Bad Kelly

[jack hershey]

Quote from bustermu:

kut2k2,

In your "Kelly for Traders" thread, you have:

k ~ sum[Ri]_n / sum[Ri²]_n

This is sometimes expressed by blackjack card counters as "expected return over expected squared return". Six little easy-to-remember words.

The best things about this approximation are (1) it can be instantly updated with each new completed trade (or each new count after a blackjack hand) and (2) it will always underestimate the actual optimal betting/trading fraction, thus reducing the dreaded "Kelly risk".

You have provided a counterexample to part (2) of the above statement.

Thanks,
Jim Murphy

the numeric that is the R value about which this stuff fouls up is R = 1.

k goes to zero unless R < 1.

But if R < 1, then there is no edge.

This thread could be in chit chat at some point.

 

[Daal]

What is the difference between your good kelly formula and the Optimal F? It seems that you are trying to reinvent the wheel here, the Optimal F already corrects lots of problems with the Kelly and it more applicable to trading.
It is based off the worst possible loss instead of 'average loss', it pays to be cautious in estimating the worst possible loss in a black swan world of course

Another consideration that can make these numbers dangerous is the fact that lots of traders have multiple bets at the same time instead of one at a time like in casino games, these bets tend to correlate given that they are derived from the same trader

A fraction of the Optimal F seem to be the way to go

 

[kut2k2]

Quote from Daal:

What is the difference between your good kelly formula and the Optimal F?

Kelly is the true optimal trading fraction, "optimal f" is just some contrived crap that Ralph Vince created to try to profit off something that is available for free.

 

[Ghost of Cutten]

Quote from kut2k2:


One form of Kelly that is much better is

K = p/S - (1-p)/R , where

K is the Kelly ratio,
p is the winrate,
R is the average winning trade return,
S is the absolute value of the average losing trade return.

The problem is you don't know the future win rate, you don't know the future average winning trade return, and you don't know the future absolute value of the average losing trade return.

Given that you don't know them, you must estimate them. But the estimates will have a large margin of error. Since there are three variables, this will compound the error margin enormously. Your 'good' Kelly fraction will therefore likely be totally out of whack.

Also, this assumes no path dependency, due to the usage of average winning and losing trade return. In the real world, a bad streak can take you out of the game before your reach your optimal long-run result.

Variables put into position sizing should be i) as few as possible ii) requiring as little estimation as possible iii) as robust against erroneous estimates as possible. Sizing calculations should be based on worst case conditions, which means consecutive losing trade streaks, plus one or more grey swans.

 

[kut2k2]

I see this thread has been resurrected by someone I put on ignore and now you know why I put him on ignore. He confuses a formula I specifically named the LessBad Kelly formula and specifically demonstrated to be an overbetter with what I called Good Kelly. His obsessing with the degree of accuracy for calculating winrate, etc in a formula that is significantly suboptimal is like rearranging the deckchairs on the Titanic.

This level of reading comprehension difficulty and inability to follow a simple linear train of logic is quite sad and pitiful. Pray for him.

 

[Pipflow]

Really didnt knew the existence of this at all until i read this post.