The objective of this thread is to share some ideas inspired by recent readings in order to answer a simple (theoretical) question:
All what follows is open to comment, criticism, etc.
We will consider two different profitable trading systems.
One trading system has a low %win (typically, a trend-following system):
- %win = 44%
- Win-Loss-Ratio = 1.5
The other trading system has opposite characteristics (typically, a scalping system):
- %win = 60%
- Win-Loss-Ratio = 0.833
Both have the same expected gain of 0.1 (for 1 unit of risk). It means that, if we risk $10 on each trade, we will gain $1 in average.
We will consider a sequence of 12 trades.
So… what is the best strategy to use in terms of position sizing? How much should we risk on each trade?
There is no unique answer to this. It depends on what we want to optimize.
We could have one of the following objectives:
1) maximize the expected final capital (
2) minimize the risk of ruin (
3) maximize the expected gain while keeping the risk reasonable; this will lead us to Kelly criterion (
4) criticism of assumptions behind Kelly criterion, and study of other utility functions (
5) a few words about other objectives (
We will study them one after the other in this series of 8 messages, and finish with an overall conclusion (.
According to the chosen scenario, two kinds of position sizing strategies will be considered:
a) at each trade, risk a fixed % of the initial capital
b) at each trade, risk a fixed % of the remaining capital
Nothing revolutionary here. However, the graphs are mine, prepared with Java with JFreeChart API.