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step1_MonteCarlo.m
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% Monte Carlo simulation script for the new data-snooping paper
% Script developed by Arman Hassanniakalager for the 3rd chapter of PhD,
% Based on the BS, 2012 paper
% Last modified 01 Feb 2018 12:13 GMT.
addpath(genpath(cd));
clc
clear
close all
delete(gcp('nocreate'))
%% Options
% BS+BS= Original BS= BB
% BS+LIANG= BL
pi0typ={'BL','BB'};
%% Initiating parallel pool
tic
%poolobj=parpool('EC2EU',18,'AttachedFiles','Arman_montecarlo4.m');
poolobj=parpool('local', 4);
%% INPUT PARAMETERS:
MC =1000; % Number of simulations
disp(['Running ',num2str(MC),' Monte Carlo simulation...']);
B = 1000; % Number of bootstrap
%% Parameters
gamma=0.4;
% BB setting
lambda=0.55;
% BL setting
lambda_max_BL=0.99;
N_BL=10;
% Sharpe Ratio or Mu
perf='_SR';
%% Loops
for outer=4:-1:2
for under=-4:1:-2
outperf_SR = outer;
underperf_SR = under;
% perf=''; % mu
% outperf_mu = .3;
% underperf_mu = -.1;
disp(['Running performance measure ',perf,' outperformers ',...
num2str(outer),' underperformer ' num2str(under)]);
pi_aplus = .2;
pi_aminus = .3;
pi_0 = 1 - pi_aplus - pi_aminus;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
q = 1/10;
sigma_thresh = 5e-4;
if strcmp(perf,'_SR')
nameSR=['AA_final_' num2str(100*pi_aplus) '_' num2str(100*pi_aminus) '_SR_'...
num2str(100*outperf_SR) '_' num2str(100*(-underperf_SR)) '.mat'];
if ~exist(nameSR,'file')
prepare_SR_Arman(outperf_SR,underperf_SR,pi_aplus,pi_aminus);
end
load(nameSR)
else
namemu=['AA_final_' num2str(100*pi_aplus) '_' num2str(100*pi_aminus) '_mu_'...
num2str(100*outperf_mu) '_' num2str(100*(-underperf_mu)) '.mat'];
if ~exist(namemu,'file')
prepare_mu_Arman(outperf_mu,underperf_mu,pi_aplus,pi_aminus);
end
load(namemu)
end
nbstrats = 21195;
nbdays = 155;
nboutperf = round(nbstrats * pi_aplus);
nbunderperf = round(nbstrats * pi_aminus);
nbnull = nbstrats - nboutperf - nbunderperf;
RETS=zeros(nbdays, nbstrats);
finalret=sum(AA_final);
%% Bootstrap generation
% Firstly for the main index
IDX=zeros(nbdays,B);
for b=1:B
IDX(1,b)=unidrnd(nbdays);
U=unifrnd(0,1,nbdays-1,1);
ind1=find(U<q)+1;
ind2=find(U>=q)+1;
IDX(ind1,b)=unidrnd(nbdays,length(ind1),1);
for i=1:length(ind2)
t=ind2(i);
IDX(t,b)=IDX(t-1,b)+1;
if IDX(t,b)>nbdays
IDX(t,b)=1;
end
end
end
% Secondly for the whole simulation
IDX_MC=zeros(nbdays,MC);
for mc=1:MC
IDX_MC(1,mc)=unidrnd(nbdays);
U=unifrnd(0,1,nbdays-1,1);
ind1=find(U<q)+1;
ind2=find(U>=q)+1;
IDX_MC(ind1,mc)=unidrnd(nbdays,length(ind1),1);
for i=1:length(ind2)
t=ind2(i);
IDX_MC(t,mc)=IDX_MC(t-1,mc)+1;
if IDX_MC(t,mc)>nbdays
IDX_MC(t,mc)=1;
end
end
