章節(jié)3數(shù)量分析組合管理講義

1、2016年CFA培訓(xùn)項目Portfolio ManagementKEL WANG金程教育資深培訓(xùn)師地點： 上海北京 Topic Weightings in CFA Level II2-80Session NO.ContentWeightingsStudy Session 1-2Ethics & Professional Standards10Study Session 3Quantitative Methods5-10Study Session 4Economic Analysis5-10Study Session 5-7Financial Statement Analysis15-2

2、5Study Session 8-9Corporate Finance5-15Study Session 10-13Equity Analysis20-30Study Session 14-15Fixed Income Analysis5-15Study Session 16-17Derivative Investments5-15Study Session 18Portfolio Management5-15Study Session 13Alternative Investments515Portfolio ManagementSS18Ø R53Ø R54Ø

3、R55Ø R56An introduction to multifactor msAnalysis of active portfolio managementEconomics and investment marketsThe portfolio Management Process and the Investment Policy Statement3-80Portfolio ManagementØ R53 An introduction to multifactor ml Arbitrage Pricing Theory (APT)l Multifactor ml

4、 Macroeconomic Factorsl Fundamental factor ml Statistical factor ml Active Riskssl Information Riskl Active risk squared4-80Arbitrage Pricing Theory (APT)Ø APTlasset pricing mdeveloped by the arbitrage pricing theoryØ AssumptionsllA factor mdescribes asset returnsThere are many assets, so

5、investors can form well-diversified portfoliosthat eliminate asset-specific riskNo arbitrage opportunities exist among well-diversified portfolioslØ Exactly formulaE(RP ) = RF + bP,1 (l1 ) + bP,2 (l2 ) + . + bP,k (lk )5-80Arbitrage Pricing Theory (APT)Ø The factor risk premium (or factor p

6、rice, j) represents the expected return inexcess of the risk free rate for a portfolio with a sensitivity of 1 to factor j and a sensitivity of 0 to all other factors. Such a portfolio is called a pure factor portfolio for factor j.Ø The parameters of the APT equation are the risk-free rate and

7、 the factor risk- premiums (the factor sensitivities are specific to individual investments).6-80Arbitrage Pricing Theory (APT)Ø Arbitrage OpportunitieslThe APT assumes there are no market imperfections preventing investorsfrom exploiting arbitrage opportunities extreme long and short positions

8、 are permitted and mispricing will disappear immediately all arbitrage opportunities would be exploited and eliminated immediately7-80Arbitrage Pricing Theory (APT)- ExampleExample: suppose that two factors, surprise in inflation (factor 1) and surprise in GDPgrowth (factor 2), explain returns. Acco

9、rding to the APT, an arbitrage opportuexistsunlessE(RP ) = RF + p,1 (1 )+p,2 (2 )Well-diversified portfolios, J, K, and L, given in table.E(RJ) = 0.14 = RF +1.01 +1.52 E(RK ) = 0.12 = RF + 0.51 +1.02 E(RL ) = 0.11 = RF +1.31 +1.12) = 0.07 - 0.02E(R+0.06Pp,1p,28-80PortfolioExpected returnSensitivity

10、to inflation factorSensitivity to GDP factorJ0.141.01.5K0.120.51.0L0.111.31.1Arbitrage Pricing Theory (APT)Ø The Carhart four-factor m(four factor m)lAccording to the m, there are three groups of stocks that tend to havehigher returns than those predicted solely by their sensitivity to the mark

11、et return:Small-capitalization stocksLow price-to book-ratio stocks, commonly referred to as “momentum” stocksStocks whose prices have been rising, commonly referred to as “momentum”stockslll9-80Multifactor MØMultifactor ms have gained importance for the practical business ofportfolio managemen

12、t for two main reasons.1.multifactor mdoes.multifactor m single factor ms explain asset returns better than the market m2.s provide a more detailed analysis of risk than does a.ØPassive management. Analysts can use multifactor ms to match an indexfund's factor exposures to the factor exposu

13、res of the index tracked.Active management. Many quantitative investment managers rely onØmultifactor ms in predicting alpha (excess risk-adjusted returns) or relativereturn (the return on one asset or asset class relative to that of another) as part of a variety of active investment strategies

