This document describes research into applying control theory and feedback strategies to stock trading. It tests several feedback-based trading strategies on stock market portfolios to investigate their ability to generate profits. The strategies tested include a classical linear feedback strategy, a strategy with feedback delay, a "trigger" strategy, and a moving average strategy. Transaction costs are later added to the models. The results show that three of the four strategies were able to produce net profits after accounting for transaction costs over the testing periods.

1. Feedback-based Stock Trading Strategies
Feedback-based Stock Trading Strategies
Cian McGowan
Supervised by Dr. Mark Burke
12135712
13 April, 2016

2. Feedback-based Stock Trading Strategies
Outline
Introduction to Feedback and Control Theory
Linking Control Theory and Stock Trading
Methods Used for the Testing of Strategies
Results of Tests
Conclusion

3. Feedback-based Stock Trading Strategies
What is Control Theory?
Interdisciplinary branch of engineering and
mathematics.
Control Theory breaks systems down into
input signals, output signals and
subsystems.
These systems can be written using block
diagrams.
The best way to understand Control Theory
is by studying examples how it is used.

4. Feedback-based Stock Trading Strategies
Feedback Loop
This block diagram depicts a closed feedback
loop.
Examples: Cruise control function of a car or
the implementation of a module satisfaction
survey.

5. Feedback-based Stock Trading Strategies
How can Control Theory be related to Trading?
The process of stock trading can be easily
broken down into input and output signals
based on stock prices.
Control Theory can be seen in many
wide-ranging areas such as engineering,
biology (homeostasis), geology (Earth’s
hydrocycle)...so why not apply it to finance?

6. Feedback-based Stock Trading Strategies
A Control System for Stock Trading
max
amount which can be invested or shorted at any time. A
classical feedback setup illustrating one possibility for the
scenario above is given in Figure 1.
Gain/Loss
Dynamics
Trading
Feedback
Strategy
stock gain g(t)
investment I(t)
stock price p(t)
CONTROLLED INPUT
UNCONTROLLED INPUT
PERFORMANCE OUTPUT
Figure 1: Control System Point of View
2.3 The Saturation Reset Controller
At the most general level, the amount invested I(t) is a
corr
men
Now
acco
or b
Not
abo
mar
3.1
Wh
is g
incr
This FYP examines different feedback-based
trading strategies and investigates their
ability to return a profit for traders.

7. Feedback-based Stock Trading Strategies
Assumptions Made for Testing
Transaction costs are ignored.
Discrete time.
Perfect liquidity.
Trader is a price taker.
Zero market spread.
Zero percent interest rates.

8. Feedback-based Stock Trading Strategies
Classical Linear Feedback Strategy
The first strategy tested used the following
function to modulate the investment level I(t).
I(t) = I0 + βg(t)
The coefficient, β, is known as the feedback
gain parameter. Its value determines how
sensitive the investment level is to changes in
stock price.

9. Feedback-based Stock Trading Strategies
Classical Linear Feedback Strategy
Days
0 200 400 600 800 1000 1200 1400
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Account Value of S&P 500 Portfolio using Feedback System
Figure 1: Account Value for Implementing the Classical Stategy on
the S&P Portfolio from 2005-2009.

10. Feedback-based Stock Trading Strategies
Feedback Strategy with Delay
The delay strategy stems from the theory that
the investment level I(t) should not only be
dependent on the gain/loss at time t but also on
a previous time t − µ.
I(t) = I0 + β[g(t) − g(t − µ)].

11. Feedback-based Stock Trading Strategies
Feedback Strategy with Delay
Days
0 200 400 600 800 1000 1200 1400
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Account Values: Delay versus No Delay
Delay
No Delay
Figure 2: Account Value for Implementing the Delay Stategy on the
S&P Portfolio from 2005-2009 versus Classical Strategy.

12. Feedback-based Stock Trading Strategies
Experimentation with Parameter Values
It was found that using a delay reduced the
volatility of the account values but that
increasing the delay above µ = 1 was not
beneficial.
It was found that it was best to use a large β
value during bullish market periods but that
overall, a value of β < 1 was more beneficial.

13. Feedback-based Stock Trading Strategies
The “Trigger” Strategy
For this system, the investment level function will
switch, depending on a triggering condition,
from I(t) to I∗
(t).
I(t) = I0 + β0g(t)
I∗
(t) = I0 + β1g(t)

14. Feedback-based Stock Trading Strategies
Days
0 200 400 600 800 1000 1200 1400
AccountValue
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Applying the use of a trigger to the S&P 500 Portfolio
Normal Feedback System
Feedback System with Trigger
Figure 3: Applying the Trigger Strategy to the S&P Portfolio versus
the Classical Strategy from 2005-2009.

15. Feedback-based Stock Trading Strategies
Transaction Costs
Two-part TC Model introduced in order to
reduce limitation of tests:
1% Stamp Duty on Purchases
0.9% of Account Value per annum in
Brokerage Fees

16. Feedback-based Stock Trading Strategies
Results after Transaction Costs are Added
System g(T) Broker Fees Taxation Profit
Classical 1.3774 0.1205 0.7071 0.5497
Moving Average 0.8658 0.1115 1.0390 -0.2847
Delay 0.8402 0.1019 0.4279 0.3105
Trigger 1.5274 0.1088 0.1251 1.2935
Table 1: Performance of the four main strategies for the FTSE 100
portfolio for the period 2004-2012.

17. Feedback-based Stock Trading Strategies
Results after Transaction Costs are Added
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Days
-1
-0.5
0
0.5
1
1.5
2
Values
FTSE 100 - Feedback System with Trigger and Transaction Costs
Gain or Loss
Profit
Total Costs
Figure 4: Perfomance of Trigger Strategy on the FTSE 100 Portfolio
from 2004-2012 with Transaction Costs.

18. Feedback-based Stock Trading Strategies
Conclusion
3 out of 4 strategies tested made a net profit.
There is certainly a place for the use of
control theory in finance.
This is a new line of research and requires
further testing and reduction of limitations.

19. Feedback-based Stock Trading Strategies
The End
Thanks for listening!