Deriving the Kelly Criterion to Maximise Profits
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Re: Deriving the Kelly Criterion to Maximise Profits
#2The Kelly criterion is almost never used as-is because it is very sensitive to probability of success, which is hard to know accurately and in many cases, dynamically changing. This is easy to see in an Excel spreadsheet. Changing the probability by even 0.01 percent can vastly shift the results. The article calls this out in the last paragraph.
The article mentions fractional Kelly is a hedge. But what fraction is optimal to use? That is also unknowable.
Finance folks, correct me if I’m wrong, but the Kelly Criterion is rarely used in financial models but is more a rule of thumb that says roughly if you have x $ and probability p, in a perfect world you should only bet y amount. But in reality y cannot be determined accurately because p is always changing or hard to measure.
Re: Deriving the Kelly Criterion to Maximise Profits
#3For the coin flipping scenario, what happens to the casino? Shouldn't they lose money in the long run as well? Or is it that they're under the kelly threshold with all the house cash?
Re: Deriving the Kelly Criterion to Maximise Profits
#4A million years ago, when you could still find video poker games with 100%+ theoretical return or poorly thought-out promotions offering enough cash-back to get you over 100%, we'd calculate the Kelly number for a given opportunity -- the bankroll necessary to ride out hills and valleys in favorable situations.
Spoiler: It's almost always 3-4x the value of a royal flush. So you needed $12-16k if you were playing a $1-per-coin game with a 1% edge at a pretty good clip.
And what do you earn with perfect play in that situation? The princely sum of around $30 an hour.
Re: Deriving the Kelly Criterion to Maximise Profits
#5The Kelly criterion is almost never used as-is because it is very sensitive to probability of success, which is hard to know accurately and in many cases, dynamically changing. This is easy to see in an Excel spreadsheet. Changing the probability by even 0.01 percent can vastly shift the results. The article calls this out in the last paragraph. The article mentions fractional Kelly is a hedge. But what fraction is o…
I am not sure what you mean by "never used as is."
The Kelly criterion is an optimization of capital growth (its logarithm) method/guide. Not using it doesn't change its correctness.
But yes you need to know the advantage/the edge you have. Like with pricing methods eg for European options for Black Scholes you need to know the volatility and there is no way to know it, you estimate. This is where all the adjusting for bias and ML comes in.
Re: Deriving the Kelly Criterion to Maximise Profits
#6For the coin flipping scenario, what happens to the casino? Shouldn't they lose money in the long run as well? Or is it that they're under the kelly threshold with all the house cash?
The casino will break even, but for the gamblers there will be a small number that win big, and a much larger number that lose out.
Consider two rounds, there's a 25% chance you 4x your money, a 50% chance you 0.75x your money and a 25% chance you 0.25x your money
Re: Deriving the Kelly Criterion to Maximise Profits
#7Here's a link to a bigger graph for the Blackjack Scenario:
https://github.com/obrhubr/kelly-criterion-blackjack/blob/ma...
I think it shows that Blackjack is not even theoretically winnable over time if you have to pay for information on the count in the form on minimum bets. The ideal case it that you bet $0.49 for every $1,000 in your investment pool when the count is extraordinarily high.
Even if you hack the casino's cameras so you know the count without having to be at the table, your reward is a growth rate that is very low per hand.
Re: Deriving the Kelly Criterion to Maximise Profits
#8A word that is good to know here is ergodic [0]. Which I must admit to not really understanding although it is something like the average system behaviour being equivalent to a typical point's behaviour. If a process is non-ergodic then E[X] is usually not as helpful as it seems in formulating a strategy.
Re: Deriving the Kelly Criterion to Maximise Profits
#9The Kelly criterion is almost never used as-is because it is very sensitive to probability of success, which is hard to know accurately and in many cases, dynamically changing. This is easy to see in an Excel spreadsheet. Changing the probability by even 0.01 percent can vastly shift the results. The article calls this out in the last paragraph. The article mentions fractional Kelly is a hedge. But what fraction is o…
I am not sure what you mean by "never used as is." The Kelly criterion is an optimization of capital growth (its logarithm) method/guide. Not using it doesn't change its correctness. But yes you need to know the advantage/the edge you have. Like with pricing methods eg for European options for Black Scholes you need to know the volatility and there is no way to know it, you estimate. This is where all the adjusting f…
But do you calibrate p (say through estimation) and then apply the Kelly criterion in your portfolio?
I don’t think it is used in this way. It swings too much with a given p.
Re: Deriving the Kelly Criterion to Maximise Profits
#10A word that is good to know here is ergodic [0]. Which I must admit to not really understanding although it is something like the average system behaviour being equivalent to a typical point's behaviour. If a process is non-ergodic then E[X] is usually not as helpful as it seems in formulating a strategy. [0] https://en.wikipedia.org/wiki/Ergodic_process
Some math/finance nerds made a whole YouTube channel about ergodicity, which I've been really enjoying: https://youtu.be/VCb2AMN87cg
Nassim Taleb also talks about this quite a lot: https://youtu.be/91IOwS0gf3g
TL;DR: while a single investment may be ergodic, portfolio management (the math behind weighting successive and concurrent investments/bets) is not, as it has a strong dependence on all prior states.