估計(jì)的參數(shù)數(shù)量大大減少例如，100種證券構(gòu)成的證券組合.3. CAPM與積極的證券組合管理為了得到最優(yōu)證券組合，我們需求估計(jì)證券組合前沿，有效集方法一：完全忽略市場(chǎng)的觀念，而估計(jì)一切證券的期望報(bào)答率、協(xié)方差例如：利用歷史的數(shù)據(jù)該方法存在問題方法二：接受市場(chǎng)的觀念，簡(jiǎn)單的持有市場(chǎng)證券組合假設(shè)他擁有市場(chǎng)價(jià)錢還沒有反映的信息，該方法并不通知該如何處置.The approach we will instead take is toCalculate betas for the securities we plan to hol

9、d Using these betas, calculate and , assuming the CAPM holds exactlyThen, incorporate our information by “perturbing the values away from the CAPM-calculated valuesFinally, using these estimates and the Markowitz portfolio optimization tools determine our optimal portfolio weights. .Note that if We

10、start with all of the assets in market portfolioWe use the unmodified and we get from step 2 aboveThen the weights we calculate in step 4 will be exactly those of the market portfolio .An exampleUsing monthly data for GE, IBM, Exxon (XON), and GM for 94:01-98:12-VW is the Value- Weighted index of al

11、l NYSE, AMEX, and NASDAQ common stocks.Rf is the (nominal) 1-month T-Bill yield, which was 4.394%/year (0.359%/month) in January 99.Excess ReturnsMean(%)Std(%)alpha(%)betaStd(%) (%)IBM3.228.441.721.147.1328.5XON1.414.030.630.593.2833.7GM0.647.34-0.691.026.1430.0GE2.265.860.901.044.1549.9VW1.314.02Rf

12、0.390.05.To get the correlation structure, we have: IBMXONGMGEIBM10.320.300.39XON0.3210.330.42GM0.300.3310.40GE0.390.420.401.Plugging the (1) expected return, (2) return standard deviation, and (3) correlation matrix into the Excel spreadsheet we get the following weights for the tangency portfolio:

13、Is this a reasonable portfolio? Why?Weight(%)IBM29.6XON49.4GM-21.4GE42.4.It seems unreasonable that we should hold such extreme portfolio positions.The equilibrium arguments we used in developing the CAPM suggest that the market knows something we dont about future expected returns! .Use the CAPM as

14、 a way of getting around this problem:Use the SML:and the past (average) return on the market to get equilibrium estimates of the expected returns: (%)IBM1.91XON0.99GM1.70GE1.73.With this equilibrium set of expected returns, we now get the portfolio weights:Is this a more reasonable portfolio?Now, w

15、hat is driving the portfolio weights?Why are these not the market weights?When would these be the actual market weights?Is this the portfolio you want to hold, given that you were constrained to hold these four assets?Weight(%)IBM13.6XON33.3GM16.4GE36.6.However, there may be times when we think that

16、 the market is a little wrong along one or more dimensions ( a very dangerous assumption!)1. First, suppose that I think that the market has underestimated the earnings that IBM will announce in the next month, and that IBMs expected return is 2% higher than the market expects. Also , I have no info

17、rmation on the other three securities that would lead me to think that they are mispriced,and I believe that the past betas, and residual std devs are good indications of the relative future values.2. In this case, we would use the same variance and covariance inputs, but would change the expected r

18、eturns to:and gives portfolio weights of: (%)IBM3.91XON0.99GM1.70GE1.73Weight(%)IBM54.1XON17.7GM8.7GE19.5.3. Alternatively, suppose that I think the risk ( ) of Exxon is increasing.4. I guess that Exxons will rise from 0.59 to 0.8First, I should recalculate almost everything using the equations:.The

19、 new correlations we come up with areas opposed to the old correlation matrix ofIBMXONGMGEIBM10.440.300.39XON0.4410.450.57GM0.300.4510.40GE0.390.570.401IBMXONGMGEIBM10.320.300.39XON0.3210.330.42GM0.300.3310.40GE0.390.420.401.If, I believe that these are the new correlations, but that the market stil

20、l believes that the past correlations represent the future (and will not discover this information over the next several months) then I would use the old , giving new portfolio weights of Weight(%)IBM17.0XON16.7GM20.5GE45.7.If, however, I believe that market knows that the of Exxon is higher, and th

21、e expected return on Exxon is higher now to compensate for the increased risk, then the expected returns and weights become:Why is the weight on Exxon higher than initially, given that the of Exxon is now higher? (%)Weight(%)IBM1.919.2XON1.3454.8GM1.7011.1GE1.7324.8.One other alternative is that I d

22、o not believe that the market yet knows that the risk of Exxon is higher, and will discover this in the next few months.What should I do in this case?Finally, if I am only somewhat confident of my belief that the market will not adjust the price of Exxon properly, I might want to adjust the portfoli

23、o weights only part wayThis is what the Black-Litterman method does, as we shall see next.Black and Litterman, Global Asset AllocationA. Introduction1. Black & Litterman develop a model analogous to what we just did with the CAPM.2. Black and Litterman use an international version of the CAPM (devel

24、oped by Fischer Black) to get the baselineexpected return.3. They assume that the estimated variances and covariances are correct, and calculate the equilibrium expected returns based on these. This is appropriate, since covariances can be estimated accurately, especially using daily data.4. Then, t

25、hey allow the portfolio manager to specify any number of market views in the form of expected returns or differences in expected returns, and a variance (measure of uncertainty) for each of the views If the manager holds no views, she will hold the equilibrium/market portfolio. Or, if her views are

26、high variance (low certainty), she will hold close to the equilibrium portfolio.When her views are low variance, she will move considerably away from the market portfolio.5. This method is useful in that it tells you how to optimally incorporate your information/views to tilt your portfolio, taking

27、advantage of the correlation structure to hedge large positions.NOTE!By itself, the equilibrium concept is interesting but not particularly useful. Its real value is to provide a neutral framework the investor can adjust according to his own views, optimization objectives and constraints.Expressing

28、viewsInvestor trying to use quantitative asset allocation models must translate their views into a complete set of expected excess returns on assets that can be used as a basis for portfolio optimization. The problem is that optimal portfolio weights from a mean-variance model are incredibly sensitive to minor changes in expected excess return