ZZBU8701 ActiveInvestingandMulti-factorModels Assignment

Project3

1Task

You are a portfolio analyst determining an optimal active portfolio management strategy for yourPortfolioManager.Youarerequiredtoconstructanappropriatelyweightedactiveportfolioandallocatebetween this active portfolio and the market portfolio. You will then determine whether the Carhart 4-factormodelsignificantlyincreasestheexplanatorypowerofyouractiveportfoliosreturnsincomparison to the SIM. Finally, you will prepare a 3-minute presentation video to your PortfolioManager,whereyouwillpresentananalysis and comparisonofyour results.

2Context

• After evaluating various U.S. equities drawn from the S&P500, a number of stocks which exhibitsignificant alpha during the period from January 2014 to December 2018 have been identified.YourPortfolioManagerwantsyoutocarryoutanex-postanalysiswhichexamineshowanoptimalactive portfolio could have been formed from these alpha stocks which, when combined with anS&P500index ETF, wouldhavemaximised thecombinations Sharpe
• Theportfoliomanagerdecidestorandomlyallocatefiveuniquestockswhichexhibitedalphaduringthe sample period to each portfolio analyst to undertake their analysis.Each portfolio analyst willuseonly thesefive uniqueallocatedstocksto construct theiractive portfolio.

3AllocatedStocksandDataDownload

• Youhavebeenallocated5alpha(Notethatthesestocksareuniquetoyouandeachstudentwill have a different combination of stocks).Your allocated stocks will be posted on Moodle withyour Student ID in the Project 3 Stock Allocation Lookup.xls excel file in the Project 3Assessmentstab.
• Each stock in the spreadsheet is identified by its Factset identifier. Using these identifiers, for theperiodfromJanuary2014throughDecember2018,downloadthemonthlyreturnsforeachallocatedstock from FactSet (60 observations). All returns should be inclusive of dividends - in the FactSetdropdownbox "TotalReturn"select%"
• For the period from January 2014 through December 2018, download from FactSet the monthlyreturns for the S&P 500 Index (FactSet identifier: SP50) (60 observations). All returns should betotal returns inclusive of dividends - FactSet dropdown box: Total Return select % Return(Gross,Unhedged).

4SingleIndexModelRegressions(SecurityCharacteristicsLine)

• Usearisk-freerateof00%APR(i.e.fixedat 0.25%monthly) forthisanalysis.
• Foreachofthefivestocksinyouractiveportfolio,calculatemonthlyexcessreturn:

=?whereisthereturnonstockformonth,andistherisk-freerate.(Note:make sureyou use the fixed monthly risk-freerateabove).

• For the S&P 500 index, calculate monthly excess return: = ? where, is the returnontheS&P500formonth.ComputetheannualisedaverageexcessreturnfortheS&P500(simplyby multiplying the monthly excess return by 12). This will be the proxy for the average annualmarketrisk premiumoverthe sample period.
• EstimatetheSingleIndexModelalphaandbeta,(i.e.theSecurityCharacteristicLine)for eachstock inyouractive portfolio usingthe regressionequation:

=++

• Determine the residual variance (²) (unsystematic risk) for each stock in your active portfolio,eitherbyusingthefollowing equation:

²=²²+²

Or byusingtheExcel regression tools.

• Annualise the alpha and the residual variance (unsystematic risk) by multiplying by 12. (Note:ensure your alphas are generated by regressing excess returns above the risk-free rate, not rawreturns).

5ConstructtheActivePortfolio

• Conduct confidence interval testing for each of your 5 stocks to confirm that the alpha is non-zero(significant) atthe 90%confidence
• As your Portfolio Manager is concerned that past alpha may not be reflected in future alpha, youarerequired torisk-weightthe alphas asfollows:
  • Only include a stock in the active portfolio if its alpha is significant. Any stock that doesnot exhibit non-zero alpha at the 90% confidence level should be excluded from the activeportfolio
  • Risk-weightthealphabymultiplyingitby10%whencalculatingeachstocksreward-to-riskForexample,iftheex-postalphawas20%p.a.fromtheSIMregression,thenumerator inyourrewardtorisk-calculationfor that stockwill be2%p.a.
• UsingtheTreynor-Blackmodel,appropriatelyweightyour active

6OptimallyCombinetheActivePortfolioandtheMarketPortfolio

• AssumeanETFthattrackstheS&P500isanappropriate proxyforthemarket portfolio.
• Derivethesamplevariance(²)oftheS&P500overthesampleperiodandannualise it.
• Usingtheactiveportfolioweightingsderivedin5above,calculatetheannualisedactiveportfolio

alpha,beta,andresidualvariance().Calculatethereward-to-riskratiofortheactive

portfolio(asa whole).