14、.l In evaluating portfolios, analysts use multi-factor ms to understand thesources of active managers' returns and assess the risks assumed relative to the manager's benchmark (comparison portfolio).10-80Types of Multifactor MsØ Macroeconomic FactorØ Fundamental factor msØ Sta

15、tistical factor msØ Mixed factor mslSome practical factor ms have the characteristics of more thanone of the above categories. We can call such ms mixed factorms.11-80Macroeconomic Factor MØ Macroeconomic Factorlassumption: the factors are surprises in macroeconomic variables thatsignifica

16、ntly explain equity returnsexactly formula for return of asset ilbi1, bi2+ b F+ e= E(R ) + b FRiii1GDPi 2QSiWhere:Ri= return for asset iE(R ) = expected return for asset iiFGDPFQSbi1= surprise in the GDP rate= surprise in the credit quality spread= GDP surprise sensitivity of asset ibi2 = credit qua

17、lity spread surprise sensitivity of asset ii = firm-specific surprise which not be explained by the m.12-80Regression (time series)ReturnFGDPFQSSurprise = actual value predicted (expected) valueMacroeconomic Factor m- What does surprise mean?ØSuppose our forecast at the beginning of the month i

18、s that inflation will be 0.4 percent during the month. At the end of the month, we find that inflation wasactually 0.5 percent during the month. During any month,ØØActual inflation = Predicted inflation + Surprise inflationIn this case, actual inflation was 0.5 percent and predicted inflat

19、ion was 0.4percent. Therefore, the surprise in inflation was 0.5 - 0.4 = 0.1 percent.13-80Macroeconomic Factor m factor sensitivity, error termØSlope coefficients are naturally interpreted as the factor sensitivities of the asset. A factor sensitivity is a measure of the response of return to e

20、ach unit of increase in a factor, holding all other factors constant.The term i is the part of return that is unexplained by expected return or the factor surprises. If we have adequately represented the sources of common risk (the factors), then i must represent an asset-specific risk. For a stock,

21、 it mightrepresent the return from an unanticipated company-specific event.Ø14-80Factor Sensitivities for a Two-Stock Portfolio (example)ØSuppose that stock returns are affected by two common factors: surprises in inflation and surprises in GDP growth. A portfolio manager is analyzing the

22、returns on a portfolio of two stocks, Manumatic (MANM) and Nextech (NXT), The following equations describe the returns for those stocks, where the factors FINFL. and FGDP, represent the surprise ininflation and GDP growth, respectively:DP + eMANM DP + e NXT= 0.09 -1FINRMANM= 0.12 + 2FINRNXTØOne

23、-third of the portfolio is invested in Manumatic stock, and two-thirds is invested in Nextech stock. Formulate an expression for the return on the portfolio.State the expected return on the portfolio.Calculate the return on the portfolio given that the surprises in inflation and GDP growth are 1 per

24、cent and 0 percent, respectively, assuming that the error terms for MANM andNXT both equal 0.5 percent.ØØ15-80Factor Sensitivities for a Two-Stock Portfolio (answer)Solution to 1:Ø The portfolio's return is the following weighted average of the returns to the two stocks: Rp = (1/3

25、)(0.09) + (2/3)(0 .12) + (1/3)(- I) + (2/3)(2) FINFL+ (1/3)(1)+ (2/3)(4)FGDP + (1/3) MANM + (2/3) NXT = 0.11 + 1 FINFL+ 3FGDP + (1/3)MANM+ (2/3) NXTSolution to 2:Ø The expected return on the portfolio is 11 percent, the value of the intercept inthe expression obtained in Part 1.Solution to 3:&#

26、216; Rp = 0.11 + 1 FINFL+ 3FGDP + (1/3) MANM + (2/3) NXT = 0.11 + 1(0.01) + 3(0) +(1/3)(0.005) + (2/3)(0.005) = 0.125 or 12.5 percent16-80Fundamental FactorØ Fundamental factor mslthe factors are attributes of stocks or companies that are important inexplaining cross-sectional differences in st