end
%% Declaring the variables
pi_0hatBB=zeros(MC,1);
pi_0hatBL=zeros(MC,1);
lambdaBL=zeros(MC,1);
pi_aplushatBB=zeros(MC,1);
pi_aminushatBB=zeros(MC,1);
pi_aplushatBL=zeros(MC,1);
pi_aminushatBL=zeros(MC,1);
FDRhat20BB=zeros(MC,1);
FDRhatbBB=zeros(MC,1);
FDRhat20BL=zeros(MC,1);
FDRhatbBL=zeros(MC,1);
FDRrealFDRbBB=zeros(MC,1);
FDRrealFDR20BB=zeros(MC,1);
FDRrealFDRbBL=zeros(MC,1);
FDRrealFDR20BL=zeros(MC,1);
FDRrealRW5=zeros(MC,1);
FDRrealRW20=zeros(MC,1);
PORTFDR20BB=nan(nbstrats,MC);
PORTFDRbBB=nan(nbstrats,MC);
PORTFDR20BL=nan(nbstrats,MC);
PORTFDRbBL=nan(nbstrats,MC);
powerFDRbBB=zeros(MC,1);
powerFDR20BB=zeros(MC,1);
powerFDRbBL=zeros(MC,1);
powerFDR20BL=zeros(MC,1);
powerRW5=zeros(MC,1);
powerRW20=zeros(MC,1);
portsizeFDRbBB=zeros(MC,1);
portsizeFDR20BB=zeros(MC,1);
portsizeFDRbBL=zeros(MC,1);
portsizeFDR20BL=zeros(MC,1);
portsizeRW5=zeros(MC,1);
portsizeRW20=zeros(MC,1);
pvalues=nan(nbstrats,MC);
ISFDRbBB=nan(1,MC);
ISFDR20BB=nan(1,MC);
ISFDRbBL=nan(1,MC);
ISFDR20BL=nan(1,MC);
RSRW5=nan(1,MC);
RSRW20=nan(1,MC);
CC_outperf = zeros(3, MC);
CC_underperf = zeros(3, MC);
rankingbestlucky=zeros(MC,1);
%% Performing the simulation
parfor i=1:MC
disp(i)
tic;
% simul by bootstrap:
RETS = AA_final(IDX_MC(:, i), :);
if strcmp(perf,'_SR')
mu_final = mean(RETS);
BB_outperf = 252 * mu_final(1:nboutperf);
BB_underperf = 252 * mu_final((nboutperf + 1):(nboutperf + nbunderperf));
BB_null = 252 * mu_final((nboutperf + nbunderperf + 1):end);
else
SR_final = mean(RETS) ./ std(RETS);
BB_outperf = sqrt(252) * SR_final(1:nboutperf);
BB_underperf = sqrt(252) * SR_final((nboutperf + 1):(nboutperf + nbunderperf));
BB_null = sqrt(252) * SR_final((nboutperf + nbunderperf + 1):end);
end
CC_outperf(:, i) = [quantile(BB_outperf, .25); quantile(BB_outperf, .5); quantile(BB_outperf, .75)];
CC_underperf(:, i) = [quantile(BB_underperf, .75); quantile(BB_underperf, .5); quantile(BB_underperf, .25)];
Perfs_B=zeros(nbstrats,B);
for b=1:B
RETS_B = RETS(IDX(:, b), :);
if strcmp(perf,'_SR')
sigma = std(RETS_B)';
mu = mean(RETS_B)';
Perfs_B(:, b) = mu ./ sigma;
Perfs_B(sigma == 0, b) = 0;
% avoid situation with sigma too small:
idx_tmp = sigma > 0 & sigma < sigma_thresh;
Perfs_B(idx_tmp, b) = mu(idx_tmp) / sigma_thresh;
else
Perfs_B(:, b) = mean(RETS_B)';
end
end
if strcmp(perf,'_SR')
sigma = std(RETS)';
mu = mean(RETS)';
Perfs = mu ./ sigma;
% if sigma == 0 => Perfs = 0:
Perfs(sigma == 0) = 0;
% avoid situation with sigma too small:
idx_tmp = sigma > 0 & sigma < sigma_thresh;
Perfs(idx_tmp) = mu(idx_tmp) / sigma_thresh;
else
Perfs = mean(RETS)';
end
pvalues(:,i) = compute_pvalues(Perfs, Perfs_B, std(RETS));
% BS Procedure for calculation of pi0
