www.gusucode.com > GAVPai_Book_MathworksCntrlFileEx_May2019 > GAVPai_Book_MathworksCntrlFileEx_May2019/Chapter7_ESHOF_PortfolioRebalancing_TrCosts.m
% Vijayalakshmi Pai G A, Metaheuristics for Portfolio Optimization, An
% Introduction using MATLAB, ISTE-Wiley, 2017.
% Evolution Stategy with Hall of Fame (ES HOF)for Portfolio Rebalancing with Transaction Costs
% Chapter 7 Sec. 7.3
% The constrained portfolio rebalancing model is represented by equations [7.8]-[7.9] for
% its objective function and equations [7.2]-[7.6] for its constraints
% The portfolio considered is a high risk portfolio of assets comprising the top 15 percentile of
% high volatility stocks of S&PBSE200 Index
% Sec. 7.4.1
% The data file S&PBSE200_RebalPortfolio.xls records the mean returns of the
% assets of the high risk portfolio, followed by variance-covariance matrix
% of returns of the assets, with the asset labels displayed in the last row
% Program coding: Dr G A Vijayalakshmi Pai
% Note: Coding style has been kept naive and direct to favor novices in
% MATLAB. Users familiar with MATLAB are encouraged to improvise the code
%------------------------------------------------------------------------
clear all
portfolio_size = 32; % 32 high risk assets comprising the portfolio
% obtain mean returns and variance-covariance matrix of returns for the
% portfolio
file_name = 'S&PBSE200_RebalPortfolio.xls';
m = xlsread(file_name);
mean_data = m(1,:);
cov_data = m(2:portfolio_size+1, :);
% obtain optimal weights, maximal diversification ratio, risk and return of
% the original portfolio
OriginalPortfolio_Optimal_Wgts = [0.0248 0.0137 0.0010 0.0010 0.0512 0.0209 0.0316 0.0576 0.0323 0.0010 0.0409 0.0010 0.0020 0.1115 0.0250 0.0010 0.0010 0.0149 0.0151 0.0316 0.0010 0.0695 0.0635 0.0687 0.0595 0.0059 0.0308 0.0617 0.0575 0.0425 0.0435 0.0171];
OriginalPortfolio_MxDR = 2.7822;
OriginalPortfolio_Daily_Risk = 0.0208;
OriginalPortfolio_Daily_Retrn = 0.0034;
% set Transaction cost
p=0.0044;
% set lower and upper bounds of buy and sell weights
buy_lowbounds = zeros(1, portfolio_size);
buy_upbounds = ones(1,portfolio_size)*0.025;
sell_lowbounds = zeros(1, portfolio_size);
sell_upbounds = OriginalPortfolio_Optimal_Wgts;
% Set Evolutionary algorithm parameters
popln_size = 320;
chromosm_length = portfolio_size;
total_generations = 100;
% Joines and Houck's (1994) dynamic penalty (dp) function strategy
% Set parameters (C, alpha, beta)
C_dp = 0.5;
beta_dp=2;
alpha_dp=2;
epsilon = 0.0009;
% initialize Hall of Fame
HOF_fitness = -9999;
fix(clock)
% generation counter
gen_indx = 1;
% index for HOF fitness trace
i1=1;
% generate random initial population of buy sell weights subject to their respective bounds
rebal_popln_raw = generate_bounded_popln(popln_size, portfolio_size,sell_lowbounds , sell_upbounds, buy_lowbounds, buy_upbounds);
% determine the respective lower and upper bounds of the genes in the
% population
low_up_bounds = determine_bounds(rebal_popln_raw, buy_lowbounds, buy_upbounds, sell_lowbounds, sell_upbounds);
% repair weights
initial_rebal_popln_stdzn = PortfolioRebalancing_WeightRepair(rebal_popln_raw, low_up_bounds,p );
% compute the population of rebalanced weights
initial_popln = ones(popln_size,1)*OriginalPortfolio_Optimal_Wgts + initial_rebal_popln_stdzn;
% compute constraint violation function
[G_parent, parent_psi] = compute_constrvioln_fn_Rebal( initial_popln, cov_data, OriginalPortfolio_Daily_Risk, C_dp, beta_dp, alpha_dp, gen_indx); %compute constraint violation functions using Joines and Houck's dynamic penalty functions
% compute fitness function
[parent_fitness ] = Rebal_comp_fitness(initial_popln, cov_data, parent_psi);
% set parent population
feasX_parent_popln = initial_rebal_popln_stdzn;
feasW_parent_popln = initial_popln;
