【代码】基于超额收益的资产组合优化

基于《现代投资组合理论与投资分析 9th》第九章；

仅包含MATLAB代码，原理请查看原书；

输入：

• Mean: 期望收益矩阵
• Beta: 市场收益变动1%时，期望变动率矩阵
• Sigma: 证券收益标准差
• Sigma_m: 市场指数标准差
• Rf: 无风险资产收益

输出：

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
证券编号	收益均值	超额收益	贝塔	超额收益/贝塔	证券收益标准差	非系统风险	超额收益*贝塔/非系统风险2	8的累加	贝塔/非系统风险2	贝塔2/非系统风险2	11的累加	截止率候选值	未调整比率	调整后比率
$i$	$R_i$	$R_i-R_f$	$\beta_i$	$\frac{R_i-R_f}{\beta_i}$	$\sigma_i$	$\sigma_{ei}$	$\frac{(R_i-R_f)\beta_i}{\sigma_{ei}^2}$	sum(8)	$\frac{\beta_i}{\sigma_{ei}^2}$	$\frac{\beta_i^2}{\sigma_{ei}^2}$	sum(11)	$c_i$	$z_i$	$x_i$

function [matrix] = portfolio_optimization_c(mean,beta,sigma,sigma_m,rf)
% mean|excess return|beta|excess return over beta|sigma_i|sigma_ei|(ri-rf)beta/sigma_ei^2|sum(8)|betai/sigma_ei^2|betai^2/sigma_ei^2|sum(11)|C*|Z|X
n = length(mean);
matrix = zeros(n,15);
matrix(:,1) = 1:1:n;
matrix(:,2) = mean;
matrix(:,3) = mean-rf;
matrix(:,4) = beta;
matrix(:,5) = matrix(:,3)./matrix(:,4);
matrix(:,6) = sigma;
matrix(:,7) = sqrt(matrix(:,6).^2-sigma_m^2*matrix(:,4).^2);
matrix(:,8) = matrix(:,3).*matrix(:,4)./matrix(:,7).^2;
matrix(:,10) = matrix(:,4)./matrix(:,7).^2;
matrix(:,11) = matrix(:,4).^2./matrix(:,7).^2;
matrix = sortrows(matrix,5,'descend');
for i = 1:1:n
    matrix(i,9) = sum(matrix(1:i,8));
    matrix(i,12) = sum(matrix(1:i,11));
end
matrix(:,13) = sigma_m^2*matrix(:,9)./(1+sigma_m^2*matrix(:,12));
C = matrix(1,13);
for i = 1:1:n
    if matrix(i,13) > matrix(i,5)
        break;
    else
        C = matrix(i,13);
    end
end
matrix(:,14) = matrix(:,10).*(matrix(:,5)-C);
matrix(:,15) = matrix(:,14)/sum(matrix(:,14));
name = {'index','mean','excess_return','beta','excess_return_over_beta','sigma','sigma_e','excess_return_time_beta_by_sigma_e2','sum_of_8','beta_by_sigma_e2','beta2_by_sigma_e2','sum_of_11','C','Z','X'};
matrix = array2table(matrix, 'VariableNames', name);
end