Backtest Strategies Using Deep Learning

priceData = load('energyPrices.mat','energyPrices');
priceData = priceData.energyPrices;
tail(priceData)

seriesLifespanPlot(priceData)

priceData = removevars(priceData,["NYDiesel","GulfDiesel","LARegular"]);

priceData = rmmissing(priceData);

returnData = tick2ret(priceData)

% Model is trained using a 30-day rolling window to predict 1 day in the
% future.
historySize = 30;
futureSize = 1;

% Model predicts returns for oil, natural gas, propane, and kerosene.
outputVarName = ["Brent" "NaturalGas", "Propane" "Kerosene"];
numOutputs = numel(outputVarName);

% start_idx and end_idx are the index positions in the returnData
% timetable corresponding to the first and last date for making a prediction.
start_idx = historySize + 1;
end_idx   = height(returnData) - futureSize + 1;
numSamples = end_idx - start_idx + 1;

% The date_vector variable stores the dates for making predictions.
date_vector = returnData.Time(start_idx-1:end_idx-1);

network_features  = cell(numSamples,1);
network_responses = zeros(numSamples,numOutputs);

for j = 1:numSamples
    network_features{j} = (returnData(j:j+historySize-1,:).Variables)';
    network_responses(j,:) = ...
        (returnData(j+historySize:j+historySize+futureSize-1,outputVarName).Variables)';
end

% Specify rows to use in the backtest (31-Dec-2015 to 2-Nov-2021).
backtest_start_idx = find(date_vector < datetime(2016,1,1),1,'last');
backtest_indices = backtest_start_idx:size(network_responses,1);

% Specify data reserved for the backtest.
Xbacktest = network_features(backtest_indices);
Tbacktest = network_responses(backtest_indices,:);

% Remove the backtest data.
network_features = network_features(1:backtest_indices(1)-1);
network_responses = network_responses(1:backtest_indices(1)-1,:);

% Partition the remaining data into training and validation sets.
rng('default');
cv_partition = cvpartition(size(network_features,1),'HoldOut',0.2);

% Training set
Xtraining = network_features(~cv_partition.test,:);
Ttraining = network_responses(~cv_partition.test,:);

% Validation set
Xvalidation = network_features(cv_partition.test,:);
Tvalidation = network_responses(cv_partition.test,:);

numFeatures = width(returnData);
numHiddenUnits_LSTM = 10;

layers_LSTM = [ ...
    sequenceInputLayer(numFeatures) 
    lstmLayer(numHiddenUnits_LSTM)
    layerNormalizationLayer
    lstmLayer(numHiddenUnits_LSTM)
    layerNormalizationLayer
    lstmLayer(numHiddenUnits_LSTM,'OutputMode','last')
    layerNormalizationLayer
    fullyConnectedLayer(numOutputs)];

max_epochs = 500;
mini_batch_size = 128;
learning_rate = 1e-4;

options_LSTM = trainingOptions('adam', ...
    'InputDataFormats',"CTB",...
    'Plots','training-progress', ...
    'Verbose',0, ...
    'MaxEpochs',max_epochs, ...
    'MiniBatchSize',mini_batch_size, ...
    'Shuffle','every-epoch', ...
    'ValidationData',{Xvalidation,Tvalidation}, ...
    'ValidationFrequency',50, ...
    'ValidationPatience',10, ...
    'InitialLearnRate',learning_rate, ...
    'GradientThreshold',1);

doTrain = false;

if doTrain
    % Train the LSTM network.
    net_LSTM = trainnet(Xtraining,Ttraining,layers_LSTM,"mse",options_LSTM);
else
    % Load the pretrained network.
    load lstmBacktestNetwork
end

% Compare the actual returns to model predicted returns.
actual    = Tvalidation;
predicted = minibatchpredict(net_LSTM,Xvalidation,InputDataFormats="CTB");

% Overlay histogram of actual vs. predicted returns for the validation set.
output_idx = 1;
figure;

[~,edges] = histcounts(actual(:,output_idx),100);
histogram(actual(:,output_idx),edges);
hold on
histogram(predicted(:,output_idx),edges)
hold off
xlabel('Percentage Change in Closing Price')
legend('Actual','Predicted')
title(sprintf('%s: Distribution of Returns, Actual vs. Predicted', outputVarName(output_idx)))

