I dont code in python and this is a new account so im just going to link matlab code
Sorry if this isnt allowed. So as stated in the title I took an example from Chan's book and wanted to backtest it with more data, so all I changed was the amount of data I put in. However the sharpe went from 1.4 to an exponential 5+ which cant be possible. Does anyone see where I went wrong? The code looks long but its a lot of comments im going to keep for context.
load('inputData_ETF', 'tday', 'syms', 'cl');
idxA=find(strcmp('EWA', syms));
idxC=find(strcmp('EWC', syms));
x=cl(:, idxA);
y=cl(:, idxC);
plot(x);
hold on;
plot(y, 'g');
legend('EWA', 'EWC');
figure;
scatter(x, y);
figure;
regression_result=ols(y, [x ones(size(x))]);
hedgeRatio=regression_result.beta(1);
plot(y-hedgeRatio*x);
% Assume a non-zero offset but no drift, with lag=1.
results=cadf(y, x, 0, 1); % cadf is a function in the jplv7 (spatial-econometrics.com) package. We pick y to be the dependent variable again.
% Print out results
prt(results);
% Output:
% Augmented DF test for co-integration variables: variable 1,variable 2
% CADF t-statistic # of lags AR(1) estimate
% -3.64346635 1 -0.020411
%
% 1% Crit Value 5% Crit Value 10% Crit Value
% -3.880 -3.359 -3.038
%----------------------------------------------------------------------------------------------------
% Combine the two time series into a matrix y2 for input into Johansen test
y2=[y, x];
results=johansen(y2, 0, 1); % johansen test with non-zero offset but zero drift, and with the lag k=1.
% Print out results
prt(results);
% Output:
% Johansen MLE estimates
% NULL: Trace Statistic Crit 90% Crit 95% Crit 99%
% r <= 0 variable 1 19.983 13.429 15.494 19.935
% r <= 1 variable 2 3.983 2.705 3.841 6.635
%
% NULL: Eigen Statistic Crit 90% Crit 95% Crit 99%
% r <= 0 variable 1 16.000 12.297 14.264 18.520
% r <= 1 variable 2 3.983 2.705 3.841 6.635
%----------------------------------------------------------------------------------------------------
% Adding IGE to the portfolio
idxI=find(strcmp('IGE', syms));
z=cl(:, idxI);
y3=[y2, z];
results=johansen(y3, 0, 1); % johansen test with non-zero offset but zero drift, and with the lag k=1.
% Print out results
prt(results);
% Output:
% Johansen MLE estimates
% NULL: Trace Statistic Crit 90% Crit 95% Crit 99%
% r <= 0 variable 1 34.429 27.067 29.796 35.463
% r <= 1 variable 2 17.532 13.429 15.494 19.935
% r <= 2 variable 3 4.471 2.705 3.841 6.635
%
% NULL: Eigen Statistic Crit 90% Crit 95% Crit 99%
% r <= 0 variable 1 16.897 18.893 21.131 25.865
% r <= 1 variable 2 13.061 12.297 14.264 18.520
% r <= 2 variable 3 4.471 2.705 3.841 6.635
results.eig % Display the eigenvalues
% ans =
%
% 0.0112
% 0.0087
% 0.0030
results.evec % Display the eigenvectors
% ans =
%
% -1.0460 -0.5797 -0.2647
% 0.7600 -0.1120 -0.0790
% 0.2233 0.5316 0.0952
yport=sum(repmat(results.evec(:, 1)', [size(y3, 1) 1]).*y3, 2); % (net) market value of portfolio
% Find value of lambda and thus the halflife of mean reversion by linear regression fit
ylag=lag(yport, 1); % lag is a function in the jplv7 (spatial-econometrics.com) package.
deltaY=yport-ylag;
deltaY(1)=[]; % Regression functions cannot handle the NaN in the first bar of the time series.
ylag(1)=[];
regress_results=ols(deltaY, [ylag ones(size(ylag))]); % ols is a function in the jplv7 (spatial-econometrics.com) package.
halflife=-log(2)/regress_results.beta(1);
fprintf(1, 'halflife=%f days\n', halflife);
% halflife=22.662578 days
% -------------------------------------------------------------------------------------------------------------------------------
% Apply a simple linear mean reversion strategy to EWA-EWC-IGE
lookback=round(halflife); % setting lookback to the halflife found above
numUnits =-(yport-movingAvg(yport, lookback))./movingStd(yport, lookback); % capital invested in portfolio in dollars. movingAvg and movingStd are functions from epchan.com/book2
positions=repmat(numUnits, [1 size(y3, 2)]).*repmat(results.evec(:, 1)', [size(y3, 1) 1]).*y3; % results.evec(:, 1)' can be viewed as the capital allocation, while positions is the dollar capital in each ETF.
