A real-time adaptive trading system
using Genetic Programming
QF5205 : Topics in Quantitative Finance
Donny Lee
Nadim Mouchonnet
Summary
1.
2.
3.
4.
5.
Introduction
Genetic Algorithm and Genetic Programming
Trading System
Genetic Program
Results
Introduction
• Many traders use indicator based trading rules
• … but they may be loss making (see chart)
• Double Objective
Create a system than trades and make profit
Emulate the behavior of a technical trader
Motivation:
“Can a technical trader consistently make a profit?”
and “should a technical trader or trading system
adapt to market conditions or is it better to use a
static system?”
Introduction(2)
• Results using only a single strategy, backtested on
historical data.
• Stochastic strategy: Buy when indicator crosses the
20% mark from below and sell when it crosses the
70% mark from above.
• Simple moving average strategy: Buy when the slow
lag (50 day look back) crosses the fast lag (20 day
look back) from below and sell when vice versa.
Introduction(3)
• Using the stochastic strategy on SIA stock from 02/11/10 to 08/26/10.
• Loss is $0.30.
Introduction(4)
• Using the SMA strategy on KEP stock from 02/11/10 to 08/26/10.
• Loss is $0.27.
Introduction(5)
• Using the GBPUSD for a period of 3 months
• Bloomberg can summarize a whole bunch of strategies
Introduction(6)
• Using the GBPUSD for a period of 3 months
• Parabolic SAR
Genetic Algorithm and Genetic Programming (1)
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GA is an iterative system
… aiming to find near-optimal solutions
… to multi-extremal problems
… by imitating the process of evolution
Rule is : SURVIVAL OF THE FITTEST
Genetic Algorithm and Genetic Programming (2)
• GA representation consists of binary strings of
fixed length.
• Search space is finite
• GA needs to be initialized …
• … by random sampling
• Difference between GA and GP is that GP
allows string length to vary within the solution
space.
Trading System : Data
• Analysis carried out on spot FX ticks for
GBP/USD from CQG Data Factory and Future
Source from 1994 to 1997
• CQG : gathered from various FX brokers
• Future Source : live feed from the Omega
TradeStation utility (major banks FX quotes)
• Got bid and ask and transforms them into mid
• Data aggregated into OHLC
Trading System : Software
• Imitating the technical trader i.e. chooses technical
strategies from a range of popular trading rules
• GP based rule selection engine choosing combinations
of such strategies
• Cash management filter exits strategies when losses >
user-defined threshold
• Each backtested strategy returns : Profit, max
drawdown, Modified Stirling ratio, number of trades
• Transaction costs are taken into account with various
slippage depending on trading time
Trading System : Software
Trading System : Strategies
• 6 Rules used : simple moving averages crossover,
adaptive moving averages, price channel
breakout, stochastic, relative strength index,
commodity channel index
• 3 Connectors : AND / OR / XOR (00/01/10)
• System rules allowed to use different
frequencies/lags
• Strategies ranked by stirling ratio (when return is
positive) or by absolute return when negative.
Genetic Program
• Representation of a strategy.
• A strategy of ours can be represented graphically.
Genetic Program(2)
• From a graphical understanding of a strategy, we can translate
to a strategy structure. or a binary string representation.
Genetic Program(3)
• Or a binary string representation.
Genetic Program(4)
• This is essential as we ultimately need to convert our strategy
into a binary string for our GP to work.
Each strategy can be written in the form
RULE | CONDITION | CONNECTOR |
RULE | CONDITION | CONNECTOR | ……… | ACTION
Genetic Program(5)
• From there, we can form our binary string representation for
our GP.
I.e., consider the rule “BUY if AMA TRUE AND CCI FALSE OR RSI
TRUE”
It would be represented in binary as,
1000011111
Genetic Program(6)
• Now with each strategy represented as a binary string, we
perform the following in each iteration.
1.
2.
3.
4.
Initialize population
Calculate Fitness
Crossover
Mutate
Genetic Program(7)
• We initial the population with a certain number of strings
which will represents the strategies we will use.
1. Assume there are a maximum of k included indicators and a
minimum of j. We may construct rules from a total of I
indicators.
2. Generate U uniform pseudo-random integer variables V
where 1 <= V <= I. For indicators to be used, we write a ‘1’ in
the structure part, otherwise a ‘0’.
3. Generate U uniform pseudo-random binary variables
corresponding to the indictor bit for each indicator.
4. Assume there are C connectors allowed. For each indicator,
we generate a fixed width binary of D(1,C) and write it next
to the corresponding indicator bit.
Genetic Program(8)
• At each trial over a user-defined period, each of these
strategies is tested by simulating their trading performance
over historical data.
• There are many ways to assess performance. The Stirling ratio
– profit divided by maximum drawdown – is often used by
traders to assess performance.
• For Crossover and Mutation, we would pick a strategies with a
certain top % in their Stirling ratio.
Genetic Program(9)
• Crossover is the process of cutting strategy string pairs at
points and exchanging tails and heads to make a new a pair.
• Only the best s% are considered for crossover. For those
strings rank i, the probability of selecting this string is
• A cut point is selected uniformly pseudo-randomly and ‘head’
and ‘tail’ parts are exchange.
Genetic Program(10)
An example of a Crossover, suppose the following two pairs of
strings are selected along with a uniformly distributed random
number:
1010001010 and 1100111100 and 3
0100100111 and 0001101110 and 8
Crossover:
101|0001010 and 110|0111100 becomes
1100001010 and 1010111100
01001001|11 and 00011011|10 becomes
0100100110 and 0001101111
Genetic Program(11)
• Mutation is the process of randomly changing appropriate bits
in a strategy string and is executed in a bitwise manner.
• Elitist model: top-ranked 5% of strings are not mutated.
• Number of strings mutated = Mutation Rate x No. of Strings.
• M uniform pseudo-random integer are generated between 1
and B, length of each string, without replacement.
• Each corresponding numbered bit is then mutated (‘0’
becomes ‘1’ and ‘1’ becomes ‘0’)
Genetic Program(12)
• Example of a mutation.
• Strings are of length 10 and four pseudo-random integers are
generated and arranged in ascending order – 3, 5, 7, 8.
• The following strings are mutated as follows:
1010001010 becomes 1000100110
1100111100 becomes 1110010000
0100100110 becomes 0110001010
0001101110 becomes 0011000010
Genetic Program : Summary
Step 1
Step 2
Step 3
Step 4
• Initialize : Generate 100 strategies randomly
• Crossover strategies using 50% of the best strategies
• Mutate the strategies outside the best 5%
• Repeat Steps 2 & 3 until convergence of the solutions
Results : Test
• Step 1 : In Sample backtesting using 15minute data used to determine the 20 best
strategies during Q1 1994
• Step 2 : Out Sample trading using the best 20
strategies over the next quarters and assess
the performance in live trading conditions
Results : Improvement of solutions (1)
Results : Improvement of solutions (2)
Results : Profit
Results : Further work
• Periodic reoptimization as performance
decreases as time out of sample increases
• Parallel optimization
Our experience
• Unsuccessful Programming in the Java
framework
• 1 solution : using the Technical Analysis tool of
Bloomberg’s Excel Add-in