• Based on the reward-to-risk ratio of the market portfolio over the sample period. appropriatelyweight between the active portfolio and the market (passive) portfolio using the Treynor-Black
• Calculatetheannualisedinformationratioforeachstockinyourportfolio,aswellastheinformationratioforthe active portfolioas a whole.
• Calculate the potential improvement in your Sharpe ratio compared to a stand-alone investment inthe market (passive) portfolio as a result of this strategy.Verify how this result relates to theinformationratioofthe active portfolio (as a whole).

7ActivePortfolioReturns

• Usingtheactiveportfolioweightingsderivedin5above,aswellasthemonthlyreturnsdownloadedin3, calculatethemonthlyweighted active portfolioreturns for the sample
• Estimate the Single Index Model alpha and beta , for your weighted active portfolio (notethisistheactive portfolioSecurityCharacteristicLine) usingtheregressionequation:

=++

• Annualise the weighted active portfolio alpha , and determine if the alpha and beta aresignificant, as well as deriving the R²for the model over the sample period.Verify that the alphaand beta for the active portfolio (and ) are the same as your answer to 6 above. (Note:remember that your alpha in 6 was risk-weighted to be only 10% of the actual alpha, so the alphaderivedfromthisportfolioregressionshouldbeexactly10xtheactiveportfolioalphacalculatedin6).

8Multi-factorModel

• Open the excel file Fama French Carhart Factors.xls. This file contains the monthly riskpremiums (stated as decimals/percentages) for the Carhart 4-factor model over the sample period.(Note: checkthatthisisina compatibleformatto yourexisting dataintermsofdecimals).
• UsingtheFama-FrenchandCarhartmonthlyfactorportfoliodataprovided(SMB,HMLandWML)undertake a multi-factor regression analysis for each stock in your active portfolio.Derive thealpha (including its significance level) and R²for these 4-factor models for each stock in youractive
• Using the Fama-French and Carhart monthly factor portfolio data provided, undertake a multi-factorregressionanalysisforyourweightedactiveportfolio(usingtheactiveportfolioweightingsderivedin 5above,as wellas themonthlyreturns downloadedin 3). Usetheregressionequation:

• Derivethealpha(includingitssignificancelevel)andR²forthis4-factormodelregressionofyourweightedactive portfolio (Note:thisisone single regression).

9VideoPresentation

• Prepare a video for your Portfolio Manager of no longer than 3 minutes which discusses yourresults, as well as the limitations of your analysis. Some suggestions of what could be covered inyourvideoinclude:
  • A brief discussion of the alpha of each stock in your active portfolio and why you believeitexists
  • Howyouconstructedtheactiveportfolioandallocatedbetweenit andtheS&P500ETF
  • A brief comment on the improvement in your Sharpe ratio arising from the addition of theactiveportfolio, comparedto holdingthe S&P500ETFalone
  • Anexaminationofthedifferencesintheresultsderivedfromtheindividualstockregressionscomparedtotheactiveportfolioregression,referencingsuchstatisticalmeasuresastheR²andthealpha,andanyotherstatisticalmeasuresyoubelievearerelevant
  • A discussion of what happens to your R²and alpha (including its significance), and anyother statistical measures you believe are relevant, when the additional Carhart factors areaddedto themodel, as wellas anexplanationforwhyyou believethis occurs
  • A discussion of the differences between your multi-factor model individual stock resultsandyourmulti-factormodel portfolio result
  • Considerationofanylimitationsorshortcomingsyoubelieveexistinyourmodels,addressingissuessuchastheriskweightingmethodology,allocationmethodologies,concentrationissuesandthe unconstrained natureofthe outcomes