The mathematical side of trading

When most people talk about how they approach the market, they refer solely to their style of trading.

In my own case, I follow price trends - I wait for a potential new trend to be signalled, and I will then 'hop on' for the ride.

However, there is another important factor you should consider, which is all to do with the mathematical side of trading.
 
Using a volatility based position sizing method can allow you to identify potential setups where volatility has contracted prior to entry. An example of this would be using a multiple of the average true range measurement. This can help you from a potential risk:reward aspect. Using such a stop would allow you to concentrate on those opportunities where price has to move a smaller distance in the direction you are trading to achieve the each unit of ‘R’ of profit.

To show this, say you have two trades which are giving an entry signal at the same time, and we will assume they are both currently priced at $20, and we will risk the same amount of equity on each trade.

The 2ATR measurement on Trade A indicates an initial stop distance of $5. This is used to help calculate your position size. The wider the initial stop, the smaller the position size should be.

Over the next few months, the stock moves up to $60 (a 200% increase), before triggering an exit. So, on that trade you have made a profit of +8R.

On Trade B, the initial stop distance is only $1, following a recent contraction in volatility. In a few weeks, the stock moved up to $30 – a 50% increase. Yet, in terms of R, the profit generated is +10R – higher than that of Trade A – and you have been in the trade a lot less time to boot. The tighter the initial stop, the more profit you have been able to generate.

Which is the better trade? Clearly, Trade B made a bigger profit when compared to the amount risked (when expressed in 'R'), yet the stock price movement, in percentage terms, was only a quarter of that of Trade A.
 
I like this concept of expressing risk and rewards in terms of 'R' - it normalizes performance and some of the associated metrics, irrespective of the equity base or the monetary or percentage risk per trade.
 
When looking at and quantifying a potential set up, looking for situations where there has been such a contraction in volatility is a key part of my trade selection process. Setups where there has been an expansion in volatility prior to an entry signal are avoided.
 
So that is the first stage. The next element that should be considered is that of trading opportunity.

Going back again to the basic mathematics, we will consider another example with two different systems:

System 1 generates an average profit per trade of say +0.5R, and you get 200 signals per year that you could act on. In theory then, that gives you a theoretical profit of +100R per year - nice.

System 2 generates a higher average profit per trade of say +1R, but you only get 50 signals in a year. That then gives you a theoretical yearly profit of +50R.

So in that example the first system would be the one to look at using, because of the increased level of trading opportunity you have and the higher potential overall returns.

A word of warning here - generally, the shorter your timeframe, the higher the number of potential trading opportunities you will get. But that brings its own issues – are you able to focus sufficiently on the markets to catch those opportunities – particularly if you are looking at very short-term or intra-day trading?
 
The shorter your timeframe, then other factors such as the impact on transaction costs need to be considered, along with the susceptibility to be whipsawed around or caught by price ‘noise’.
 
You should also consider what happens should there be a price gap which goes against you. If price gaps through your intended stop level, then the tighter the stop, the bigger the potential loss (in 'R') you would suffer. Risking only a small amount of your equity on each trade is the first stage in ensuring such an event won't destroy your equity.
 
Finally as part of this mathematical equation, you need to factor in the number of trading mistakes you make over the course of a year (which again you could keep track of and quantify in ‘R’). This can quickly draw up a picture of how effective you have been as a trader following your own rules. Identifying and tracking this profit 'leakage' is the first part in working on a plan to improve your performance.