MATLAB基于遗传算法的债券投资组合优化

1. 主程序框架

%% 基于遗传算法的债券投资组合优化
clear; clc; close all;%% 债券数据生成（实际应用中替换为真实数据）
nBonds = 50;  % 债券数量
bondData = generateBondData(nBonds);%% 遗传算法参数设置
gaOptions = setupGAOptions();%% 运行遗传算法优化
fprintf('开始债券投资组合优化...\n');
[optimalWeights, optimalFitness, exitFlag, output] = ...runBondPortfolioGA(bondData, gaOptions);%% 结果分析与可视化
analyzeResults(optimalWeights, optimalFitness, bondData, output);

2. 债券数据结构

function bondData = generateBondData(nBonds)% 生成模拟债券数据rng(42);  % 设置随机种子保证可重复性bondData = struct();bondData.nBonds = nBonds;% 债券基本属性bondData.yield = 0.02 + 0.08 * rand(nBonds, 1);      % 收益率 2%-10%bondData.duration = 1 + 9 * rand(nBonds, 1);         % 久期 1-10年bondData.convexity = 0.5 + 4.5 * rand(nBonds, 1);    % 凸性bondData.creditRating = randi([1, 10], nBonds, 1);   % 信用评级 (1最好,10最差)bondData.sector = randi([1, 5], nBonds, 1);          % 行业分类bondData.liquidity = 0.1 + 0.9 * rand(nBonds, 1);    % 流动性指标% 风险参数bondData.targetDuration = 5.0;      % 目标久期bondData.maxSectorWeight = 0.3;     % 单一行业最大权重bondData.budget = 1.0;              % 总预算
end

3. 遗传算法配置

function gaOptions = setupGAOptions()% 配置遗传算法参数gaOptions = optimoptions('ga');% 算法参数gaOptions.PopulationSize = 100;      % 种群大小gaOptions.MaxGenerations = 200;      % 最大代数gaOptions.CrossoverFraction = 0.8;   % 交叉比例gaOptions.EliteCount = 2;            % 精英个体数量% 显示设置gaOptions.Display = 'iter';gaOptions.PlotFcn = {@gaplotbestf, @gaplotdistance};% 停止条件gaOptions.FunctionTolerance = 1e-6;gaOptions.StallGenLimit = 50;
end

4. 适应度函数

function fitness = bondPortfolioFitness(weights, bondData)% 债券投资组合适应度函数% 确保权重为行向量weights = weights(:)';% 约束检查[valid, penalty] = checkConstraints(weights, bondData);if ~validfitness = -1e6 * penalty;  % 严重惩罚违反约束return;end% 计算收益目标portfolioReturn = sum(weights .* bondData.yield');% 计算风险惩罚项riskPenalty = calculateRiskPenalty(weights, bondData);% 适应度函数：收益 - 风险调整fitness = portfolioReturn - riskPenalty;
endfunction [valid, penalty] = checkConstraints(weights, bondData)% 检查投资组合约束penalty = 0;% 预算约束weightSum = sum(weights);if abs(weightSum - bondData.budget) > 1e-6penalty = penalty + 100 * abs(weightSum - bondData.budget);end% 非负约束negativeWeights = sum(weights(weights < 0));if negativeWeights < 0penalty = penalty + 1000 * abs(negativeWeights);end% 单一债券权重约束 (最大20%)maxWeightViolation = max(0, max(weights) - 0.2);penalty = penalty + 500 * maxWeightViolation;% 行业分散约束sectorPenalty = checkSectorConstraints(weights, bondData);penalty = penalty + sectorPenalty;valid = (penalty == 0);
endfunction sectorPenalty = checkSectorConstraints(weights, bondData)% 检查行业分散约束sectorPenalty = 0;uniqueSectors = unique(bondData.sector);for i = 1:length(uniqueSectors)sectorMask = (bondData.sector == uniqueSectors(i));sectorWeight = sum(weights(sectorMask));% 检查是否超过最大行业权重if sectorWeight > bondData.maxSectorWeightsectorPenalty = sectorPenalty + 200 * (sectorWeight - bondData.maxSectorWeight);endend
endfunction riskPenalty = calculateRiskPenalty(weights, bondData)% 计算风险惩罚项% 久期偏差惩罚portfolioDuration = sum(weights .* bondData.duration');durationDeviation = abs(portfolioDuration - bondData.targetDuration);durationPenalty = 0.1 * durationDeviation;% 信用风险惩罚creditRisk = sum(weights .* (bondData.creditRating' / 10));creditPenalty = 0.05 * creditRisk;% 流动性惩罚liquidityPenalty = 0.02 * sum(weights .* (1 - bondData.liquidity'));% 集中度风险惩罚concentrationPenalty = 0.1 * (sum(weights.^2));  % Herfindahl指数riskPenalty = durationPenalty + creditPenalty + liquidityPenalty + concentrationPenalty;
end

