Excellent post and totally agree. I wrote investment bankers for effect as opposed to hedge funds since people who I have spoken to are fixated on investment banks so I have written the example in that manner. I am well aware of the Volcker rule and the effect it has had on the banking industry and will be coming back to that in the future hopefully as a bigger topic. But thanks very much for your informative and accurate point.
Part 3: Probability and drawdown
Let us imagine for now that you have gone back to your math textbooks and you now know how to work out the chances of failure of a system (note there are weaknesses to this using just permutations that I will come onto in another post). The next topic is about applying probability and risk to drawdown. Again, we are looking at the coin flipper in particular and of course, we do not think that he has a very high survival rate. What if he cut down his risk? Instead of risking 20% on each coin flip, he had a bigger equity size and decided just to risk 10%. He goes and talks to his manager and they agree. We can then work out the risk compared to his coin flipper neighbour who has also been given a raise (investment bankers (or read hedge fund if you prefer) are fair to their employees). However, this coin flipper is still risking 20%.
Lets simplify and say that we discount the different combinations and say that only 5 in a row losers will blow an account. The 20% coin flipper has 1/32 per flip chance of blowing up, whereas the 10% coin flipper has 1/1024 chance of blowing up. All things considered, the lifespan of the 20% flipper is 32 flips, whereas the lifespan of the 10% flipper is 1024 flips (ignoring combinations which would reduce both flippers lifespans).
The 20% flipper starts with $10 million and ends up with $3 418 000 000 at his 32nd flip where he is past his time to blow up.
The 10% flipper starts with $10 million and ends up with $24,328,178,969,536,839,355,491,975,986,536,468,220,739,584, 000, 000 after 1024 flips. Of course at 32 flips, the 10% flipper only has $211 million and feels a fool compared to the 20% flipper, but in the end has a far superior account.
Applying this to trading directly - I realise few people trade 20% risk, but there are plenty of people who trade 2% risk as opposed to 1% risk. The calculations would be very similar in how much would be made overall, and the lifespan of the trading account. I was messaged by someone recently who asked if I provided trading signals (I do not) and I mentioned that signals were a bad idea because money management was a large part of trading, and that signal followers would multiply up their risk without understanding the consequences - the underlying assumption is that if you double risk you just double the drawdown but the consequences are far more far reaching as I have posted.