lambdaBB = lambda;
pi_0hatBB(i) = compute_pi_0hat(pvalues(:,i), lambdaBB);
gammaBB = gamma;
[pi_aplushatBB(i), pi_aminushatBB(i)] = compute_pi_ahat(pvalues(:,i), Perfs, pi_0hatBB(i), gammaBB);
% Liang Procedure
[pi_0hatBL(i),lambdaBL(i)]=est_pi0_disc(pvalues(:,i), N_BL,lambda_max_BL);
gammaBL = gammaBB;
[pi_aplushatBL(i), pi_aminushatBL(i)] = compute_pi_ahat(pvalues(:,i), Perfs, pi_0hatBL(i), gammaBL);
% Portfolio construction based on the FDR+
[PORTFDR20BB(:,i), FDRhat20BB(i)] = my_portfolio_FDR(.2, Perfs, pvalues(:,i), pi_0hatBB(i));
[PORTFDRbBB(:,i), FDRhatbBB(i)] = my_portfolio_FDR(.1, Perfs, pvalues(:,i), pi_0hatBB(i));
[PORTFDR20BL(:,i), FDRhat20BL(i)] = my_portfolio_FDR(.2, Perfs, pvalues(:,i), pi_0hatBL(i));
[PORTFDRbBL(:,i), FDRhatbBL(i)] =my_portfolio_FDR(.1, Perfs, pvalues(:,i), pi_0hatBL(i));
PORTRW20(:,i) = portfolio_RW(.2, Perfs, Perfs_B);
PORTRW5(:,i) = portfolio_RW(.05, Perfs, Perfs_B);
% ranking of best lucky rule:
idx = (1:nbstrats)';
A = [Perfs idx];
A = sortrows(A, -1);
rankingbestlucky(i) = find(A(:, 2) > nboutperf, 1, 'first');
[FDRrealFDRbBB(i), portsizeFDRbBB(i)] = ComputeRealFDR(PORTFDRbBB(:,i), nboutperf);
[FDRrealFDR20BB(i), portsizeFDR20BB(i)] = ComputeRealFDR(PORTFDR20BB(:,i), nboutperf);
[FDRrealFDRbBL(i), portsizeFDRbBL(i)] = ComputeRealFDR(PORTFDRbBL(:,i), nboutperf);
[FDRrealFDR20BL(i), portsizeFDR20BL(i)] = ComputeRealFDR(PORTFDR20BL(:,i), nboutperf);
[FDRrealRW5(i), portsizeRW5(i)] = ComputeRealFDR(PORTRW5(:,i), nboutperf);
[FDRrealRW20(i), portsizeRW20(i)] = ComputeRealFDR(PORTRW20(:,i), nboutperf);
% % In-sample return
% ISFDRbBB(i)=finalret*PORTFDRbBB(:,i)/portsizeFDRbBB(i);
% ISFDR20BB(i)=finalret*PORTFDR20BB(:,i)/portsizeFDR20BB(i);
% ISFDRbBL(i)=finalret*PORTFDRbBL(:,i)/portsizeFDRbBL(i);
% ISFDR20BL(i)=finalret*PORTFDR20BL(:,i)/portsizeFDR20BL(i);
% ISRW5(i)=finalret*PORTRW5/max(portsizeRW5(i),1);
% ISRW20(i)=finalret*PORTRW20/max(portsizeRW20(i),1);
toc;
end
for i=1:MC
powerFDRbBB(i)=sum(PORTFDRbBB(1:nboutperf,i))/nboutperf;
powerFDR20BB(i)=sum(PORTFDR20BB(1:nboutperf,i))/nboutperf;
powerFDRbBL(i)=sum(PORTFDRbBL(1:nboutperf,i))/nboutperf;
powerFDR20BL(i)=sum(PORTFDR20BL(1:nboutperf,i))/nboutperf;
powerRW5(i)=sum(PORTRW5(1:nboutperf,i))/nboutperf;
powerRW20(i)=sum(PORTRW20(1:nboutperf,i))/nboutperf;
end
%% Outputs
AA_BB=[mean(FDRhatbBB) std(FDRhatbBB); mean(FDRhat20BB) std(FDRhat20BB)]';
AA_BL=[mean(FDRhatbBL) std(FDRhatbBL); mean(FDRhat20BL) std(FDRhat20BL)]';
BB_BB=[mean(FDRrealFDRbBB) std(FDRrealFDRbBB);...
mean(FDRrealFDR20BB) std(FDRrealFDR20BB);...
mean(FDRrealRW5) std(FDRrealRW5);...
mean(FDRrealRW20) std(FDRrealRW20)];
BB_BL=[mean(FDRrealFDRbBL) std(FDRrealFDRbBL);...
