Kelly Criterion & Risk Of Ruin As Risk Management Tool

srinir said:
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.

https://elliotnoma.wordpress.com/20...-size-and-number-of-bets-affect-max-drawdown/

Conclusion:
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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In my simulations I did find that the median drawdown improves a lot (less than half) with 1/2 kelly vs full kelly. But since the max DD needs to happen only once to have it be computed, at some point (in the super long-run) there will be an unlucky streak that will lead to a big drawdown.
I suspect that this author found that small trials tend to improve max DDs simply because small trials dont have enough data for them to be unlucky enough. After all the long-run is a series of short runs
 
Yes. If criterion is max DD, then only way to reduce that number is the leverage. He states that in his study.

In my opinion, Max DD can be curtailed by cheap option cutting the very left tail off. Personally i am more interested in Median DD rather than max DD for leveraged trading back test.
 
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nonlinear5 said:
I believe your assessment is too apocalyptic. Here are the actual numbers:

Full-Kelly bet:
Probability of a 99.9% drawdown is 0.1%.
Probability of a 90% drawdown is 10%.

Half-Kelly bet:
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)

Where:
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).
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Where can I find a derivation of the formula?
 
srinir said:
Personally i am more interested in Median DD rather than max DD for leveraged trading back test.
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I agree. From my monte carlo simulations, using 1/2 Kelly doubles the return/median DD (CAGR/Median DD) ratio while cutting returns by 33%. So it looks like a good choice. Something that I need to research going forward is to find the optimal kelly fraction that maximizes that ratio (Return/Median DD). I will try to find that when I have some time
 
Daal said:
Something that I need to research going forward is to find the optimal kelly fraction that maximizes that ratio (Return/Median DD). I will try to find that when I have some time
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From my initial tests it looks like this is not worth pursuing. Usually, for most systems I tested the lower the kelly fraction the better that ratio is. So if someone wanted to maximize for that, they would just bet a really tiny amount that wouldn't be worth if at all. In general it seems that the closer to the full kelly one gets, the more capital growth vs max DD is maximized
(which can be measured by things like the MAR ratio). This leads to other risk adjusted metrics (like Sharpe, K-Ratio or that CAGR/Median DD ratio) look worse relative to smaller fractions. But if someone wants to maximize for those metrics, than they might just keep decreasing their bets to the point its a waste of time. So in the end its all about a balance that one has to find
 
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Jason11111111 said:
Suppose my portfolio is 10k.
Kelly criterion = 10%.
It's saying i should risk bet 1k /trade position or I should risk 1k as my stop loss?
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The Kelly criterion defines how much of your account value you should put at risk. In your example is this 10% of 10k, so 1k. This is the total risk of all open bets that you are having. So if you have one trade open, you can place a stop at a loss of 1k. However, if you are having multiple trades open at the same time, the total risk of these trades should be capped at 1k. Thus, not 1k for each position, but a smaller value for each position.
 
HobbyTrading said:
The Kelly criterion defines how much of your account value you should put at risk. In your example is this 10% of 10k, so 1k. This is the total risk of all open bets that you are having. So if you have one trade open, you can place a stop at a loss of 1k. However, if you are having multiple trades open at the same time, the total risk of these trades should be capped at 1k. Thus, not 1k for each position, but a smaller value for each position.
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That's like I had I to all in for each trade . lol
 
I have a strategy :
The strategy is used in forex and futures.
Win rate is 90%;
Winning amount is 6 times of loss amount.(I set a stop,the stop hit 9 out of 10 times)
Can Kelly solve this?
If not, what method can be used to solve it?
When I used this strategy, I set my leverage at a level that if my stop hit, l will lose 50% of my capital. Is this leverage too aggressive?
 
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