27数量组合二级基础班portfoio management

1、【】专业提供CFA FRM全程+讲义2016年CFA培训项目Portfolio ManagementKEL WANG金程教育资深培训师地点： 上海北京 【】专业提供CFAFRM全程+讲义Topic Weightings in CFA Level II2-80Session NO.ContentWeightingsStudy Session 1-2Ethics & Professional Standards10Study Session 3Quantitative Methods5-10Study Session 4Economic Analysis5-10Study Session

2、5-7Financial Statement Analysis15-25Study 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 Investments515【】专业提供CFAFRM全程+讲

3、义Portfolio ManagementSS18Ø R53Ø R54Ø R55Ø R56An introduction to multifactor msAnalysis of active portfolio managementEconomics and investment marketsThe portfolio Management Process and the Investment Policy Statement3-80【】专业提供CFAFRM全程+讲义Portfolio ManagementØ R53 An introduc

4、tion to multifactor ml Arbitrage Pricing Theory (APT)l Multifactor ml Macroeconomic Factorsl Fundamental factor ml Statistical factor ml Active Riskssl Information Riskl Active risk squared4-80【】专业提供CFA FRM全程+讲义Arbitrage Pricing Theory (APT)Ø APTlasset pricing mdeveloped by the arbitrage pricin

5、g theoryØ AssumptionsllA factor mdescribes asset returnsThere are many assets, so investors can form well-diversified portfoliosthat eliminate asset-specific riskNo arbitrage opportunities exist among well-diversified portfolioslØ Exactly formulaE(RP ) = RF + bP,1 (l5-80【】专业提供CFA FRM全程+讲义A

6、rbitrage Pricing Theory (APT)Ø The factor risk premium (or factor price, 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 facto

7、r j.Ø The parameters of the APT equation are the risk-free rate and the factor risk- premiums (the factor sensitivities are specific to individual investments).6-80【】专业提供CFA FRM全程+讲义Arbitrage Pricing Theory (APT)Ø Arbitrage OpportunitieslThe APT assumes there are no market imperfections pr

8、eventing investorsfrom exploiting arbitrage opportunities extreme long and short positions are permitted and mispricing will disappear immediately all arbitrage opportunities would be exploited and eliminated immediately7-80【】专业提供CFA FRM全程+讲义Arbitrage Pricing Theory (APT)- ExampleExample: suppose th

9、at two factors, surprise in inflation (factor 1) and surprise in GDPgrowth (factor 2), explain returns. According 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 + 0.5

10、1 +1.02 E(RL ) = 0.11 = RF +1.31 +1.12) = 0.07 - 0.02E(RPp8-80PortfolioExpected returnSensitivity to inflation factorSensitivity to GDP factorJ0.141.01.5K0.120.51.0L0.111.31.1【】专业提供CFA FRM全程+讲义Arbitrage Pricing Theory (APT)Ø The Carhart four-factor m(four factor m)lAccording to the m, there are

11、 three groups of stocks that tend to havehigher returns than those predicted solely by their sensitivity to the market 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”st

12、ockslll9-80【Multifactor M】专业提供CFA FRM全程+讲义ØMultifactor ms have gained importance for the practical business ofportfolio management 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 t

13、han does a.ØPassive management. Analysts can use multifactor ms to match an indexfund's factor exposures to the factor exposures of the index tracked.Active management. Many quantitative investment managers rely onØmultifactor ms in predicting alpha (excess risk-adjusted returns) or re

14、lativereturn (the return on one asset or asset class relative to that of another) as part of a variety of active investment strategies.l In evaluating portfolios, analysts use multi-factor ms to understand thesources of active managers' returns and assess the risks assumed relative to the manage

15、r's benchmark (comparison portfolio).10-80【】专业提供CFAFRM全程+讲义Types of Multifactor MsØ Macroeconomic FactorØ Fundamental factor msØ Statistical factor msØ Mixed factor mslSome practical factor ms have the characteristics of more thanone of the above categories. We can call such