mean(FDRrealFDR20BL) std(FDRrealFDR20BL);...
mean(FDRrealRW5) std(FDRrealRW5);...
mean(FDRrealRW20) std(FDRrealRW20)];
CC_BB=[mean(powerFDRbBB) std(powerFDRbBB);...
mean(powerFDR20BB) std(powerFDR20BB);...
mean(powerRW5) std(powerRW5);...
mean(powerRW20) std(powerRW20)];
CC_BL=[mean(powerFDRbBL) std(powerFDRbBL);...
mean(powerFDR20BL) std(powerFDR20BL);...
mean(powerRW5) std(powerRW5);...
mean(powerRW20) std(powerRW20)];
DD_BB=[mean(portsizeFDRbBB) std(portsizeFDRbBB);...
mean(portsizeFDR20BB) std(portsizeFDR20BB);...
mean(portsizeRW5) std(portsizeRW5);...
mean(portsizeRW20) std(portsizeRW20)];
DD_BL=[mean(portsizeFDRbBL) std(portsizeFDRbBL);...
mean(portsizeFDR20BL) std(portsizeFDR20BL);...
mean(portsizeRW5) std(portsizeRW5);...
mean(portsizeRW20) std(portsizeRW20)];
EE_BB=[mean(pi_0hatBB) std(pi_0hatBB);...
mean(pi_aplushatBB) std(pi_aplushatBB);...
mean(pi_aminushatBB) std(pi_aminushatBB)];
EE_BL=[mean(pi_0hatBL) std(pi_0hatBL);...
mean(pi_aplushatBL) std(pi_aplushatBL);...
mean(pi_aminushatBL) std(pi_aminushatBL)];
ratio_pi_a_BB = ((mean(pi_aplushatBB) + mean(pi_aminushatBB)) / (1 - mean(pi_0hatBB)))^-1;
ratio_pi_a_BL = ((mean(pi_aplushatBL) + mean(pi_aminushatBL)) / (1 - mean(pi_0hatBL)))^-1;
FF_BB=[mean(pi_0hatBB) std(pi_0hatBB);...
mean(pi_aplushatBB) * ratio_pi_a_BB std(pi_aplushatBB) * ratio_pi_a_BB;...
mean(pi_aminushatBB) * ratio_pi_a_BB std(pi_aminushatBB) * ratio_pi_a_BB];
FF_BL=[mean(pi_0hatBL) std(pi_0hatBL);...
mean(pi_aplushatBL) * ratio_pi_a_BL std(pi_aplushatBL) * ratio_pi_a_BL;...
mean(pi_aminushatBL) * ratio_pi_a_BL std(pi_aminushatBL) * ratio_pi_a_BL];
GG=[median(rankingbestlucky) mean(rankingbestlucky) std(rankingbestlucky)];
HH_BB=[BB_BB CC_BB DD_BB];
HH_BL=[BB_BL CC_BL DD_BL];
II = [mean(CC_outperf, 2) std(CC_outperf, 0, 2) mean(CC_underperf, 2) std(CC_underperf, 0, 2)];
KK=mean(lambdaBL);
% LL=[mean(ISFDRbBL),std(ISFDRbBL);...
% mean(ISFDRbBB),std(ISFDRbBB);...
% mean(ISFDR20BL),std(ISFDR20BL);...
% mean(ISFDR20BB),std(ISFDR20BB);...
% mean(ISRW5),std(ISRW5);...
% mean(ISRW20),std(ISRW20)];
%% Write to file
if exist('adj','var')
switch adj
case 1
adjlbl='UNADJ';
case 2
adjlbl='ADJ';
end
else
adjlbl='RAW';
end
suff=['-BB_BL-' num2str(N_BL)];
if strcmp(perf,'_SR')
save(['MCresults_' num2str(MC) '_' num2str(100*pi_aplus) '_' num2str(100*pi_aminus) '_SR_'...
num2str(100*outperf_SR) '_' num2str(100*(-underperf_SR)) suff '.mat'])
else
save(['MCresults_' num2str(MC) '_' num2str(100*pi_aplus) '_' num2str(100*pi_aminus) '_mu_'...
num2str(100*outperf_mu) '_' num2str(100*(-underperf_mu)) suff '.mat'])
end
end
end
toc
delete(poolobj);