利用Matlab計(jì)算有效前沿

利用Matlab計(jì)算有效前沿三一重工月份月開(kāi)盤價(jià)月收盤價(jià)月收益率601601保險(xiǎn)12345678910111211.3813.8213.6316.8717.8317.3522.2827.7718.5822.723.824.613.713.5816.7817.5517.1522.3827.7719.6122.2724.4724.5725.20.203866-0.017370.2311080.040308-0.038140.2899140.246409-0.293840.1986010.0779740.0323530.041463寶鋼股份月份月開(kāi)盤價(jià)月收盤價(jià)月收益率600019鋼鐵1234567891011124.755.545.35.755.836.147.029.696.416.56.78.25.485.255.745.786.117.049.636.426.466.848.179.660.153684-0.052350.0830190.0052170.0480270.146580.371795-0.337460.00780.0285710.2194030.178049強(qiáng)生控股月份月開(kāi)盤價(jià)月收盤價(jià)月收益率600662運(yùn)輸物流1234567891011123.674.525.186.116.266.296.627.016.16.186.58.214.575.176.16.36.246.66.946.076.116.658.258.590.2452320.1438050.1776060.031097-0.003190.0492850.048338-0.134090.0016390.0760520.2692310.046285海通證券月份月開(kāi)盤價(jià)月收盤價(jià)月收益率600837券商1234567891011128.2511.5211.114.1512.8814.316.3519.2512.6513.413.741611.4611.2414.0912.7914.1516.4518.9412.813.1914.1516.0619.190.389091-0.024310.269369-0.096110.0986020.150350.15841-0.335060.0426880.055970.168850.199375東風(fēng)科技月份月開(kāi)盤價(jià)月收盤價(jià)月收益率600081汽車1234567891011123.393.83.754.54.595.786.456.645.035.986.487.823.833.83.484.595.776.486.635.15.96.646.48.510.1297940.0078950.1946670.020.2570810.1211070.027907-0.231930.1729620.110368-0.012350.088235第一醫(yī)藥月份月開(kāi)盤價(jià)月收盤價(jià)月收益率600833醫(yī)藥1234567891011125.23.9567.027.757.997.938.8388.319.6710.395.94677.857.997.918.818.058.299.7210.3911.240.1357550.0084030.1666670.1182340.030968-0.010010.110971-0.088340.036250.1696750.0744570.081809浦發(fā)銀行月份月開(kāi)盤價(jià)月收盤價(jià)月收益率600000銀行12345678910111213.5116.817.7922.0523.2726.0523.0627.3517.7620.1621.221.8816.6917.7821.9223.1725.6523.0227.1717.8419.6521.7422.0221.690.2353810.0583330.2321530.0507940.102278-0.116310.178231-0.347710.1064190.0783730.038679-0.00868申能股份月份月開(kāi)盤價(jià)月收盤價(jià)月收益率600642電力1234567891011126.126.37.178.329.449.529.8113.810.510.611.5911.946.217.168.339.359.429.8613.6510.5710.4212.1211.511.380.0147060.1365080.1617850.123798-0.002120.0357140.391437-0.23406-0.007620.143396-0.00777-0.0469上海建工月份月開(kāi)盤價(jià)月收盤價(jià)月收益率600170建筑1234567891011129.221010.6212.8913.1912.718.4817.312.714.3614.7115.489.9110.6212.7713.1712.6516.817.612.5814.0114.9115.5515.460.0748370.0620.2024480.021722-0.040940.322835-0.04762-0.272830.103150.0383010.057104-0.00129錦江股份月份月開(kāi)盤價(jià)月收盤價(jià)月收益率600754旅游酒店1234567891011129.1611.6510.5314.216.9918.919.0123.4718.4618.1519.8722.0911.5510.6814.116.9518.8119.0623.3920.5117.7320.1522.2823.570.260917-0.083260.3390310.1936620.1071220.0084660.230405-0.12612-0.039540.1101930.1212880.066999其中各股票分紅情況如下：600170上海建工 建筑 每10股分紅1.25元600642申能股份 電力 每10股分2元600000浦發(fā)銀行 銀行 每10股分4.5元600754錦江股份 旅游酒店 每10股分紅3.6元600833第一醫(yī)藥 醫(yī)藥 每10股分紅0.8元600081東風(fēng)科技 汽車 無(wú)分紅600837海通證券 券商 每10股分2元600662強(qiáng)生控股 運(yùn)輸物流 每10股0.8元601601中國(guó)太保 保險(xiǎn) 每10股3元600019寶鋼股份 鋼鐵 每10股2元Step1：建立月收益率矩陣： x=x1 x2 x3 x4 x5 x6 x7 x8 x9 x10求得十只股票間的協(xié)方差：cov(x,1)=0.0244 0.0191 0.0077 0.0209 0.0120 0.0063 0.0157 0.01390.0172 0.01170.0191 0.0274 0.0098 0.0233 0.0091 0.0069 0.0159 0.01520.0102 0.01380.0077 0.0098 0.0118 0.0142 0.0037 0.0046 0.0105 0.00490.0076 0.00800.0209 0.0233 0.0142 0.0317 0.0147 0.0083 0.0204 0.00940.0148 0.01650.0120 0.0091 0.0037 0.0147 0.0146 0.0044 0.0130 0.00530.0103 0.00740.0063 0.0069 0.0046 0.0083 0.0044 0.0055 0.0091 0.00660.0033 0.00860.0157 0.0159 0.0105 0.0204 0.0130 0.0091 0.0233 0.01470.0087 0.01570.0139 0.0152 0.0049 0.0094 0.0053 0.0066 0.0147 0.02090.0063 0.01110.0172 0.0102 0.0076 0.0148 0.0103 0.0033 0.0087 0.00630.0189 0.00540.0117 0.0138 0.0080 0.0165 0.0074 0.0086 0.0157 0.01110.0054 0.0186Step2:計(jì)算平均收益率x0=0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1mean(x)=（）Step3：建立模型，約束條件如下Subject to 其中權(quán)數(shù)可以為負(fù)，即允許融券（short-sell）.使用Matlab軟件：a=linspace(0,0.2,100);for i=1:100beq=1;a(i);x,f=fmincon(n