1、ObjectiveTo understand the theory of personalportfolio selection in theory and in practice123678Security Prices101001000100001000000510152025303540YearsValue(Log)StockBondStock_MuBond_Mu9101112Security Prices101001000100001000000510152025303540YearsValue(Log)StockBondStock_MuBond_Mu13Security Prices
2、101001000100001000000510152025303540YearsValue(Log)StockBondStock_MuBond_Mu14Security Prices101001000100001000000510152025303540YearsValue(Log)StockBondStock_MuBond_MuSecurity Prices101001000100001000000510152025303540YearsValue(Log)StockBondStock_MuBond_MuSecurity Prices1010010001000010000005101520
3、25303540YearsValue(Log)StockBondStock_MuBond_MuSecurity Prices101001000100001000000510152025303540YearsValue(Log)StockBondStock_MuBond_Mu151617Security Prices101001000100001000000510152025303540YearsValue(Log)StockBondStock_MuBond_Mu181920Probability of Future Price0.0000.0050.0100.0150.0200.0250.03
4、00.035050100150200250300ValueProbability DensityProb_Stock_2Prob_Bond_2Prob_Stock_5Prob_Bond_5Prob_Stock_10Prob_Bond_10Prob_Stock_40Prob_Bond_402122Probabilistic Stock Price Changes Over Time0.0000.0020.0040.0060.0080.0100.0120.0140.0160.0180.0200200400600800PriceProbability DensityStock_Year_1Stock
5、_Year_2Stock_Year_3Stock_Year_4Stock_Year_5Stock_Year_6Stock_Year_7Stock_Year_8Stock_Year_9Stock_Year_10232425Probabilistic Bond Price Changes over Time0.0000.0050.0100.0150.0200.0250.0300.0350.0400.0450100200300400PriceProbability DensityBond_Year_1Bond_Year_2Bond_Year_3Bond_Year_4Bond_Year_5Bond_Y
6、ear_6Bond_Year_7Bond_Year_8Bond_Year_9Bond_Year_1026272829301-Year Out0.00000.00500.01000.01500.02000.02500.03000.03500.04000.0450020406080100120140160180200PriceDensityStock_1_YearBond_1_YearMode=104Mode=106Median=104Mean=104Median=111Mean=11331Two Years Out0.0000.0050.0100.0150.0200.0250.0300.0350
7、20406080100120140160180200PriceDensityStock_2_YearBond_2_Year325-Years Out0.0000.0020.0040.0060.0080.0100.0120.0140.0160.0180.0200100200300400500PriceDensityStock_5_YearBond_5_YearMode=122 Mode=135 Median=126Mean=128Median=165Mean=1823310-Years Out0.0000.0020.0040.0060.0080.0100.01202004006008001,00
8、0ValueDensityStock_10_YearBond_10_Year3440 Years Out0.0000.0000.0000.0010.0010.0010.0010.0010.00205,00010,00015,00020,00025,00030,000ValueDensityStock_40_YearBond_40_YearMode=503 Mode=1,102 Median=650Mean=739Median=5,460Mean=12,1513536Value of Central Tendency Statistics for the LogNormal1_Year2_Yea
9、rs5_Years10_Years 40_YearsAssume:Sig=0.20,Mu=0.12mode$106.18$112.75$134.99$182.21$1,102.32median$110.52$122.14$164.87$271.83$5,459.82mean$112.75$127.12$182.21$332.01$12,151.04Assume:Sig=0.08,Mu=0.05mode$104.12$108.42$122.38$149.78$503.29median$104.79$109.81$126.36$159.68$650.13mean$105.13$110.52$128
10、.40$164.87$738.91modeThe most probable pricemedian50%of prices are equal or lower that thismeanThe expected or average price37383940414243Mortality Table Male FemaleAge MDePm MExLife FDePmFExLife6016.0817.519.4721.256117.5416.7910.1320.446525.4214.0414.5917.327039.5110.9622.1113.677564.198.3138.2410