27、ock priceslexactly formula求出FP/E, Fsize不同公司的R和對應(yīng)的bi1，bi2e.g. the return difference between low and high P/E stocksR = a + b F+ b F+ eiii1 P/Ei2 SIZEiNo economic interpretationl asset return can be explained by the price-earningsratio, market capitalization= Asset i's attribut value - average att

28、ribute valuebijs (attribute value)= (P/E)1 - P/Ee.g. bsi1P / E 17-80Regression (crosssectional data)Returnbi1bi2Standardized betaØDividend yield example:l after standardization a stock with an average dividend yield will have a factor sensitivity of 0,l a stock with a dividend yield one standar

29、d deviation above the average will have a factor sensitivity of 1,l and a stock with a dividend yield one standard deviation below the average will have a factor sensitivity of -1.Suppose, for example, that an investment has a dividend yield of 3.5 percent and that the average dividend yield across

30、all stocks being considered is 2.5 percent. Further, suppose that the standard deviation of dividend yields across all stocks is 2 percent.l The investment's sensitivity to dividend yield is (3.5% - 2.5%)/2% = 0.50,or one-half standard deviation above average.Ø18-80Standardized betaØTh

31、e scaling permits all factor sensitivities to be interpreted similarly, despite differences in units of measure and scale in the variables.The exception to this interpretation is factors for binary variables such as industry membership. A company either participates in an industry or it does not.l T

32、he industry factor sensitivities would be 0 - 1 dummy variables;Øl in ms that recognize that companies frequently operate in multipleindustries, the value of the sensitivity would be 1 for each industry in whicha company operated.19-80Statistical Factor msØ Statistical factor msluses multi

33、variate statistics (factor analysis or principal components) to identify multiple statistical factors that explain the covariance among asset returnsmajor weakness: the statistical factors do not lend themselves well toeconomic interpretationl20-80Arbitrage Pricing Theory (APT)Ø The relation be

34、tween APT and multifactor ms21-80APTMultifactor msCharacteristicscross-sectional equilibrium pricing mthat explains the variation across assets expected returnstime-series regression that explains the variation over time in returns for one assetAssumptionsequilibrium-pricing mthat assumes no arbitra

35、ge opportunitiesad hoc (i.e., rather than being derived directly from an equilibrium theory, the factors are identified empirically by looking for macroeconomic variables that best fit the data)Interceptionrisk-free rateexpected return derived from the APT equation in macroeconomic factormArbitrage

36、Pricing Theory (APT)Ø Comparison CAPM and APT22-80CAPMAPTAssumptionsAll investors should hold some combination of the market portfolio and the risk-free asset. To control risk, less risk averse investors simply hold more of the market portfolio and less of the risk-free asst.APT gives no specia

37、l role to the market portfolio, and is far more flexible than CAPM. Asset returns follow a multifactor process, allowing investors to manage several risk factors, rather than just one.sThe risk of the investors portfolio is determined solely by the resulting portfolio beta.Investors unique circumsta

38、nces may drive the investor to hold portfolios titled away from the market portfolio in order to hedge or speculate on multiple risk factors.Active RiskØ Active risklActive returnüDefinition: the differences in returns between a managed portfolioand its benchmarkExactly formula: active ret

39、urn = RP - RBülActive risk (tracking error)üDefinition: the standard deviation of active returnsüExactly formula:å(R- R)2active risk = s=PtBt( RP -RB )n -123-80Information RiskØ Information RisklllDefinition: the ratio of mean active return to active riskPurpose: a tool for

40、evaluating mean active returns per unit of active riskExactly formula- RBIR = RPs(R -R )PB24-80Information ratio - exampleØTo illustrate the calculation, if a portfolio achieved a mean return of 9 percent during the same period that its benchmark earned a mean return of 7.5 percent, and the por

41、tfolio's tracking risk was 6 percent, we would calculate aninformation ratio of (9% - 7.5%)/6% = 0.25.ØSetting guidelines for acceptable active risk or tracking risk is one of the waysthat some institutional investors attempt to assure that the overall risk and stylecharacteristics of their

42、 investments are in line with those desired.25-80Active risk squaredØWe can separate a portfolio's active risk squared into two components:Active risk squared = s2 (R- R )PBØActive factor risk is the contribution to active risk squared resulting from theportfolio's different-than-b

