Talk at NVIDIA GTC 2015

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 ?