5. 遗传算法执行

function [optimalWeights, optimalFitness, exitFlag, output] = runBondPortfolioGA(bondData, gaOptions)% 运行遗传算法优化nVars = bondData.nBonds;% 约束定义A = []; b = [];  % 线性不等式约束 A*x <= bAeq = ones(1, nVars);  % 权重和为1beq = bondData.budget;% 变量边界 [0, 0.2]lb = zeros(1, nVars);ub = 0.2 * ones(1, nVars);% 非线性约束nonlcon = @(weights) nonLinearConstraints(weights, bondData);% 适应度函数fitnessFcn = @(weights) -bondPortfolioFitness(weights, bondData);% 运行遗传算法[optimalWeights, optimalFitness, exitFlag, output] = ...ga(fitnessFcn, nVars, A, b, Aeq, beq, lb, ub, nonlcon, gaOptions);% 转换回正适应度值optimalFitness = -optimalFitness;
endfunction [c, ceq] = nonLinearConstraints(weights, bondData)% 非线性约束函数c = [];  % 非线性不等式约束 c(x) <= 0% 行业权重约束 (非线性等式约束)uniqueSectors = unique(bondData.sector);ceq = zeros(length(uniqueSectors), 1);for i = 1:length(uniqueSectors)sectorMask = (bondData.sector == uniqueSectors(i));sectorWeight = sum(weights(sectorMask));% 允许轻微偏差ceq(i) = max(0, sectorWeight - bondData.maxSectorWeight);end
end

6. 结果分析

function analyzeResults(optimalWeights, optimalFitness, bondData, output)% 分析并可视化优化结果fprintf('\n=== 优化结果分析 ===\n');fprintf('最优适应度值: %.4f\n', optimalFitness);fprintf('组合收益率: %.4f%%\n', 100 * sum(optimalWeights .* bondData.yield'));fprintf('组合久期: %.4f 年\n', sum(optimalWeights .* bondData.duration'));% 投资组合统计nSelected = sum(optimalWeights > 0.001);fprintf('选择的债券数量: %d/%d\n', nSelected, bondData.nBonds);% 权重分布figure('Position', [100, 100, 1200, 800]);subplot(2, 3, 1);bar(optimalWeights(optimalWeights > 0.001));title('债券权重分布');xlabel('债券编号');ylabel('权重');grid on;% 收益率 vs 久期散点图subplot(2, 3, 2);scatter(bondData.duration, bondData.yield, 50, optimalWeights, 'filled');colorbar;xlabel('久期 (年)');ylabel('收益率');title('债券特征与权重');grid on;% 行业分布subplot(2, 3, 3);uniqueSectors = unique(bondData.sector);sectorWeights = zeros(size(uniqueSectors));for i = 1:length(uniqueSectors)sectorMask = (bondData.sector == uniqueSectors(i));sectorWeights(i) = sum(optimalWeights(sectorMask));endpie(sectorWeights);title('行业权重分布');legend(arrayfun(@(x) sprintf('行业 %d', x), uniqueSectors, 'UniformOutput', false));% 收敛曲线subplot(2, 3, 4);plot(output.fitness);title('遗传算法收敛曲线');xlabel('代数');ylabel('最佳适应度');grid on;% 风险贡献分析subplot(2, 3, 5);riskContribution = optimalWeights .* bondData.creditRating';riskContribution = riskContribution / sum(riskContribution);bar(riskContribution(optimalWeights > 0.001));title('信用风险贡献');xlabel('债券编号');ylabel('风险贡献比例');grid on;% 权重与流动性关系subplot(2, 3, 6);scatter(bondData.liquidity(optimalWeights > 0.001), ...optimalWeights(optimalWeights > 0.001), 50, 'filled');xlabel('流动性指标');ylabel('权重');title('权重 vs 流动性');grid on;% 详细统计信息fprintf('\n投资组合详细统计:\n');fprintf('信用风险加权平均: %.4f\n', sum(optimalWeights .* bondData.creditRating'));fprintf('流动性加权平均: %.4f\n', sum(optimalWeights .* bondData.liquidity'));fprintf('凸性加权平均: %.4f\n', sum(optimalWeights .* bondData.convexity'));% 显示前10大持仓[sortedWeights, sortedIdx] = sort(optimalWeights, 'descend');fprintf('\n前10大持仓:\n');fprintf('债券#\t权重\t收益率\t久期\t信用评级\n');for i = 1:min(10, nSelected)idx = sortedIdx(i);fprintf('%d\t%.4f\t%.4f\t%.2f\t%d\n', ...idx, sortedWeights(i), bondData.yield(idx), ...bondData.duration(idx), bondData.creditRating(idx));end
end

7. 高级功能扩展

%% 多目标优化版本
function [weights, scores] = multiObjectiveBondOptimization(bondData)% 多目标优化：同时优化收益和风险fitnessFcn = @(weights) [ -sum(weights .* bondData.yield'), ...  % 目标1: 最大化收益calculateTotalRisk(weights, bondData) ]; % 目标2: 最小化风险nVars = bondData.nBonds;A = []; b = [];Aeq = ones(1, nVars);beq = 1;lb = zeros(1, nVars);ub = 0.2 * ones(1, nVars);[weights, scores] = gamultiobj(fitnessFcn, nVars, A, b, Aeq, beq, lb, ub);
endfunction totalRisk = calculateTotalRisk(weights, bondData)% 计算总风险度量durationRisk = abs(sum(weights .* bondData.duration') - bondData.targetDuration);creditRisk = sum(weights .* (bondData.creditRating' / 10));concentrationRisk = sum(weights.^2);totalRisk = 0.1 * durationRisk + 0.05 * creditRisk + 0.1 * concentrationRisk;
end