OnaSaturdaymorninginlateSeptember 2015,Desiree Mofakyesatoverherbreakfast,whichwasrapidlyturning cold,and reflectedontheperformanceofher personalinvestmentportfoliooverthe past sevenyears.She recalledthat,afterthefinancial crisisin2008,shehadbeenadvisedtoavoidU.S.stocksandtoputher savingsintheemergingeconomiesofGHANAandSA.Atthetime,shehadchosentoallocateherfunds totwoexchange tradedfunds(ETF)investedintheequitymarketsofGHANAandSA,namelyALUWORKSandAGA,intheratioof60percentand40percentrespectively. ALUWORKSwasan ETFinvestedinthepublicequitymarketsof SA.TheETFinvestedin thestocksoflarge-capcompaniesoperatingacrossdiversifiedsectors. AGA wasanETFthatinvested inthepublicequitymarketsofGHANA.TheETFinvested inthe stocksoflarge-capandmid-capcompaniesoperatingacrossdiversified sectors,andtrackedthe performanceoftheGhana Stock Exchange All Share Index (GSI). AlthoughDesiree Mofakyehadbeensatisfiedwithherportfolioperformance overthepastsevenyears,thehigh growthinthesetwoemerging marketshadfizzledoutlately.However, theadviceshehadgatheredfrom analysts reportsimpliedthatsheshouldstayinvestedinthesemarkets,albeitwithmoreattentiontothe volatileswings.Desiree Mofakyehadenrolledinacorporatefinanceclassat UPSA onriskandreturntoimproveherinvestment knowledge. Duringherclasses,Desiree Mofakyelearnedthattheriskofaportfolio wasnotsimplyaweighted averageofthe individualvariancesofthecomponentassets.Rather,itwasdeterminedtoalargeextentbytheco-movementbetweenthereturnsofthecomponentassets.Consequently,Desiree Mofakyereasonedthatdiversification toincludeanassetthatwasimperfectlycorrelated withtheexistingcomponents ofherportfolioshould reduceherriskwithoutsacrificingreturns,ifshehadunderstoodcorrectly. Withthisobjectiveinmind,Desiree MofakyestartedtosearchforanassetthatwasnotcorrelatedwithALUWORKSorAGA.Desiree Mofakyewondered whethersheshouldmovesomeofherfundstoU.S.equity.TheU.S.economyappeared tohavebenefittedfromtheroundsofquantitative easingandwasfinallyrecoveringfromthedoldrums. Surely, thefactthattheUnited StateswaspickingupatatimewhenSAandGHANA wereslowingdownwasindicativeoflowcorrelationamongthethreeeconomies. EXAMINERS: DOKU, BOADI, BOAMAH &AGOBA Page 3of 4Moreover, toconfirmherbelief,Desiree MofakyedecidedtopickanETFthattrackedtheU.S.equitymarket. Shenoticedthat LyxorUnitedStatesDowJonesIndustrialAverage(USDJIA)wasinvestedinthepublicequitymarkets oftheUnitedStates,inthestocksofcompaniesoperating acrossdiversifiedsectors,excluding transportationandutilitiessectors.Sheproceeded togatherpastreturndataonALUWORKS,AGA, andUSDJIA (see Exhibit1).AllthreeETFswerelistedontheNairobiStock Exchange. Asaproxyforthemarketportfolio, Desiree MofakyedownloadedcorrespondingreturndataforLyxorWorld(seeExhibit1). LyxorWorldwasanETFthatinvestedinthepublicequitymarketsofdeveloped countriesacrossthe globe.Itinvestedinthestocksoflarge-capandmid-capcompanies, andprovidedresultsthatclosely correspondedtotheperformanceoftheGhana Stock Exchange All Share Index (GSI). Desiree Mofakyesideawastocomparethemeanreturnsandstandarddeviations ofherexistingportfoliowithan alternativeportfoliothatwouldinvest40 percentin SA,30 percentin GHANA,and30 percentin United States(seeExhibit2).Shehopedthattheanalysiswouldhelpherdecidewhethertodiversifyher portfolioorremaininvestedinSAandGHANAonly. Inaddition,sheintendedtocomputethebetasofALUWORKS,AGA,andUSDJIA usingtheircovariance withthemarketproxy,whichwouldhelpherfigureouttheirrequiredreturns, assumingarisk-freerateof 2.5percentandamarketriskpremiumof 5.5percent. Desiree Mofakyewasexcitedtogetstartedandtoapplythefinancialconceptsthatshehadgleanedfromher corporatefinanceclass.Theclass mighthaveturnedouttobeherbestinvestmentyet.EXHIBIT1: ANNUALRETURNS(%)YearALUWORKSAGA Lyxor USDJIALyxor World20092.005.865.567.6920104.2522.406.115.792011-29.40-27.077.94-3.28201213.230.6018.2920.7520138.86-6.8417.0914.1420142.3133.8714.2015.062015-2.96-9.28-4.71-4.28 EXHIBIT 2: PORTFOLIOWEIGHTS (%)AssetsExisting PortfolioWeightsNewPortfolioWeightsALUWORKS6040AGA 4030Lyxor USDJIA30Required1.Using the annual return data provided in Exhibit 1 of the case for ALUWORKS and AGA, calculate their mean returns, standard deviations, covariance, and correlation. With these numbers, calculate the standard deviation and return for Desiree Mofakyes entire portfolio (6marks).2.After adding Lyxor USDJIA, what is the portfolios new standard deviation and return? How does thenew portfolio compare with the calculation in Question 1? (6marks).3.Based on your data analysis, should Desiree Mofakyediversify her portfolio or remain invested in SA andGHANA only? (6marks).4.Calculate the betas of ALUWORKS, AGA, and Lyxor USDJIA. To calculate thecovariance with the market proxy, use the Lyxor World return data shown in Exhibit 1 in the case.Assuming a risk-free rate of 2.5 per cent and a market risk premium of 5.5 per cent, what are therequired returns for each of the three ETFs? (6marks).5.Calculate the existing portfolios beta and the new portfolios beta. Assuming a risk-free rate of 2.5 percent and a market risk premium of 5.5 per cent, what are the two portfolios required returns? (6marks).Total Marks (30)