% Display the predicted vs. actual daily returns for the validation set.
figure
plot(actual(:,output_idx))
hold on
plot(predicted(:,output_idx))
yline(0)
legend({'Actual','Predicted'})
title(sprintf('%s: Daily Returns, Actual vs. Predicted', outputVarName(output_idx)))

% Examine the residuals.
residuals = actual(:,output_idx) - predicted(:,output_idx);
figure;
normplot(residuals);

backtestPred_LSTM = minibatchpredict(net_LSTM,Xbacktest,InputDataFormats="CTB");

backtestSignalTT = timetable(date_vector(backtest_indices),backtestPred_LSTM);

backtestPriceTT = priceData(date_vector(backtest_indices),outputVarName);

risk_free_rate = 0.01;

% Specify 10 basis points as the trading cost.
tradingCosts = 0.001;

% Invest in long positions proportionally to their predicted return.
LongStrategy = backtestStrategy('LongOnly',@LongOnlyRebalanceFcn, ...
    'TransactionCosts',tradingCosts, ...
    'LookbackWindow',1);

% Invest in both long and short positions proportionally to their predicted returns.
LongShortStrategy = backtestStrategy('LongShort',@LongShortRebalanceFcn, ...
    'TransactionCosts',tradingCosts, ...
    'LookbackWindow',1);

% Invest 100% of capital into single asset with highest predicted returns.
BestBetStrategy = backtestStrategy('BestBet',@BestBetRebalanceFcn, ...
    'TransactionCosts',tradingCosts, ...
    'LookbackWindow',1);

% For comparison, invest in an equal-weighted (buy low and sell high) strategy.
equalWeightFcn = @(current_weights,prices,signal) ones(size(current_weights)) / numel(current_weights);
EqualWeightStrategy = backtestStrategy('EqualWeight',equalWeightFcn, ...
    'TransactionCosts',tradingCosts, ...
    'LookbackWindow',0);

strategies = [LongStrategy LongShortStrategy BestBetStrategy EqualWeightStrategy];

bt = backtestEngine(strategies,'RiskFreeRate',risk_free_rate);

bt = runBacktest(bt,backtestPriceTT,backtestSignalTT)

summary(bt)

figure;
equityCurve(bt)

function new_weights = LongOnlyRebalanceFcn(current_weights,pricesTT,signalTT) %#ok<INUSD> 
% Long only strategy, in proportion to the signal.

signal = signalTT.backtestPred_LSTM(end,:);

if any(0 < signal)
    signal(signal < 0) = 0;
    new_weights = signal / sum(signal);
else
    new_weights = zeros(size(current_weights));
end

end


function new_weights = LongShortRebalanceFcn(current_weights,pricesTT,signalTT) %#ok<INUSD> 
% Long/Short strategy, in proportion to the signal

signal = signalTT.backtestPred_LSTM(end,:);
abssum = sum(abs(signal));

if 0 < abssum
    new_weights = signal / abssum;
else
    new_weights = zeros(size(current_weights));
end

end


function new_weights = BestBetRebalanceFcn(current_weights,pricesTT,signalTT) %#ok<INUSD> 
% Best bet strategy, invest in the asset with the most upside.

signal = signalTT.backtestPred_LSTM(end,:);
new_weights = zeros(size(current_weights));
new_weights(signal == max(signal)) = 1;

end


function seriesLifespanPlot(priceData)
% Plot the lifespan of each time series.

% Specify all time series end on same day.
d2 = numel(priceData.Time);

% Plot the lifespan patch for each series.
numSeries = size(priceData,2);
for i = 1:numSeries
    % Find start date index.
    d1 = find(~isnan(priceData{:,i}),1,'first');
    % Plot patch.
    x = [d1 d1 d2 d2];
    y = i + [-0.4 0.4 0.4 -0.4];
    patch(x,y,[0 0.4470 0.7410])

    hold on
end
hold off

% Set the plot properties.
xlim([-100 d2]);
ylim([0.2 numSeries + 0.8]);

yticks(1:numSeries);
yticklabels(priceData.Properties.VariableNames');
flipud(gca);

years = 1990:5:2021;
xtick_idx = zeros(size(years));
for yidx = 1:numel(years)
    xtick_idx(yidx) = find(years(yidx) == year(priceData.Time),1,'first');
end
xticks(xtick_idx);
xticklabels(string(years));

title('Time Series Life Span');

end