A New Kelly Formula

Given years' historical data for 500 symbols in SnP500. (2000 rows and 500 columns, e.g.)

Why don't you try simulation, for profit based on the new formula?

and compare with plain Kelly.
 
I think you misunderstand. I think the Kelly Criterion and Optimal-f are useful metrics. Thinking about your strategies both from the point of view of system logic and optimal allocation is correct. What I am suggesting is that the single most important thing to understand when using quantitative strategies is a knowledge of how they can distort reality. This is true up and down the entire technology stack.

When you know that your suspension can only handle a 150 bank turn, you don't attempt a 200 mph turn. Knowing your tools and their strengths and weaknesses can keep a system out of trouble.
 
I agree with Nitro...also it seems as if very few have read, let alone understood "The Leveraged Space Model" and where it takes you.
 
nitro said:
I think you misunderstand. I think the Kelly Criterion and Optimal-f are useful metrics. Thinking about your strategies both from the point of view of system logic and optimal allocation is correct. What I am suggesting is that the single most important thing to understand when using quantitative strategies is a knowledge of how they can distort reality. This is true up and down the entire technology stack.

When you know that your suspension can only handle a 150 bank turn, you don't attempt a 200 mph turn. Knowing your tools and their strengths and weaknesses can keep a system out of trouble.
More...
I never claimed the formula I posted is perfect. All Kelly formulae are necessarily approximations, except for the binary case (i.e., coin flips and the simplest casino bets). The problem with the 'classic' Kelly formula for traders is that it tries to fit the complexity of trading into the binary straitjacket, with silly stats like winrate, average win and average loss. My formula avoided that trap, which is why it produces generally better estimations of true Kelly.

As far as correlations, that's something I have to work on but there are shortcut techniques that can be imported from the gamblers, e.g., how to resize the Kelly fraction when playing multiple hands of blackjack against the same dealer hand. Of course one can always just go directly to fractional Kelly (half or less) and save a lot of time and effort. Probably still beats the hell out of the 2% rule.

But I am curious: do you still prefer optimal-f to Kelly?
 
kut2k2 said:
OK, this is my last post on this sub-topic .

After one loss, your drawdown is 1-(1-.05*7.5) = 37.5%
After 2 losses, your drawdown is 1-(1-.05*7.5)^2 = 61%
After 3 losses, your drawdown is 1-(1-.05*7.5)^3 = 76%
After 4 losses, your drawdown is 1-(1-.05*7.5)^4 = 85%
After 5 losses, your drawdown is 1-(1-.05*7.5)^5 = 90.5%

More importantly, your expectation is √((1+.20*7.5)*(1-.05*7.5)) = 1.25 : when you bet 7.5 times your equity in [ +.20, -.05 ], you can expect to gain 25 cents on average for every equity dollar wagered.

Thorp's ratio = mu/sigma^2.
Mu = .5*.2 - .5*.05 = .075 ; sigma^2 = 0.015625
Thorp's ratio = 4.8

Thorp's expectation = √((1+.2*4.8)*(1-.05*4.8)) = 1.2204917 :
When you bet 4.8 times your equity, you can expect to gain 22 cents on average for every equity dollar wagered.

That is all.
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your drawdown numbers look wrong. if i start with 750k and i lose 5% and then 5% again, i lose 73125 in total, which is 73.125% of my 100k initial equity, not 61%.
 
actually, scrap that, i get it....you take whatever equity u have left and multiply that by 7.5, to obtain a new account balance.....apols.
 
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