16、ms mixed factorms.11-80【】专业提供CFA FRM全程+讲义Macroeconomic Factor MØ Macroeconomic Factorlassumption: the factors are surprises in macroeconomic variables thatsignificantly explain equity returnsexactly formula for return of asset ilbi1, bi2+ b F+ e= E(R ) + b FRiii1GDPi 2QSiWhere:Ri= return for as

17、set 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 quality spread surprise sensitivity of asset ii = firm-specific surprise which not be explained by the m.12-80Regression (time series)

18、ReturnFGDPFQSSurprise = actual value predicted (expected) valueMacroecon【om cr】ml -专W业提供hCFaA FtRM全d程os+讲u义rprise mean?ØSuppose our forecast at the beginning of the month is that inflation will be 0.4 percent during the month. At the end of the month, we find that inflation wasactually 0.5 perc

19、ent during the month. During any month,ØØActual inflation = Predicted inflation + Surprise inflationIn this case, actual inflation was 0.5 percent and predicted inflation was 0.4percent. Therefore, the surprise in inflation was 0.5 - 0.4 = 0.1 percent.13-80Macroecon【om cr】ml 专业f提a供cCFtAoFR

20、rM全程sn i+t讲i义vity, 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 each unit of increase in a factor, holding all other factors constant.The term i is the part of return that is unex

21、plained 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, it mightrepresent the return from an unanticipated company-specific event.Ø14-80【】专业提供CFA FRM全程+讲义Factor Sen

22、sitivities 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 returns on a portfolio of two stocks, Manumatic (MANM) and Nextech (NXT), The following equation

23、s describe the returns for those stocks, where the factors FINFL. and FGDP, represent the surprise ininflation and GDP growth, respectively:= 0.09 -1FINRMANMD= 0.12 + 2FINRNXTDØOne-third of the portfolio is invested in Manumatic stock, and two-thirds is invested in Nextech stock. Formulate an e

24、xpression 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 percent and 0 percent, respectively, assuming that the error terms for MANM andNXT both equal 0.5 percent.ØØ

25、15-80【】专业提供CFA FRM全程+讲义Factor 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)(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)

26、 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:Ø Rp = 0.11 + 1 FINFL+ 3FGDP + (1/3) MANM + (2/3) NXT = 0.11 + 1(0.01) + 3(0) +(1/3)(0.005) +

27、(2/3)(0.005) = 0.125 or 12.5 percent16-80【Fundamental Factor】专业提供CFA FRM全程+讲义Ø Fundamental factor mslthe factors are attributes of stocks or companies that are important inexplaining cross-sectional differences in stock priceslexactly formula求出FP/E, Fsize不同公司的R和对应的bi1，bi2e.g. the return differe

28、nce 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 - averagebijs (attribute value)= (P/E)1 - P/Ee.g. bsi1P / E 17-80Regression (crosssectional

29、data)Returnbi1bi2【Standardized beta】专业提供CFA FRM全程+讲义ØDividend 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 standard deviation above the average will have a factor sensitivity of 1,l and a sto

30、ck 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 all stocks being considered is 2.5 percent. Further, suppose that the standar

31、d 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.Ø18-80【Standardized beta】专业提供CFA FRM全程+讲义ØThe scaling permits all factor sensitivities to be interprete

32、d 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 The industry factor sensitivities would be 0 - 1 dummy varia

33、bles;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.19-80【Statistical Factor m】专业提供CFA FRM全程+讲义sØ Statistical factor msluses multivariate statistics (factor analysis or pr

34、incipal components) to identify multiple statistical factors that explain the covariance among asset returnsmajor weakness: the statistical factors do not lend themselves well toeconomic interpretationl20-80【】专业提供CFAFRM全程+讲义Arbitrage Pricing Theory (APT)Ø The relation between APT and multifacto