feasW_parent_fitness = parent_fitness;
feasW_parent_psi = parent_psi;
% counter for P measure
pa_count =1;
% ES HOF generation cycles begin
while (gen_indx <= total_generations)
gen_indx
% perform cross over on the parent population
offsprngX_popln_raw= rand_varpt_arith_crossover(feasX_parent_popln, popln_size, chromosm_length);
% perform mutation to yield offspring population
offsprngX_popln_mutat = realnum_unifrm_mutation(offsprngX_popln_raw, popln_size, chromosm_length);
% Normalize offspring population
offsprngX_popln_norm = normalize_weight(offsprngX_popln_mutat, sell_lowbounds , sell_upbounds, buy_lowbounds, buy_upbounds);
% determine lower and upper bounds of the buy sell weights
low_up_bounds = determine_bounds(offsprngX_popln_norm, buy_lowbounds, buy_upbounds, sell_lowbounds , sell_upbounds);
% repair weights of the offspring population
offsprngX_popln = PortfolioRebalancing_WeightRepair(offsprngX_popln_norm, low_up_bounds,p );
% compute the population of rebalanced weights
offsprngW_popln = ones(popln_size,1)*OriginalPortfolio_Optimal_Wgts + offsprngX_popln; % Xi
% compute constraint violation function
[G_offsprngW, offsprngW_psi] = compute_constrvioln_fn_Rebal(offsprngW_popln, cov_data, OriginalPortfolio_Daily_Risk, C_dp, beta_dp, alpha_dp, gen_indx); %compute constraint violation functions using Joines and Houck's dynamic penalty functions
% compute fitness function
[offsprngW_fitness] = Rebal_comp_fitness(offsprngW_popln, cov_data, offsprngW_psi);
% construct the new generation selecting the best of parent and
% offspring population
[NextGenPool_X, NextGenPool_W, NextGenPool_fitness, NextGenPool_psi] = construct_newgen(feasX_parent_popln, feasW_parent_popln, feasW_parent_fitness, feasW_parent_psi , offsprngX_popln, offsprngW_popln, offsprngW_fitness, offsprngW_psi);
%induct best fit individual into Hall of Fame
for i=1:popln_size
if (NextGenPool_psi(i)== 0)
if (NextGenPool_fitness(i) > HOF_fitness)
HOF_fitness = NextGenPool_fitness(i)
HOF_individualW = NextGenPool_W(i,:);
HOF_individualX = NextGenPool_X(i,:);
HOF_genarray(i1) = gen_indx;
HOF_fitarray(i1) = HOF_fitness;
i1=i1+1;
end
else continue;
end
end
% compute Population measure
p_measure_gen = compute_Pmeasure(NextGenPool_W);
perfanaly_pmeasure(pa_count, :)= [gen_indx, p_measure_gen];
pa_count=pa_count+1;
% set parent population for the next generation cycle
feasX_parent_popln = NextGenPool_X;
feasW_parent_popln = NextGenPool_W;
feasW_parent_fitness = NextGenPool_fitness;
feasW_parent_psi = NextGenPool_psi;
gen_indx = gen_indx + 1;
end
fix (clock)
% extract the optimal solution (rebalanced weights) from the Hall of Fame
disp('Optimal Rebalanced Portfolio Weights')
Optimal_RebalWeights = HOF_individualW
% compute risk, return and Diversification Ratio of the optimal rebalanced
% portfolio
daily_rebal_portfolio_return = sum(mean_data .* Optimal_RebalWeights);
disp('Rebalanced portfolio annualized return %')
ann_rebal_portfolio_return = 261 * daily_rebal_portfolio_return*100
rebal_portfolio_risk = sqrt(Optimal_RebalWeights * cov_data * Optimal_RebalWeights');
disp('Rebalanced portfolio annualized risk %')
ann_rebal_portfolio_risk = sqrt(261)* rebal_portfolio_risk*100
stdev_portfolio = sqrt(diag(cov_data));
disp('Rebalanced portfolio Diversification Ratio')
rebal_portfolio_DR = (sum(stdev_portfolio .* Optimal_RebalWeights') / rebal_portfolio_risk)
% compare risk, return and Diversification Ratio of the original portfolio
disp('Original portfolio annualized return %')
original_portfolio_return = OriginalPortfolio_Daily_Retrn * 261*100
disp('Original portfolio annualized risk %')
original_portfolio_risk = OriginalPortfolio_Daily_Risk * sqrt(261)*100
disp('Original portfolio Diversification Ratio')
original_portfolio_DR = OriginalPortfolio_MxDR
disp('Successful Execution');