金融學(xué)課件：第12章 投資組合選擇

1、1Copyright Prentice Hall Inc. 2000. Author: Nick Bagley, bdellaSoft, Inc.學(xué)習(xí)目的學(xué)習(xí)目的了解資產(chǎn)組合的理論與應(yīng)用234Security Prices101001000100001000000510152025303540YearsValue (Log)StockBondStock_MuBond_Mu5Security Prices101001000100001000000510152025303540YearsValue (Log)StockBondStock_MuBond_Mu6Security Prices10100

2、1000100001000000510152025303540YearsValue (Log)StockBondStock_MuBond_Mu7Security Prices101001000100001000000510152025303540YearsValue (Log)StockBondStock_MuBond_MuSecurity Prices101001000100001000000510152025303540YearsValue (Log)StockBondStock_MuBond_MuSecurity Prices1010010001000010000005101520253

3、03540YearsValue (Log)StockBondStock_MuBond_MuSecurity Prices101001000100001000000510152025303540YearsValue (Log)StockBondStock_MuBond_Mu8Security Prices101001000100001000000510152025303540YearsValue (Log)StockBondStock_MuBond_Mu9Probability of Future Price0.0000.0050.0100.0150.0200.0250.0300.0350501

4、00150200250300ValueProbability DensityProb_Stock_2Prob_Bond_2Prob_Stock_5Prob_Bond_5Prob_Stock_10Prob_Bond_10Prob_Stock_40Prob_Bond_4010Probabilistic Stock Price Changes Over Time0.0000.0020.0040.0060.0080.0100.0120.0140.0160.0180.0200200400600800PriceProbability DensityStock_Year_1Stock_Year_2Stock

5、_Year_3Stock_Year_4Stock_Year_5Stock_Year_6Stock_Year_7Stock_Year_8Stock_Year_9Stock_Year_1011Probabilistic 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_Year_6Bond_Year_7

6、Bond_Year_8Bond_Year_9Bond_Year_10121-Year Out0.00000.00500.01000.01500.02000.02500.03000.03500.04000.0450020406080100120140160180200PriceDensityStock_1_YearBond_1_YearMode =104Mode =106Median=104Mean =104Median=111Mean = 11313Two Years Out0.0000.0050.0100.0150.0200.0250.0300.03502040608010012014016

7、0180200PriceDensityStock_2_YearBond_2_Year145-Years Out0.0000.0020.0040.0060.0080.0100.0120.0140.0160.0180.0200100200300400500PriceDensityStock_5_YearBond_5_YearMode = 122 Mode = 135 Median= 126Mean = 128Median= 165Mean = 1821510-Years Out0.0000.0020.0040.0060.0080.0100.01202004006008001,000ValueDen

8、sityStock_10_YearBond_10_Year1640 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 =12,15117Value of Central Tendency Statistics for the LogNormal1_Year2_Years5_Yea

9、rs10_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.

10、52$128.40$164.87$738.91modeThe most probable pricemedian50% of prices are equal or lower that thismeanThe expected or average price18Mortality Table Male FemaleAge MDePm MExLife FDePmFExLife6016.0817.519.4721.256117.5416.7910.1320.446525.4214.0414.5917.327039.5110.9622.1113.677564.198.3138.2410.3280

11、98.846.1865.997.4885152.954.46116.15.1890221.773.18190.753.4595329.961.87317.321.9119Deaths Per Thousand M & F0501001502002503003506065707580859095AgeDeaths / 1000MDePmFDePm20Life Expection05101520256065707580859095AgeRemaining Expected LifeMExLifeFExLife2122232425A Portfolio of a Risky and a Ri

12、skless Security-0.20-0.15-0.10-0.050.000.000.250.300.0000.400.50VolatilityReturn26Capital Market Line0.000.000.250.300.000.000.250.300.350.400.450.50VolatilityReturn Long risky and short risk-free Long both risky and risk-free 100% Risky 100% Risk-less2

13、7YTD1-Yr3-Yrs5-Yrs10-Yrs Life14.81 30.4015.8714.1516.5316.96282930311 with ;212211wwrwrwrp322211wwp33(wrong) 2211wwp22222 , 12121212122wwwwp3435W1*Sig1W2*Sig2W1*Sig11Rho(1,2)W2*Sig2Rho(2,1)12 , 121212222212122wwwwp36W1*Sig1 W2*Sig2W3*Sig3W1*Sig11Rho(1,2) Rho(1,3)W2*Sig2 Rho(2,1)1Rho(2,3)W3*Sig3 Rho(

14、3,1) Rho(3,2)13 , 232323 , 131312 , 121212323222221212222wwwwwwwwwp37382-Shares: Is One Better? 00.020.040.060.040.1600.00.250.3Standard Deviation Expected Return 39Share Prices050100150200250300350012345678910YearsValue (adjusted for Splits)ShareP_1ShareP_240Portfolio of Two S

15、ecurities0.000.0030.250.270.29Standard Deviation Expected Return Share 1Share 2EfficientSub-optimalMinimumVariance41Data For two securitiesThis data has been constructed to produce the mean-varience paradoxmu_115.00%mu_210.00%sig_120.00%sig_225.00%rho90.00%w_1w_2Po

16、rt_SigPort_Mu-2.503.500.4776-0.0250-2.403.400.4674-0.0200-2.303.300.4573-0.0150-472-0.0100-372-0.0050-2.003.000.42720.0000-1.902.900.41730.0050-1.802.800.40740.0100-1.702.700.39760.01501.30-0.300.19530.16501.40-0.400.19490.17001.50-0.500.19530.17501.60-0.600.19620.18001.70-0.70

17、0.19780.18501.80-0.800.20000.19001.90-0.900.20280.19502.00-1.000.20620.20002.10-1.100.21010.20502.20-1.200.21450.21002.30-1.300.21940.21502.40-1.400.22470.22002.50-1.500.23050.2250-0.301.300.27230.0850-6460.0900-5710.09500.001.000.25000.10000.100.900.24320.10500.200.800.23660.1

18、1000.300.700.23050.115042w_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*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_2