生活˙投资˙理财

Life,Investment,andWealthManagement:EverythingisMathematics?生活˙投資˙理財，源來是數?DrChanYanChong曾淵滄博士CityUniversityofHongKongExpectationofLifeinHongKong0102030405060708090196019701980199020002010malefemaleLongLife•Someresearcherssaythat50%ofbabygirlsborntodaywillreachage100.•Theaveragelifeexpectancyin1900was49years.•Intenyearsmidlifecriseswillstartatage64,accordingtoarecentsurvey.EconomicProblemsofLongLife•Tomaintainthestandardofliving•Decliningemploymentopportunities•RelativelysmallindividualsavingsThecauseofPensionPlanningproblems•Retirementhasbeenaproblemsincetheancienttime.•Eitherinagriculture,primitiveornaturaleconomy,takingcareoftheoldsisoneoftheinstinctivefunctionsamongfamilies.Therefore,theideaofpensionplanningneverexists.Howmuchyouhave?•Assumethatyoustartworkattheageof21.Yourearningis$120,000peryear.Youandyouremployerbothcontribute5%ofyourpayofMPF,andyourretirementageis65.Howmuchyouhavewhenyouretired?HowmuchyouhavePaygrowROI3%ROI5%ROI8%ROI10%2%$0.28M$3.89M$5.22M$9.25M$14.82M5%$1.03M$1.95M$3.29M$7.68M$14.01M10%$7.95M$2.09M$3.58M$8.53M$15.71MHowmuchyouneededforretirement?$1,000,000?$10,000,000?$100,000,000?ComponentsofPersonalSavings•BankAccounts•IndividualRetirementAccounts•LifeInsurance•MutualFunds•StocksandBondsRetirementPlan•Assumethatyouare60yearoldnow.•Yearlyspendingis$200,000•Inflationrate1%•Expectedlifeis85yearold•Howmuchyouneed?HowmuchyouneedInvestmentReturnMoneyneeded1%$5,150,0002%$4,520,0003%$4,000,0005%$3,200,00010%$1,990,00015%$1,380,000Howmuchmoneyrequired?•Ifyourspendingis$100,000peryear•Yearlyspendingincrementis2%•HoldingGovernmentBondwith3%return•$2,000,000enableyoutolivefor22yearsand$5,000,000enableyoutolivefor71years•Ifyouinvestinstockmarketwith10%return•$1,000,000enableyoutolivefor21yearsand$1,500,000enableyoutoliveforwholelife.ReturnMoney3%5%8%9%10%15%.5M5567681M10121618211001.5M1620401001002M22311002.5M29473M36793.5M441004M524.5M615M71InvestmentPlan•Assumethatyouare21yearoldnow.•Yourearningis$120,000peryear•Yourpaygrowat3%peryear•Yourretirementageis60•Yoursaving+MPFis20%ofyourearning•Howmuchyouhavefortheretirement?HowmuchyouhaveInvestmentReturnMoneyneeded1%$3,300,5902%$3,868,7803%$4,582,0905%$6,632,88010%$19,816,09015%$70,738,570TheArtofInvestmentisaCombinationofPsychology&StatisticsPsychology•HumanWeaknesses•Self-analysis•Patience•Adventurous•Pressure5001000150020002500300035004000450050005500199620012000199919981997NASDAQIndexSource:Bloomberg，Jan1,1996toApr30,2001GreedyAfraidEmotionofInvestorsAninvestorwantstomakeaweekbasisinvestmentonStockAwiththeinformationbelow.PricechangeofStockAafteroneweek($)210+1+2Probability0.20.40.20.10.1Fromtheprincipleofexpectedvalue,theexpectedpricechangeinStockA(inoneweek)=$[2×0.2+(1)×0.4+0×0.2+(+1)×0.1+(+2)×0.1]=$0.5AnegativeexpectedpricechangeindicatesthatthepriceofStockAislikelytodecreaseafteroneweek.Inotherwords,theinvestorislikelytolosemoneyifhemakestheinvestmentonStockA.DifferencebetweenInvestmentandGambling3DiceGameProbabilityofBIGorSMALL=1/2-1/36=17/36ExpectedValuefor$300game=$300X17/36-$300X19/36=-$16.67ExpectedValuefor500$300games=-$16.67X500=-$8333.303DiceGamePayWin/LossCash1.$300L-$3002.$600L-$9003.$1200W$3004.$300L05.$600L-$6006.$1200W-$6007.$300W-$9008.$300L-$6009.$600W-$120010.$300L-$90011.$600W-$1500ExpectedValuefor500games=$300X17/36X500=$70833.33Riskof3DiceGamePayGain/LossCash1.$300L-$3002.$600L-$9003.$1200L-$21004.$2400L-$45005.$4800L-$93006.$9600L-$189007.$19200L-$381008.$38400L-$765009.$76800L-$15330010.$153600L-$30690011.$307200L-$614100AssessingRiskRiskhasmanyconnotations.Inthefieldofinvestment,theconceptofriskhasslowlychangedovermanyyears.•Riskisdebtandvariabilityofnetassetvalue•RiskisthebetavalueofCPAM•RiskisthevariabilityofrateofreturnwhichcanbemeasuredbystandarddeviationBetaValue:CAPM•CAPM:CapitalAssetPricingModel•Y=A+BX•A:Alphavalue•B:Betavalue•Y:portfolio`sreturn•X:market`sreturnStandardDeviationniinERR121=standarddeviationofsingleassetninjjiijPWWCov11p:standarddeviationofaportfolioWi:weightofstockiintheportfolioHowtouselogarithm(log)applicationforanalyzingstockmarkettendency？Y=logbXequaltoby=Xb=baseY=exponentWhatislog?XLog2X1020=12121=24222=48323=816424=1632525=32LinearRegressionLineHowthismethodisusedtoanalyzethestockmarkettendencyandthecycle?y=a+bxb=nΣxy–ΣxΣynΣx2-(Σx)2a=Σx2Σy-ΣxΣxynΣx2-(Σx)2MovingAveragen•MA(t,n)=P(t-k+1)/nk=1•MA(t,n):ndaymovingaverageonperiodt•P(t):priceonperiodt