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Resolving a dispute over the Kelly formula
- Thread starter Ghost of Cutten
- Start date
Quote from Peternam:
for this reason , a monte carlo simulation is a better approach, no ?
Monte Carlo solves some problems but has other pitfalls. The bottom line with all these mathematical games is that you're trying to optimize future position size based on past events, it's usually in the future where the unexpected happens. It all really depends on the nature of your edge, true edges may only be limited only by liquidity, but for statistical edges, the only thing you can be sure of is that shit is going to happen and all the clever position sizing isn't going to help at that point.
Quote from Visaria:
Your calculations, ghost, are correct. Note that both of you had the same answer, 5.5%, for setup B.
However, your conclusion that set up A is better because the Kelly fraction is higher than that of setup B is incorrect. All the Kelly fraction says is how much you should bet, on each trade, of your existing bankroll, in order to maximise the long run return.
Good second point. B does have a much higher expectancy, which more than offsets the lower bet size, and gives higher % return potential over the long run. In theory you would make more money from it, although in the real world such a low win rate would be very difficult to trade due to the potentially huge losing streaks.
Quote from Ghost of Cutten:
Good second point. B does have a much higher expectancy, which more than offsets the lower bet size, and gives higher % return potential over the long run. In theory you would make more money from it, although in the real world such a low win rate would be very difficult to trade due to the potentially huge losing streaks.
No, it's as the previous poster says, same expectancy.
I think you are a little confused, ghost. I will help you out!
If you did 100 trades using setup A and 100 trades using setup B, you would "expect" to make 55 x 100 = £5500 in each case. Each of the trades in setup A, you risk £407 and each trade using setup B, you risk £50. Your total risk for the 100 trades is £407 x 100 = £40,700 using setup A and £50 x 100 = £5000 for setup A
At the end, though you expect to make the same amount.
Quote from Eight:
I've never understood that either. What, one of your OTHER systems placed a trade and you don't know which system will hit it's target first?
I've never needed to fully understand Kelly so I never fully investigated it but I suspect that Kelly's formula is just too elegant and too simple to be accepted by some... I noticed something a very long time ago: really smart people, I mean IQ >175 maybe, they come up with very simple solutions to complex problems. I love to work with people like that, they are rare but I found that trying to emulate the way they approach things can be very helpful. I'm assuming that Kelly's thingy is one of those very simple solutions. The simplifying assumptions are that all the trades have about the same win/lose probability and the same win/loss sizes. It's all normalized to percent of account size so it does indeed appear elegant.
Investing pros argue against it because of the potential for account volatility. They know their clients won't like it at some point. Those arguments mean nothing in the context of an individual trader seeking the steepest account balance curve.
No. The Kelly formula may look elegant and simple but it's derivation is somewhat more complex as is its proof.
Investing"pros" may argue against it. They have good reason to. If you don't really know p (probability of a winning trade), your estimate of p could be way off and hence using Kelly could bankrupt you.
Quote from Visaria:
No. The Kelly formula may look elegant and simple but it's derivation is somewhat more complex as is its proof.
Investing"pros" may argue against it. They have good reason to. If you don't really know p (probability of a winning trade), your estimate of p could be way off and hence using Kelly could bankrupt you.
well wtf, it's made to apply to systems with a known rate of wins and known win/loss size ratio. Investment "pros" that can't beat the indexes should stay away from it LOL.