AUDCAD_unequal.m

clear;

% get the files from my dropbox (see the readme), and change
% the base paths below
usdcad=load('/home/burak/Dropbox/Public/data/inputData_USDCAD_20120426', 'tday', 'hhmm', 'cl');
audusd=load('/home/burak/Dropbox/Public/data/inputData_AUDUSD_20120426', 'tday', 'hhmm', 'cl');

firstDate=20090101;

idx=find(usdcad.tday>firstDate & usdcad.hhmm==1659);
usdcad.tday=usdcad.tday(idx);
usdcad.hhmm=usdcad.hhmm(idx);
usdcad.cl=usdcad.cl(idx);

idx=find(audusd.tday>firstDate & audusd.hhmm==1659);
audusd.tday=audusd.tday(idx);
audusd.hhmm=audusd.hhmm(idx);
audusd.cl=audusd.cl(idx);

tday=audusd.tday;

% Need to invert currency pair so that each unit has same capital in local
% currency
cad=1./usdcad.cl;
aud=audusd.cl;

y=[ aud cad   ];
trainlen=250;
lookback=20;
hedgeRatio=NaN(size(y));
numUnits=NaN(size(y, 1), 1);

for t=trainlen+1:size(y, 1)
    res=johansen(y(t-trainlen:t-1, :), 0, 1);
    hedgeRatio(t, :)=res.evec(:, 1)';

    % yport is the market value of a unit portfolio of AUDUSD and CADUSD expressed in US$.
    yport=sum(y(t-lookback+1:t, :).*repmat(hedgeRatio(t, :), [lookback 1]), 2);
    ma=mean(yport);
    mstd=std(yport);
    zScore=(yport(end)-ma)/mstd;

    % numUnits are number of units of unit portfolio of AUDUSD and CADUSD
    numUnits(t)=-(yport(end)-ma)/mstd;

end


% positions are market values of AUDUSD and CADUSD in portfolio expressed
% in US$.
positions=repmat(numUnits, [1 size(y, 2)]).*hedgeRatio.*y; 

% daily P&L of portfolio in US$.
pnl=sum(lag(positions, 1).*(y-lag(y, 1))./lag(y, 1), 2); 
ret=pnl./sum(abs(lag(positions, 1)), 2); 
ret(isnan(ret))=0;


plot(cumprod(1+ret(trainlen+1:end))-1); % Cumulative compounded return

fprintf(1, 'APR=%f Sharpe=%f\n', prod(1+ret(trainlen+1:end)).^(252/length(ret(trainlen+1:end)))-1, sqrt(252)*mean(ret(trainlen+1:end))/std(ret(trainlen+1:end)));
% APR=0.112410 Sharpe=1.610890


% Kelly leverage
f=mean(ret(trainlen+1:end))/std(ret(trainlen+1:end))^2;
fprintf(1, 'f=%f\n', f);
% f=23.845328

ret=ret(trainlen+1:end);
save('../Data/AUDCAD_unequal_ret', 'ret');