How can risk management significantly increase your gains? This post looks at how simple maths, Monte Carlo simulations and understanding probability can help you.

Firstly, a simple example using the flipping of a coin.

Imagine for this example you have a 50% chance of heads and a 50% chance of tails. If the coin lands on heads you win £1.20 and if it lands on tails you lose £1. Due to knowing the probability of winning and expected value for wins and losses we can calculate the expected value and expected return over a given number of coin flips. The maths is as follows:

Expected Value = % of Wins x Unit of Risk - % of Losses x Unit of Risk

Expressed another way using the above coin flipping example, Expected Value = [0.5(1.2) - 0.5(1)] = 0.1

Therefore, the coin flipping strategy has an expected value of 0.1. Our coin flipping strategy having a positive expectancy is essential to the remainder of this post. If you want to consistently lose money, look no further than having a negative expectancy for your strategy.

Let's progress with our coin flipping strategy and imagine you had a portfolio balance of £100,000. What would you risk per coin flip (trade)? 2%? 4%? 8%? 10% 25%? Would you then keep this at a fixed amount, such as £2,000 (2%) for every coin flip (trade) even if your account value was growing or shrinking? Or would you use a fixed fractional percentage of your account value so your bet size in monetary terms increases or decreases subject to your account size but your risk is fixed and remains the 'relative' same.

Do you have any idea what is optimal? This is where this post gets exciting if you're this way inclined. Otherwise, you probably stopped reading at the first Expected Value calculation! Onward!

So let's say you use 'conventional wisdom' and decide to risk 2% of your account equity per flip (trade) which is £2,000. You also decided not to use 2% as a fixed fractional percentage and thus bet the £2,000 on each flip (note, you could go bankrupt doing this and the Monte Carlo simulations expand on this point). What is your expected return over the course of 250 coin flips (trades) I hear you ask.

Remember our Expected Value formula from earlier, it all leads into this example:

Expected Value… 