GPU Accelerated Backtesting and Machine Learning for Quant Trading Strategies
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This document discusses using GPU acceleration for quant trading strategies. It describes challenges in engineering trading strategies, using random forests to generate buy/sell signals from market data, and optimizing strategies through walk-forward testing on GPUs. Random forests are trained on features and market returns to produce signals. Strategies are backtested on markets by calculating P&L from signals and returns. The best strategy is selected, and hypothesis tests determine if strategy returns are statistically greater than zero. GPUs can accelerate this process through parallelism at multiple levels.
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GPU Accelerated Backtesting and Machine Learning for Quant Trading Strategies
- 1. GPU Accelerated Backtesting and ML for Quant Trading Strategies GTC 2015 | San José | California Dr. Daniel Egloff daniel.egloff@quantalea.net March 18, 2015
- 2. Motivation Goals – Execute automated algorithmic trading strategies – Optimize risk return Procedure – Extract signals and build price forecasting indicators from market data – Transform indicators into buy / sell decisions – Apply portfolio risk management Challenges – Find relevant signals and indicators – Engineer and parameterize trading decision – Find optimal parameters Approach – Exploit parallelism in the computations – Accelerate calculations by using a GPU cluster
- 3. Algo Trading Strategies Market data Input Trading decision Mathematical operations Output Configurations Rules
- 4. Example fast moving average slow moving average Buy signal Sell signal
- 5. Markets Futures market – CME 50 liquid futures – Other exchanges Equity markets – World stock indices FX markets – 10 major currency pairs – 30 alternative currency pairs Options markets – Options on futures – Options on indices
- 6. Strategy Universe Configuration c Trading decision s(c) 1 -1 buy sell Utility U(s(c)) P&L / drawdown Strategy configurations
- 7. Strategy Engineering Challenge 1: How can we engineer a strategy producing buy / sell decisions ?
- 8. Random Forests Fi < ti Fj < tj Buy Buy Fi < ti Sell Fk < tk Sell Fi < ti Fi < ti Buy Fk < tk Fi < ti Fj < tj Sell Fi < ti Sell Buy Sell Buy Sell Buy Sell Buy Sell Buy
- 9. Random Forests Strategy configuration c Features Random forest Trading decision s(c) 1 -1 buy sell
- 10. Training Random Forests Bootstrapping to create training sets C 4.5 algorithm for individual tree construction Selecting subset of features for tree construction Each node is associated with a subset of training samples Recursive, starting at the root node At each node execute divide and conquer algorithm to find locally optimal choice – If samples are in same class (or few class) node is a leaf associated with that class – If samples are in two or more classes Calculate information gain for each feature Select feature if largest information gain for splitting
- 11. Entropy 𝑇 = set of samples associated with node 𝐶1, … , 𝐶 𝑛= classes of samples Entropy 𝐸𝑛𝑡 𝑇 = − 𝑖=1 𝑛 𝑓𝑟𝑒𝑞(𝐶 𝑖,𝑇) 𝑇 𝑙𝑜𝑔2 𝑓𝑟𝑒𝑞(𝐶 𝑖,𝑇) 𝑇 Characterizes impurity of samples Measure of uncertainty Additive: impurity of several subsets is sum of impurities
- 12. Information Gain 𝑇1, … , 𝑇𝑠 = subsets of 𝑇 generated by splitting on selected attribute Information gain discrete feature 𝑔𝑎𝑖𝑛 𝑇1, … , 𝑇𝑠 = 𝐸𝑛𝑡 𝑇 − 𝑖=1 𝑠 𝑇 𝑖 𝑇 𝐸𝑛𝑡 𝑇𝑖 Information gain continuous feature with optimal splitting threshold 𝑔𝑎𝑖𝑛 𝑡 = 𝑔𝑎𝑖𝑛 𝑇≤𝑡, 𝑇>𝑡 𝑡∗ = 𝑎𝑟𝑔𝑚𝑎𝑥 𝑔𝑎𝑖𝑛 𝑡 Actual implementation uses ratio information gain over split ratio
- 13. Training Individual Trees Labels from positive or negative market returns Selected features Permuted labels Label Permutations to sort features All features Samples / observations
- 14. Training Individual Trees Selected features Permuted labels Permutations to sort features Weights Permuted weights Permutations to sort features Label All features 2 0 1 4 0 2 ………
- 15. Training Individual Trees Entropy criterion for best feature and split Entropy for every split Permuted labels Permuted weights 2. Optimal feature Fi 1. Optimal split ti Fi < ti
- 16. Training Individual Trees Recursively refine classification: mask data according to classification Selected features Permuted labels Label Permutations to sort features Weight Permuted weights Permutations to sort features
- 17. Training Individual Trees Features Permuted labels Label Permutations to sort features Weight Permuted weights Permutations to sort features Recursively refine classification: mask data according to classification
- 18. GPU Implementation Parallelism at multiple levels – Multiple trees, one for each set of weights – Independent features – Independent split points – Multiple nodes further down the tree GPU kernels can be implemented with standard primitives – Random number generation for weights – Parallel scan (cumulative sum) – Parallel map – Parallel reduction to find optimal feature and split
- 19. Speedup 0 10 20 30 40 50 60 20 50 100 20 50 100 20 50 100 20 50 100 1 2 4 8 20000 50000 100000 Depth Features Samples
- 20. Strategy Backtesting Challenge2: How to choose best trading strategy ?
- 21. Walk Forward Optimization In sample Out of sample 3-6 months 1 month In sample Out of sample In sample Out of sample shift by 1 month
- 22. Trading P&L Market returns r(ti) r(ti) = log(P(ti) / P(ti-1)) ti-1 ti P(ti-1) P(ti) r Trading decision s(c) P&L(c) = <s(c), r> r r r r 1 -1 1 1 -1 ….. ….. ….. ….. Market prices Market returns time
- 23. Optimal Configuration s(c) s(c) r s(c) s(c) s(c) s(c) s(c) s(c) P&L = Configurations pick configuration with largest P&L x
- 24. Bootstrapping Trading P&L s(c) s(c) r s(c) s(c) s(c) s(c) s(c) s(c) P&L = Configurations pick configuration with largest P&L x w w w w x x x x x ww Weights r .* w
- 25. Hypothesis Tests Null Hypothesis Trading P&L<= 0 Alternative Hypothesis Trading P&L > 0
- 26. Trading P&L Distribution optimal configurations for each weight c* for w = 1 p-value for test0 P&L x x x x x x
- 27. White Reality Check Scale exposure according to distance from 0 Do not trade if negative returns c* for w = 1 0 p-value c* for w = 1 0 p-value Market 1 Market n……
- 28. GPU Implementation Parallelism at multiple levels – Multiple markets – Independent in-sample / out-of-sample windows – Independent strategy configurations – Independent time steps for utility functions such as mean return GPU kernels can be implemented with standard primitives – Random number generation – Matrix multiplication (almost, up to return vector scaling the weights) – Parallel reduction
- 29. GPU Implementation GPU grid – Multiple markets – Independent in-sample / out-of-sample windows Per GPU – Independent strategy configurations – Independent time steps for utility functions such as mean return
- 30. Dr. Daniel Egloff daniel.egloff@quantalea.net March 18, 2015 Questions ?