calendarSpdsMeanReversion.m

clear;

% load('inputDataDaily_VX_20120507', 'tday', 'contracts', 'cl');
load('//dellquad/Futures_data/inputDataDaily_CL_20120813', 'tday', 'contracts', 'cl');
% load('//dellquad/Futures_data/inputDataDaily_TU_20120813', 'tday', 'contracts', 'cl');
% load('//dellquad/Futures_data/inputDataDaily_BR_20120813', 'tday', 'contracts', 'cl');
% load('//dellquad/Futures_data/inputDataDaily_HG_20120813', 'tday', 'contracts', 'cl');
% load('//dellquad/Futures_data/inputDataDaily_C2_20120813', 'tday', 'contracts', 'cl');
% load('//dellquad/Futures_data/inputDataDaily_HO2_20120813', 'tday', 'contracts', 'cl');

% Find spot prices
spotIdx=find(strcmp(contracts, '0000$'));
spot=cl(:, spotIdx);
cl(:, spotIdx)=[];
contracts(spotIdx)=[];

% T=[1:length(spot)]';
% isBadData=~isfinite(spot);
% spot(isBadData)=[];
% T(isBadData)=[];
% res=ols(log(spot), [T ones(size(T, 1), 1)]);
% 
% fprintf(1, 'Average annualized spot return=%f\n', 252*smartmean(res.beta(1)));



% Fitting gamma to forward curve
gamma=NaN(size(tday));
for t=1:length(tday)
   
    FT=cl(t, :)';
    idx=find(isfinite(FT));
    idxDiff=fwdshift(1, idx)-idx; % ensure consecutive months futures
    if (length(idx) >= 5 && all(idxDiff(1:4)==1))
        FT=FT(idx(1:5)); % only uses the nearest 5 contracts
        T=[1:length(FT)]';
%         scatter(T, log(FT));
        res=ols(log(FT), [T ones(size(T, 1), 1)]);
        gamma(t)=-12*res.beta(1);
    end
end
gamma=fillMissingData(gamma);

% plot(gamma);


%print -r300 -djpeg fig5_4
% hold on;

% fprintf(1, 'Average annualized roll return=%f\n', smartmean(gamma));
isGoodData=find(isfinite(gamma));
results=adf(gamma(isGoodData), 0, 1);
prt(results);

gammalag=lag(gamma(isGoodData), 1);  
deltaGamma=gamma(isGoodData)-gammalag;
deltaGamma(1)=[]; 
gammalag(1)=[];
regress_results=ols(deltaGamma, [gammalag ones(size(gammalag))]);
halflife=-log(2)/regress_results.beta(1);

fprintf(1, 'halflife=%f days\n', halflife);
% halflife=36.394034 days


lookback=round(halflife);
ma=movingAvg(gamma, lookback);
mstd=movingStd(gamma, lookback);
zScore=(gamma-ma)./mstd;

% linear mean reversion strategy
isExpireDate=false(size(cl));
positions=zeros(size(cl));

isExpireDate=isfinite(cl) & ~isfinite(fwdshift(1, cl));

holddays=3*21;
numDaysStart=holddays+10;
numDaysEnd=10;
spreadMonth=12; % No. months between far and near contracts.
for c=1:length(contracts)-spreadMonth
    expireIdx=find(isExpireDate(:, c));
    expireIdx=expireIdx(end); % There may be some missing data earlier on
    if (c==1)
        startIdx=max(1, expireIdx-numDaysStart);
        endIdx=expireIdx-numDaysEnd;
    else % ensure next front month contract doesn't start until current one ends
        myStartIdx=endIdx+1;
        myEndIdx=expireIdx-numDaysEnd;
        if (myEndIdx-myStartIdx >= holddays)
            startIdx=myStartIdx;
            endIdx=myEndIdx;
        else
            startIdx=NaN;
        end
    end
        
    if (~isempty(expireIdx) & endIdx > startIdx)
        positions(startIdx:endIdx, c)=-1; % Presume we long spread (long back contract, short front contract)
        positions(startIdx:endIdx, c+spreadMonth)=1;
    end
end



positions(isnan(zScore), :)=0;
positions(zScore > 0, :)=-positions(zScore > 0, :);
% positions(zScore > 1, :)=-positions(zScore > 1, :);

ret=smartsum(lag(positions).*(cl-lag(cl, 1))./lag(cl, 1), 2)/2;
ret(isnan(ret))=0;

idx=find(tday==20080102);
% idx=1;

cumret=cumprod(1+ret(idx:end))-1;
plot(cumret); % Cumulative compounded return

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

[maxDD maxDDD]=calculateMaxDD(cumret);
fprintf(1, 'maxDD=%f maxDDD=%i\n', maxDD, maxDDD);
% APR=0.083406 Sharpe=1.288661
% maxDD=-0.053222 maxDDD=206