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Why Size Matters?

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The Most Important Factor

Most people think that the most crucial characteristic of a trading strategy is per cent winners and net profit. But they consider the later as the result of the first one. To try to improve this beloved parameter, people dedicate hours, days, and months to study the most reliable entry methods possible. But my thesis is that the most critical element in a strategy is a position sizing methodology.

So, let’s do a small example. Let’s say we have two traders Bob and Rachel. Bob is from the old school of “give max per cent winners, and I’ll do the rest”. Rachel is from a new school that think give me a profitable system, and I’ll do the rest.

So, Bob chooses a 75% profitable system and made the following results, with nominal risk of $200.

Total ten trades:

200, 180, -400, 150, 90, -350, 250, 350, 100, -250

Final profit: 320

Rachel mimicked Bob’s trades because she trusted the system. So, she focused on what she considered more important: Position size and loss control. She had decided to trade 2% of the running account balance, and she started with 10K dollars. Therefore, the same initial risk than Bob but cutting losses short.

So here we show Rachel Trades:

200, 183,6, -207.7, 152.6, 93, -208.4, 255.32, 366, 108,4 -218

Final Profit: 724,82

If, both Bob and Rachel had the same initial 10,000 dollar amount in their trading accounts then at the end of the ten trades Bob would have made 3,2% on his account and Rachel  7.25%, slightly doubling Bob’s profits.

What have we learned?

Profits improved by two key elements:

  1. Cutting losses short
  2. Position sizing proportional to the account balance.

However, to optimise position size, the trader needs a trading system, a systematic methodology to take trades and manage the positions. And, also, he needs to record all the trades for further analysis. Which type of analysis? There are several analyses that can be made using a trading track record. The study that is related to the position size is mainly drawdown analysis.

Position size and Risk

We have already dealt with this before. The fact is that the drawdown of a trading strategy is not constant. It is linked to the position size. That will appear obvious when I’ll explain why.

Let’s say we have a system that is 50% profitable with a mean reward-to-risk ratio of 2. That is a fantastic system. It’s similar to a coin toss, but we win 2 dollars per dollar risked if heads and lose one if tails. That means we would earn fifty cents per dollar risk on every trade on average.

The logic then tells that if we bet 100 dollars on every trade, we will get 500 dollars after ten trades. And if we bet 1000 dollars, we will get $5,000 after that, and so on.

The problem arises from two issues:

  1. There is only a 50% chance to win on every trade
  2. Leveraged bets may carry ruin if the trade wipes all the available funds.

On this case, it is evident that if we have only 1000 dollars, bet 5,000 and we get a tail, we went broke.  Therefore, we need to know the characteristics of the trading game we are doing to optimise the trading size to it.

Why does drawdown happen?

Drawdown happens because there are losing streaks. A losing streak is a repeated occurrence of losses. This is related to the probability of losing, which is 1-percent_win

let’s analyse the current case of a fair coin toss. The probability of one losing play is 0.5 or 50%.  What is the probability of two losing tosses? it seems intuitive that to be 0.5 x 0.5 = 0.25 or 25%, because there are two instances with 50% chance each.

If we add another losing position to this one, we should multiply again by 0.5 the previous value 0.5 x 0.5 x 0.5 = 0.125 or 12.5% and so on.

The general formula to compute the drawdown is:

Prob_n_streak  = Prob_Loss^n

where Prob_Loss is the probability of a single loss and n is the number of streaks we want to compute.

As an example, the probability of getting eight tails in a row in a fair coin toss is 0.39%. It seems tiny, but over thousands of trades, the likelihood of getting one event like that grows and grows. That means,  0.39% is the probability when the trader makes a limited amount of bets. When continually betting, in the end, the probability approaches one.

That means treaders must be prepared to withstand drawdowns because they will happen.

How to approximate your ideal Position Size?

You should, first, honestly, decide how much of your capital are willing to lose before it’s too much for you and close the account. Let’s say you can withstand 20% drawdown.

What you need is to split this 20% drawdown so that the chances of reaching it is minimised. In systems with reward-to-risk factors higher than one and per cent winners equal or better than 50%, it is ok to assume that it is unlikely to get more than ten losers in a row, but you can add extra protection and decide you wanted to be protected for 15 consecutive losers. That will come at the expense of a reduction in profits.

Then, the equation is easy:

My individual positional risk = 20%/15 = 1.33%

That risk will be dynamic. Therefore the dollar risk will vary in sync with your account balance. That means that as the balance decreases with the incurred losses, your dollar risk will diminish, and as the balance grows with the gains, your risk will increase.

Using this strategy, the probability of ruin is also minimised.

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