Thoughts on | Probability Distribution based Position Sizing, Entries and Exits

With the long weekend ahead of us, here in India, I thought of spending a good amount of that time writing, so I went through my notebook for ideas to blog about and this one stood right out.

So here it is, this is how I go about marrying NIFTY stats with my sizing, entries, exits and risk management.

I typically structure the markets (^NIFTY)  in four parts, ie from a time of the day perspective and the probability of range formation in that time window.

For example - I look at the average range formation / time. In other words the average of each of the columns that you see below.

That gives you a sense of the probable range in terms of Points.

Meaning if the average range is 100, 26 happens in the first minute and 26 in the next hour and so on.

So as you can see the 2nd and the last time segments are the ones which offer the maximum probability of range formation. No sense in betting on the other time segments when you know, there is no statistical edge in there.

This becomes your first filter or framework on which you will now build the Position Sizing logic.

Position Sizing

Start with defining what would constitute 100% Size. This 100% should be such that, even if you size down to say 25% you should still be able to follow your scale out plan.

Example - For NIFTY since the lot size is 75 - and assuming you will do scale out in three parts t1, t2 and t3 with 50:25:25 % ratio (We will come to scale outs later in blog). You will need to trade with a minimum of 16 lots. So that even if you do 25% of your full size you will still be able to scale out with the defined ratio.

Risk Per Trade - We will maintain a risk per trade of 1% or 10 points or Rs. Assuming we trade slight ITM calls/puts for trading with an average cost of Rs. 200 Per Contract. 1200 which is our full size would cost us Rs. 2,40,000. The recommended capital allocation for this would be 5x meaning you will need to have Rs. 12,00,000 in your account assuming there is no leverage available for long option trades. So even if your stop hits for a given trade you will lose Rs. 12000 which is 1% of your total allocated capital.

Entries - The logic of Entries is largely based on the following data

  1. What time segment did we get the entry signal?

  2. How much of the day’s range is already done?

  3. Are the internals supporting or confirming the move?

Based on these inputs we decide to go with anywhere between 25% to 100% of our defined sizing.

Exits - Scale outs offer the most optimal risk-reward ratio based on my backtests. To understand why scale-outs work best one needs to understand the idea of Probability Distribution.

Look at the image below, you will see range and next to it the probability of that range occurring in that time window. As the range extends (with Mean as the reference) you will see the the probability of further extension only reduces.

For Illustration Only!

As common sense would dictate, you need to scale out of your position as the probability of your targets’ being achieved starts reducing.

Likewise for entries, if you are entering a breakout trade and the probability of further extension in that time window is only say 30%, where is the edge there?

I hope this approach, based on simple market statistics. helps you in structuring your trade sizing, entries and exits.

Again, do remember that markets are dynamic and these distributions have a seasonality to them, so you need to keep an eye on the changing market structure and trade accordingly.