103 lines
2.8 KiB
Matlab
103 lines
2.8 KiB
Matlab
clear;
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% Daily data on EWA-EWC
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load('inputData_ETF', 'tday', 'syms', 'cl');
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idxA=find(strcmp('EWA', syms));
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idxC=find(strcmp('EWC', syms));
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x=cl(:, idxA);
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y=cl(:, idxC);
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% Augment x with ones to accomodate possible offset in the regression
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% between y vs x.
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x=[x ones(size(x))];
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delta=0.0001; % delta=1 gives fastest change in beta, delta=0.000....1 allows no change (like traditional linear regression).
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yhat=NaN(size(y)); % measurement prediction
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e=NaN(size(y)); % measurement prediction error
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Q=NaN(size(y)); % measurement prediction error variance
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% For clarity, we denote R(t|t) by P(t).
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% initialize R, P and beta.
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R=zeros(2);
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P=zeros(2);
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beta=NaN(2, size(x, 1));
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Vw=delta/(1-delta)*eye(2);
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Ve=0.001;
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% Initialize beta(:, 1) to zero
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beta(:, 1)=0;
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% Given initial beta and R (and P)
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for t=1:length(y)
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if (t > 1)
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beta(:, t)=beta(:, t-1); % state prediction. Equation 3.7
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R=P+Vw; % state covariance prediction. Equation 3.8
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end
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yhat(t)=x(t, :)*beta(:, t); % measurement prediction. Equation 3.9
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Q(t)=x(t, :)*R*x(t, :)'+Ve; % measurement variance prediction. Equation 3.10
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% Observe y(t)
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e(t)=y(t)-yhat(t); % measurement prediction error
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K=R*x(t, :)'/Q(t); % Kalman gain
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beta(:, t)=beta(:, t)+K*e(t); % State update. Equation 3.11
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P=R-K*x(t, :)*R; % State covariance update. Euqation 3.12
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end
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plot(beta(1, :)');
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figure;
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plot(beta(2, :)');
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figure;
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plot(e(3:end), 'r');
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hold on;
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plot(sqrt(Q(3:end)));
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y2=[x(:, 1) y];
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longsEntry=e < -sqrt(Q); % a long position means we should buy EWC
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longsExit=e > -sqrt(Q);
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shortsEntry=e > sqrt(Q);
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shortsExit=e < sqrt(Q);
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numUnitsLong=NaN(length(y2), 1);
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numUnitsShort=NaN(length(y2), 1);
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numUnitsLong(1)=0;
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numUnitsLong(longsEntry)=1;
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numUnitsLong(longsExit)=0;
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numUnitsLong=fillMissingData(numUnitsLong); % fillMissingData can be downloaded from epchan.com/book2. It simply carry forward an existing position from previous day if today's positio is an indeterminate NaN.
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numUnitsShort(1)=0;
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numUnitsShort(shortsEntry)=-1;
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numUnitsShort(shortsExit)=0;
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numUnitsShort=fillMissingData(numUnitsShort);
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numUnits=numUnitsLong+numUnitsShort;
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positions=repmat(numUnits, [1 size(y2, 2)]).*[-beta(1, :)' ones(size(beta(1, :)'))].*y2; % [hedgeRatio -ones(size(hedgeRatio))] is the shares allocation, [hedgeRatio -ones(size(hedgeRatio))].*y2 is the dollar capital allocation, while positions is the dollar capital in each ETF.
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pnl=sum(lag(positions, 1).*(y2-lag(y2, 1))./lag(y2, 1), 2); % daily P&L of the strategy
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ret=pnl./sum(abs(lag(positions, 1)), 2); % return is P&L divided by gross market value of portfolio
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ret(isnan(ret))=0;
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figure;
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plot(cumprod(1+ret)-1); % Cumulative compounded return
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fprintf(1, 'APR=%f Sharpe=%f\n', prod(1+ret).^(252/length(ret))-1, sqrt(252)*mean(ret)/std(ret));
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% APR=0.262252 Sharpe=2.361162
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