pnl=sum(lag(positions, 1).*(y3-lag(y3, 1))./lag(y3, 1), 2); % daily P&L of the strategy
ret=pnl./sum(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=0.125739 Sharpe=1.391310
Thats his, and mine is here; with only data input being changed. Formulas all the same.
load('inputData_ETF', 'tday', 'syms', 'cl');
idxA=find(strcmp('EWA', syms));
idxC=find(strcmp('EWC', syms));
x=cl(:, idxA);
y=cl(:, idxC);
plot(x);
hold on;
plot(y, 'g');
legend('EWA', 'EWC');
figure;
scatter(x, y);
figure;
regression_result=ols(y, [x ones(size(x))]);
hedgeRatio=regression_result.beta(1);
plot(y-hedgeRatio*x);
% Assume a non-zero offset but no drift, with lag=1.
results=cadf(y, x, 0, 1); % cadf is a function in the jplv7 (spatial-econometrics.com) package. We pick y to be the dependent variable again.
% Print out results
prt(results);
% Output:
% Augmented DF test for co-integration variables: variable 1,variable 2
% CADF t-statistic # of lags AR(1) estimate
% -3.64346635 1 -0.020411
%
% 1% Crit Value 5% Crit Value 10% Crit Value
% -3.880 -3.359 -3.038
%----------------------------------------------------------------------------------------------------
% Combine the two time series into a matrix y2 for input into Johansen test
y2=[y, x];
results=johansen(y2, 0, 1); % johansen test with non-zero offset but zero drift, and with the lag k=1.
% Print out results
prt(results);
% Output:
% Johansen MLE estimates
% NULL: Trace Statistic Crit 90% Crit 95% Crit 99%
% r <= 0 variable 1 19.983 13.429 15.494 19.935
% r <= 1 variable 2 3.983 2.705 3.841 6.635
%
% NULL: Eigen Statistic Crit 90% Crit 95% Crit 99%
% r <= 0 variable 1 16.000 12.297 14.264 18.520
% r <= 1 variable 2 3.983 2.705 3.841 6.635
%----------------------------------------------------------------------------------------------------
% Adding IGE to the portfolio
idxI=find(strcmp('IGE', syms));
z=cl(:, idxI);
y3=[y2, z];
results=johansen(y3, 0, 1); % johansen test with non-zero offset but zero drift, and with the lag k=1.
% Print out results
prt(results);
% Output:
% Johansen MLE estimates
% NULL: Trace Statistic Crit 90% Crit 95% Crit 99%
% r <= 0 variable 1 34.429 27.067 29.796 35.463
% r <= 1 variable 2 17.532 13.429 15.494 19.935
% r <= 2 variable 3 4.471 2.705 3.841 6.635
%
% NULL: Eigen Statistic Crit 90% Crit 95% Crit 99%
% r <= 0 variable 1 16.897 18.893 21.131 25.865
% r <= 1 variable 2 13.061 12.297 14.264 18.520
% r <= 2 variable 3 4.471 2.705 3.841 6.635
results.eig % Display the eigenvalues
% ans =
%
% 0.0112
% 0.0087
% 0.0030
results.evec % Display the eigenvectors
% ans =
%
% -1.0460 -0.5797 -0.2647
% 0.7600 -0.1120 -0.0790
% 0.2233 0.5316 0.0952
yport=sum(repmat(results.evec(:, 1)', [size(y3, 1) 1]).*y3, 2); % (net) market value of portfolio
% Find value of lambda and thus the halflife of mean reversion by linear regression fit
ylag=lag(yport, 1); % lag is a function in the jplv7 (spatial-econometrics.com) package.
deltaY=yport-ylag;
deltaY(1)=[]; % Regression functions cannot handle the NaN in the first bar of the time series.
ylag(1)=[];
regress_results=ols(deltaY, [ylag ones(size(ylag))]); % ols is a function in the jplv7 (spatial-econometrics.com) package.
halflife=-log(2)/regress_results.beta(1);
fprintf(1, 'halflife=%f days\n', halflife);
% halflife=22.662578 days
% -------------------------------------------------------------------------------------------------------------------------------
% Apply a simple linear mean reversion strategy to EWA-EWC-IGE
lookback=round(halflife); % setting lookback to the halflife found above
numUnits =-(yport-movingAvg(yport, lookback))./movingStd(yport, lookback); % capital invested in portfolio in dollars. movingAvg and movingStd are functions from epchan.com/book2
positions=repmat(numUnits, [1 size(y3, 2)]).*repmat(results.evec(:, 1)', [size(y3, 1) 1]).*y3; % results.evec(:, 1)' can be viewed as the capital allocation, while positions is the dollar capital in each ETF.
pnl=sum(lag(positions, 1).*(y3-lag(y3, 1))./lag(y3, 1), 2); % daily P&L of the strategy
ret=pnl./sum(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=1.47 Sharpe=5.6
Any ideas?
