Discussion in 'Risk Management' started by ironchef, Jul 4, 2017.
It arbitrary. To me there are no significant price points.
Maybe so but for someone who has been in this game for so long and is a successful professional money manager, your instinct must mean something? I would have guessed $14-$15.
Thank you for responding, I appreciate it.
Your advice is invaluable for days like today and weeks like last week:
By trading at < 1/4 Kelly, I am also limiting my losses. So, thanks to all you folks that help me understand Kelly and the risk of ruin.
Regards to all,
Here is a fun fact, if you bet the full kelly over a long enough period of time you are guaranteed to have a 99.9% drawdown. If you bet 1/2 Kelly, you would think that number would drop a lot but no, you will still very likely to have a -~90% drawdown. The frequency of the significant drawdowns decrease but they are still likely to happen at some point
But after trading a long enough period, with positive expectancy, you will be up 100x, 1000x...., you can survive a 90% drawdown.
I believe your assessment is too apocalyptic. Here are the actual numbers:
Probability of a 99.9% drawdown is 0.1%.
Probability of a 90% drawdown is 10%.
Probability of a 99.9% drawdown is 0.0000001%.
Probability of a 90% drawdown is 0.1%.
The corresponding formula is:
p(f, d) = (1 - d)^(2/f - 1)
f: Kelly fraction (such as 0.5 for half-kelly)
d: drawdown (such as 0.9 for 90% drawdown)
p(f, d): probability of drawdown d while betting Kelly fraction f
I believe the quarter-Kelly is a reasonable leverage to take. There is a sufficient degree of risk aversion built into that quarter-Kelly bet. The full Kelly bet is risk-neutral (i.e. there is no risk aversion at all).
Thing is, if you trade long-enough, its a near certainty. So I guess it depends on how frequently does your system generate trades. A 0.1% probability of death is no big deal if it happens every 10 years but if it happens every day, its certain to be a disaster. Also, wont your figures change depend on how good the system is?
The 0.1% probability is over the infinite time horizon.
No, these probabilities are the same, no matter how good or how bad the system is. What would change is the magnitude of the Kelly bet.
I run several monte carlo simulations with for a 50/50 system with a 2 to 1 payoff (2 gain or 1 loss). 5000 trades each for 34 trials. With full-kelly the avg max DD -99.4% and it reached that DD in almost every trial and when it didn't, it got close (-98%, etc)
With half-kelly the avg max DD was -89% in each of the trials and it reached that (or gotten close) in almost every trial.
My point is that it seems counter intuitive that risking half as much would still yield DDs that are similar to the full thing. -85%+ DD is quite typical in half kelly system betting and I wasn't aware of that. Advocators of half kelly betting never bring that up
It is also function of number of bets. It is true that if the number of bets is very large, then difference in draw-down between full kelly and half kelly is not that great.
We found that maximum drawdown depends on both the Kelly size and the number of bets. For example, the differences between the medians of the maximum drawdown of full Kelly and half Kelly were 0.18 , 0.3 and 0.1 respectively for 30 , 1000 and 100,000 bets. Therefore the half Kelly has a larger effect on reduction of maximum drawdown in the mid range (100 to 1000 bets) compared to other ranges. If one plans to play 100 bets, using the half Kelly size is a good strategy to reduce the maximum drawdown. However, if one plans to play more than 1000 times, the half Kelly may not have as much of an effect on reducing maximum drawdown.
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