43、enchmark exposures relative to factors specified inthe risk m.ØActive specific risk or asset selection risk is the contribution to active risk squared resulting from the portfolio's active weights on individual assets as those weights interact with assets' residual risk."Active ris

44、k squared = Active factor risk + Active specific riskØ26-80Portfolio ManagementSS18Ø R53Ø R54Ø R55Ø R56An introduction to multifactor msAnalysis of active portfolio managementEconomics and investment marketsThe portfolio Management Process and the Investment Policy Statement

45、27-80Value addedØThe value added or active return is defined as the difference between the return on the manage portfolio and the return on a passive benchmark portfolio.RA = RP - RBValue added is related to active weights in the portfolio, defined as differences between the various asset weigh

46、ts in the managed portfolio and their weights in the benchmark portfolio. Individual assets can be overweighed (have positive active weights) or underweighted (have negative active weights), but thecomplete set of active weights sums to zero.RA = åDwi Rii=1RA = åDwi RAii=1ØNN28-80Deco

47、mposition of value addedØThe common decomposition: value added due to assadded due to security selection.location and valueØThe total value added is the difference between the actual portfolio and thebenchmark return:MM= åwP, j RP, j- åwB, j RB, jRAj =1j =1MM= åDwj RB, j + &

48、#229;wP, j RA, jRAj =1j =1= (Dwstocks RB,stocks + Dwbonds RB,bonds ) + (wP,stocks RA,stocks+ wP,bonds RA,bonds )RA29-80The Sharpe ratioØThe sharpe ratio measures reward per unit of risk in absolute returns.RP - RFSR = SRPSTD(R)PØAn important property is that the Sharpe ratio is unaffected

49、by theaddition of cash or leverage in a portfolio.- RF= wP (RP - RF）= SRSR = RCPSTDw STD(R )(Rc)PP30-80Information ratioØThe information ratio measures reward per unit of risk in benchmark relativereturns.RP - RBRAIR =STD(RP - RB )STD(RA )ØAn important property is that the Information rati

50、o is unaffected by theaddition of benchmark portfolio in a portfolio.= wRP + (1- w) RB - RBRC - RB STD (RC - RB )wRARAIR =wSTD(RP - RB )wSTD(RA )STD(RA )31-80Constructing Optimal PortfoliosØGiven the opportuto adjust absolute risk and return with cash or leverage,the overriding objective is to

51、find the single risky asset portfolio with theum Sharpe ratio, whatever the investors risk aversion.ØA similarly important property in active management theory is that, given theopportuto adjust active risk and return by investing in both the activelymanaged and benchmark portfolios, the square

52、d Sharpe ratio of an activelymanaged portfolio is equal to the squared Sharpe ratio of the benchmark plus the information ratio squared:SR2 = SR2 + IR2PB32-80Constructing Optimal PortfoliosØThe preceding discussion on adjusting active risk raises the issue of determining the optimal amount of a

53、ctive risk, without resorting to utility functions that measure risk aversion. For unconstrained portfolios, the level of active risk thatleads to the optimal portfolio is:IRSTD(R) =STD(R)ABSRBØBy definition, the total risk of the actively managed portfolio is the sum of thebenchmark return var

54、iance and active return variance.STD(RP ) = STD(RB ) +STD(RA )22233-80Examples-1ØSuppose that the historical performance of the Fidelity Magellan and Vanguard Windsor mutual funds in Exhibits 2 and 3 are indicative of the future performance of hypothetical funds “Fund I” and “Fund II.” In addit

55、ion, suppose that the historical performance of the S&P 500 benchmark portfolio shown in Exhibit 1 is indicative of expected returns and risk going forward, as shown below. We use historical values in this problem for convenience, but in practice the forecasted, or expected, values for both the

56、benchmark portfolio and theactive funds would be subjectively determined by the investor.34-80Examples-235-80Excerpted from Exhibit 3Fidelity Magellan (Fund I)Vanguard Windsor (Fund II)Active return1.5%0.4%Active risk6.1%7.4%Information ratio0.250.05BenchmarkS&P 500S&P 500Excerpted from Exhibits 1 and 2 (based on a risk-free rate of 2.8%)S&P 500Fideli