35、r 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 arbitrage opportunitiesad hoc (

36、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 factorm【】专业提供CFAFRM全程+讲义Arbitrage Pricing

37、 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 special role

38、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 circumstances ma

39、y drive the investor to hold portfolios titled away from the market portfolio in order to hedge or speculate on multiple risk factors.【Active Risk】专业提供CFA FRM全程+讲义Ø Active risklActive returnüDefinition: the differences in returns between a managed portfolioand its benchmarkExactly formula:

40、 active return = RP - RBülActive risk (tracking error)üDefinition: the standard deviation of active returnsüExactly formula:åactive risk = s=( RP -RB )23-80【Information Risk】专业提供CFA FRM全程+讲义Ø Information RisklllDefinition: the ratio of mean active return to active riskPurpos

41、e: a tool for evaluating mean active returns per unit of active riskExactly formula- RBIR = RPs(R -R )PB24-80【】专业提供CFA FRM全程+讲义Information 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 re

42、turn of 7.5 percent, and the portfolio'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 a

43、nd stylecharacteristics of their investments are in line with those desired.25-80【Active risk squared】专业提供CFA FRM全程+讲义ØWe can separate a portfolio's active risk squared into two components:Active risk squared = s2 (RØActive factor risk is the contribution to active risk squared resulti

44、ng from theportfolio's different-than-benchmark 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

45、 assets' residual risk."Active risk squared = Active factor risk + Active specific riskØ26-80【】专业提供CFAFRM全程+讲义Portfolio ManagementSS18Ø R53Ø R54Ø R55Ø R56An introduction to multifactor msAnalysis of active portfolio managementEconomics and investment marketsThe port

46、folio Management Process and the Investment Policy Statement27-80【Value added】专业提供CFA FRM全程+讲义ØThe 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 we

47、ights in the portfolio, defined as differences between the various asset weights 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 w

48、eights sums to zero.RA = åDwi Rii=1RA = åDwi RAii=1ØNN28-80【】专业提供CFA FRM全程+讲义Decomposition 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 a

49、nd thebenchmark return:MM= åwP, j RP, j- åwB, j RB, jRAj =1j =1MM= åDwj RB, j + åwP, j RA, jRAj =1j =1= (Dwstocks RB,stRA29-80【The Sharpe ratio】专业提供CFA FRM全程+讲义ØThe sharpe ratio measures reward per unit of risk in absolute returns.RP - RFSR = SRPSTD(R)PØAn important pro

50、perty is that the Sharpe ratio is unaffected by theaddition of cash or leverage in a portfolio.- RF= wP (RP - RSR = RCSTD(Rc)wPSTD(R30-80【Information ratio】专业提供CFA FRM全程+讲义ØThe information ratio measures reward per unit of risk in benchmark relativereturns.RP - RBRAIR =STD(RP - RB )STD(RA )

51、6;An important property is that the Information ratio is unaffected by theaddition of benchmark portfolio in a portfolio.RC - RB STD (RC - RB )IR = 31-80【】专业提供CFA FRM全程+讲义Constructing Optimal PortfoliosØGiven the opportuto adjust absolute risk and return with cash or leverage,the overriding obj

52、ective is to 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 portfolio

53、s, the squared Sharpe ratio of an activelymanaged portfolio is equal to the squared Sharpe ratio of the benchmark plus the information ratio squared:SR2 = SR2 + IR2PB32-80【】专业提供CFA FRM全程+讲义Constructing Optimal PortfoliosØThe preceding discussion on adjusting active risk raises the issue of dete

54、rmining the optimal amount of active 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

55、 sum of thebenchmark return variance and active return variance.STD(RP ) = STD(RB ) +2233-80【Examples-1】专业提供CFA FRM全程+讲义ØSuppose 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 addition, suppose that the historical performance of the S&P 500 benchmark portfolio shown i