www.gusucode.com > GAVPai_Book_MathworksCntrlFileEx_May2019 > GAVPai_Book_MathworksCntrlFileEx_May2019/Chapter5_EMNP_DEHOF_Rand5Dir4.m
% Vijayalakshmi Pai G A, Metaheuristics for Portfolio Optimization, An
% Introduction using MATLAB, ISTE-Wiley, 2017.
% Differential Evolution with Hall of Fame (DE HOF) and Rand5/Dir4 strategy
% (DE/Rand5/Dir4) for metaheuristic optimization of risk budgeted
% equity market neutral portfolios
% Chapter 5 Secs. 5.6 B, C, D, E, F
% The Risk budgeted equity market neutral portfolio is represented by equations [5.14]-[5.19] for
% its objective function and equations [5.20]-[5.25] for its constraints
% The portfolio considered is a long-short portfolio of 49 long positions
% followed by 49 short positions over Nikkei225 Index
% Sec. 5.5 Portfolio C
% The data file Nikkei225_PortfolioC.xls records the mean returns of the
% assets of Portfolio C, followed by variance-covariance matrix of returns of the assets
% and betas of the assets, with the colour coded 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
% number of long positions in the portfolio
L_col = 49;
% number of short positions in the portfolio
S_col = 49;
% portfolio size
portfolio_size = L_col+S_col;
% serial number of high volatility assets in the portfolio
Highvolat_assets = [97 98]; % Softbank Corp and Pacific Metals Co Ltd
% obtain mean returns, variance-covariance matrix of returns and asset
% betas
filename = 'Nikkei225_PortfolioC.xls';
m = xlsread(filename);
mean_data = m(1,:);
cov_data = m(2:portfolio_size+1, :);
Beta_assets = m(portfolio_size+2, :);
% input differential evolution parameters
popln_size = 980;
chromosm_length = portfolio_size;
total_generations = 5000;
beta = 0.5;
pr_recombi = 0.87;
% input portfolio parameters
Long_low_bound = 0.0001;
Long_up_bound=1;
Short_low_bound = -1;
Short_up_bound=-0.0001;
% initialize Hall of Fame
HOF_fitness = -9999;
HOF_individual = zeros(1, portfolio_size);
% generation counter
gen_indx = 1;
% Hall of Fame induction counter
i1=1;
fix(clock)
% generate initial population representing long short portfolio
initial_popln_raw= EMNP_gen_longshort_popln(popln_size, L_col, S_col, Long_low_bound, Long_up_bound, Short_low_bound, Short_up_bound);
% undertake weight repair of long and short positions
initial_popln_longstd = EMNP_eqconstr_wgtstd(initial_popln_raw, 1, L_col, Long_low_bound, Long_up_bound, 1);
initial_popln_firststd = EMNP_eqconstr_wgtstd(initial_popln_longstd, L_col+1, L_col+S_col, -Short_up_bound, -Short_low_bound,0);
initial_popln = initial_popln_firststd;
% compute constraint violation functions
[psi_i, initial_G1, initial_G2] = EMNP_compute_constr_violn_fn( initial_popln, cov_data, Beta_assets, Highvolat_assets);
[initial_popln_fitness, initial_popln_obj_val] = EMNP_comp_fitness_function(initial_popln, mean_data, psi_i);
% DE generation cycles begin
while (gen_indx <= total_generations)
gen_indx
feas_parent_popln = initial_popln;
feas_parent_popln_fitness = initial_popln_fitness;
psi_p = psi_i;
feas_parent_G1= initial_G1;
feas_parent_G2 = initial_G2;
feas_parent_obj_val = initial_popln_obj_val;
% perform mutation
trial_vector_popln = DE_Rand5Dir4_Operator(feas_parent_popln, feas_parent_popln_fitness, beta, popln_size, chromosm_length);
% perform crossover
offsprng_popln_raw = DE_bin_Crossover(feas_parent_popln, trial_vector_popln, pr_recombi, chromosm_length);
% undertake weight repair of long/short positions
offsprng_popln_longstd = EMNP_eqconstr_wgtstd(offsprng_popln_raw, 1, L_col, Long_low_bound, Long_up_bound, 1);
offsprng_popln_shortstd = EMNP_eqconstr_wgtstd(offsprng_popln_longstd, L_col+1, L_col+S_col, -Short_up_bound, -Short_low_bound,0);
offsprng_popln = offsprng_popln_shortstd;
% compute constraint violation functions
[psi_o,offsprng_G1, offsprng_G2] = EMNP_compute_constr_violn_fn( offsprng_popln, cov_data, Beta_assets, Highvolat_assets);
% compute fitness functions
[offsprng_popln_fitness, offsprng_obj_val] = EMNP_comp_fitness_function(offsprng_popln, mean_data, psi_o);
% Tournament selection of individuals for the next generation
[next_gen_pool, next_gen_pool_obj_val, Psi_fun, G1_nextgen,G2_nextgen, next_gen_pool_fitness] = EMNP_DE_selection(feas_parent_popln, psi_p, feas_parent_G1,feas_parent_G2, feas_parent_obj_val, feas_parent_popln_fitness, offsprng_popln, psi_o, offsprng_G1, offsprng_G2, offsprng_obj_val, offsprng_popln_fitness, popln_size);
% induct best individual into Hall of Fame
for i=1:popln_size
if (Psi_fun(i)== 0)
if (next_gen_pool_fitness(i) > HOF_fitness)
HOF_fitness = next_gen_pool_fitness(i);
HOF_individual = next_gen_pool(i,:);
HOF_genarray(i1) = gen_indx;
HOF_fitarray(i1) = HOF_fitness;
i1=i1+1;
end
else continue;
end
end
% increment generation counter
gen_indx = gen_indx + 1;
% reset initial population and parameters
initial_popln = next_gen_pool; % move to the next generation
initial_popln_fitness= next_gen_pool_fitness;
psi_i= Psi_fun;
initial_G1=G1_nextgen;
initial_G2 = G2_nextgen;
initial_popln_obj_val=next_gen_pool_obj_val;
end % while loop for DE generation cycle ends
fix(clock)
% record the individual in the Hall of Fame as the optimal solution
x_star = HOF_individual; % optimal weights
% portfolio characteristics
portfolio_return = 261 * sum(mean_data .* x_star);
risk = sqrt( 261*x_star * cov_data * x_star');
disp('Equity Market Neutral Portfolio Optimization results:')
disp('Annualized risk')
disp(risk)
disp('Expected portfolio Annualized return')
disp(portfolio_return)
disp('Optimal weights')
disp( x_star)
disp('Successful execution!');