indexArb.m

clear;


stks=load('inputDataOHLCDaily_stocks_20120424', 'stocks', 'tday','cl');
etf=load('inputData_ETF', 'tday', 'syms', 'cl');

% Ensure data have same dates
[tday idx1 idx2]=intersect(stks.tday, etf.tday);
stks.cl=stks.cl(idx1, :);
etf.cl=etf.cl(idx2, :);

% Use SPY
idxS=find(strcmp('SPY', etf.syms));
etf.cl=etf.cl(:, idxS);

trainDataIdx=find(tday>=20070101 & tday<=20071231);
testDataIdx=find(tday > 20071231);

isCoint=false(size(stks.stocks));
for s=1:length(stks.stocks)
    % Combine the two time series into a matrix y2 for input into Johansen test
    y2=[stks.cl(trainDataIdx, s), etf.cl(trainDataIdx)];
    badData=any(isnan(y2), 2);
    y2(badData, :)=[]; % remove any missing data

    if (size(y2, 1) > 250)
        results=johansen(y2, 0, 1); % johansen test with non-zero offset but zero drift, and with the lag k=1.
        if (results.lr1(1) > results.cvt(1, 1))
            isCoint(s)=true;
        end
    end    
end

length(find(isCoint))
% 98: there are 98 stocks that are cointegrating with SPY

% Form a long-only portfolio with all stocks that cointegrate with SPY, with equal
% capital allocation
yN=stks.cl(trainDataIdx, isCoint);
logMktVal_long=sum(log(yN), 2); % The net market value of the long-only portfolio is same as the "spread"

% Confirm that the portfolio cointegrates with SPY
ytest=[logMktVal_long, log(etf.cl(trainDataIdx))]; 
results=johansen(ytest, 0, 1); % johansen test with non-zero offset but zero drift, and with the lag k=1.
prt(results);

% Output:
%  Johansen MLE estimates 
% NULL:                  Trace Statistic         Crit 90%         Crit 95%         Crit 99% 
% r <= 0   variable   1           15.869           13.429           15.494           19.935 
% r <= 1   variable   2            6.197            2.705            3.841            6.635 
% 
% NULL:                  Eigen Statistic         Crit 90%         Crit 95%         Crit 99% 
% r <= 0   variable   1            9.671           12.297           14.264           18.520 
% r <= 1   variable   2            6.197            2.705            3.841            6.635 

results.evec
% 
% ans =
% 
%     1.0939   -0.2799
%  -105.5600   56.0933


% Apply linear mean-reversion model on test set
yNplus=[stks.cl(testDataIdx, isCoint), etf.cl(testDataIdx)]; % Array of stock and ETF prices
weights=[repmat(results.evec(1, 1), size(stks.cl(testDataIdx, isCoint))), ...
       repmat(results.evec(2, 1), size(etf.cl(testDataIdx)))]; % Array of log market value of stocks and ETF's
   
logMktVal=smartsum(weights.*log(yNplus), 2); % Log market value of long-short portfolio

lookback=5;
numUnits=-(logMktVal-movingAvg(logMktVal, lookback))./movingStd(logMktVal, lookback); % capital invested in portfolio in dollars.  movingAvg and movingStd are functions from epchan.com/book2
positions=repmat(numUnits, [1 size(weights, 2)]).*weights; % positions is the dollar capital in each stock or ETF.
pnl=smartsum(lag(positions, 1).*(log(yNplus)-lag(log(yNplus), 1)), 2); % daily P&L of the strategy
ret=pnl./smartsum(abs(lag(positions, 1)), 2); % return is P&L divided by gross market value of portfolio
ret(isnan(ret))=0;

figure;
plot(cumprod(1+ret)-1); % Cumulative compounded return

fprintf(1, 'APR=%f Sharpe=%f\n', prod(1+ret).^(252/length(ret))-1, sqrt(252)*mean(ret)/std(ret));
% APR=0.044930 Sharpe=1.319397