11、.328098.846.1865.997.4885152.954.46116.15.1890221.773.18190.753.4595329.961.87317.321.9144Deaths Per Thousand M&F0501001502002503003506065707580859095AgeDeaths/1000MDePmFDePm45Life Expectancy05101520256065707580859095AgeRemaining Expected LifeMExLifeFExLife4647484950515253545556575859A Portfolio of
12、a Risky and a Riskless Security-0.20-0.15-0.10-0.050.000.050.100.150.200.250.300.000.100.200.300.400.50VolatilityReturn6061Capital Market Line0.000.050.100.150.200.250.300.000.050.100.150.200.250.300.350.400.450.50VolatilityReturn Long risky and short risk-free Long both risky and risk-free 100%Risk
13、y 100%Risk-less62636465YTD1-Yr3-Yrs5-Yrs10-Yrs Life14.81 30.4015.8714.1516.5316.9666676869707172737475761 with;212211wwrwrwrp77782211wwp79(wrong)2211wwp22222,12121212122wwwwp8081W1*Sig1W2*Sig2W1*Sig11Rho(1,2)W2*Sig2Rho(2,1)12,121212222212122wwwwp82W1*Sig1 W2*Sig2W3*Sig3W1*Sig11Rho(1,2)Rho(1,3)W2*Sig
14、2 Rho(2,1)1Rho(2,3)W3*Sig3 Rho(3,1)Rho(3,2)13,232323,131312,121212323222221212222wwwwwwwwwp8384852-Shares:Is One Better?00.020.040.060.080.10.120.140.1600.050.10.150.20.250.3Standard Deviation Expected Return 86878889Share Prices050100150200250300350012345678910YearsValue(adjusted for Splits)ShareP_
15、1ShareP_2909192Portfolio of Two Securities0.000.050.100.150.200.250.150.170.190.210.230.250.270.29Standard Deviation Expected Return Share 1Share 2EfficientSub-optimalMinimumVariance9394959697Data For two securitiesThis data has been constructed to produce the mean-varience paradoxmu_115.00%mu_210.0
16、0%sig_120.00%sig_225.00%rho90.00%w_1w_2Port_SigPort_Mu-2.503.500.4776-0.0250-2.403.400.4674-0.0200-2.303.300.4573-0.0150-2.203.200.4472-0.0100-2.103.100.4372-0.0050-2.003.000.42720.0000-1.902.900.41730.0050-1.802.800.40740.0100-1.702.700.39760.01501.30-0.300.19530.16501.40-0.400.19490.17001.50-0.500
17、.19530.17501.60-0.600.19620.18001.70-0.700.19780.18501.80-0.800.20000.19001.90-0.900.20280.19502.00-1.000.20620.20002.10-1.100.21010.20502.20-1.200.21450.21002.30-1.300.21940.21502.40-1.400.22470.22002.50-1.500.23050.2250-0.301.300.27230.0850-0.201.200.26460.0900-0.101.100.25710.09500.001.000.25000.
18、10000.100.900.24320.10500.200.800.23660.11000.300.700.23050.115098w_1w_2Port_SigPort_Mu-2.5=1-A14=SQRT(w_12*sig_12+2*w_1*w_2*sig_1*sig_2*rho+w_22*sig_22)=w_1*mu_1+w_2*mu_2=A14+0.1=1-A15=SQRT(w_12*sig_12+2*w_1*w_2*sig_1*sig_2*rho+w_22*sig_22)=w_1*mu_1+w_2*mu_2=A15+0.1=1-A16=SQRT(w_12*sig_12+2*w_1*w_2
19、*sig_1*sig_2*rho+w_22*sig_22)=w_1*mu_1+w_2*mu_2=A16+0.1=1-A17=SQRT(w_12*sig_12+2*w_1*w_2*sig_1*sig_2*rho+w_22*sig_22)=w_1*mu_1+w_2*mu_2=SQRT(w_12*sig_12+2*w_1*w_2*sig_1*sig_2*rho+w_22*sig_22)=w_1*mu_1+w_2*mu_299*122212,121212,121*222212,121212,122*1122www10010132tan232tan1222tan11tan2221212,12121221
20、2,12221tan11225.0*10.025.0*20.0*90.0*05.010.020.0*05.025.0*20.0*90.0*05.025.0*10.01wwwwwrrrrrrwffffff1021261.005.010.02409.005.02333.02409.090.0*25.0*2.0*3538225.03520.03822333.010.03515.038tantantan22222tan2,121tan2tan1222tan2212tan12tantantan2tan21tan1tanffrrwwwwww1031043636.105.02333.005.030.01111ftangentfcriterionftangentcriterionrrwwrw1053285.02409.0*3636.11tangentw106COMPUTATIONWEIGHTRISKLESS-0.3636-0.3636ASSET 11.3636*2.66673.6363ASSET 21.3636*(-1.6667)-2.2727TOTAL1.0000107108109110111112113114115116
