Resolving a dispute over the Kelly formula

You have a distribution of returns, not binary outcomes.
For an intelligent discussion of this matter see Sinclair's first book.

 

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.

 

Which Sinclair? I found a ton of Sinclairs on Amazon. What's the title of the book?

 

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.

 

According to my calculations, both A and B have the same expectancy:

E(A) = 0.55 * 433 + 0.45 * (-407) = 55
E(B) = 0.1 * 1000 + 0.9 * (-50) = 55

 

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.

 

In this PARTICULAR case, we have a binary distribution. Either you win X or you lose Y. No other outcomes.

 

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.