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Originally Posted by BrianTheMick2
They don't actually ever use the Kelly criterion. They instead use an extension of it that can be found here:
https://arxiv.org/abs/1411.3615 or they use Nikhil Khana's simplified formula.
More commonly they use MPT or PMPT.
Okay, we cleared that up. So you substituted "Kelly Criteria" (sic) for "kelly ratios", LOL.
Here is a link to a sportsbettingreview.com thread posted years ago by the famous Thremp, asking about deriving kelly ratios for correlated teaser wagers. Ganchrow, who undoubtedly applied theoretical math concepts to wagering better than anyone in the public space, avoided the theoretical solution in this case and instead recommended a direct numerical method, Solver. His approach works equally as well with investing, which is simply another form of wagering.
And the link you provided is for a single investment vehicle with a distribution of payoffs. Not exactly what we are discussing.
Here is a link from Pinnacle for deriving proper kelly ratios for a mix of wagers. Basically what Ganchrow posted. Any idiot familiar with Excel/Solver can do it.
You're welcome.
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One, your guess on the ratio is incorrect, and it isn't close. The variance of QYLD is not 1/3 of QQQ.
So kelly ratios of 2 investments is 1:1 inversely related to their respective variances? Seems like you are missing something important here in deriving kelly ratios in a portfolio. I will let you slip that in like "Kelly Criteria".
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Two, if we pretend that the 3x is correct(which it isn't) that leaves you with less money to allocate to the rest of the portfolio.
You have to subtract out the risk free rate (at the very least) for the additional capital outlay. The proper allocation is approximately 0x given that it doesn't even diversify away any risk.
So do I have this right? A covered call strategy on a stock does not reduce risk compared to holding the stock alone? Hence a portfolio should hold zero covered calls in a portfolio?
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It is calculable. Commonly, we multiply the (known) sample variance and mean returns by constants to be safer when there isn't enough data to be confident that it reflects the population mean and variance.
I'll take Ganchrow's word for it, there are better ways to do it.
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More to the point, it is silly to just throw an utterly random* 3x as a solution instead of at least doing something approaching math.
Sure, I pulled it from thin air. That being said I have not seen any refutation from you on what exactly it is (unless you stand by zero, which has to be a joke). The point being I can create any hypothetical return model to yield a 3x kelly ratio for QYLD and QQQ. As nobody can predict the future, the model may be grossly in error, or it could be close to optimum.
I have no idea the holding periods for the call options, nor do I know the ratio of covered calls IRT the underlying. I also don't know the ETF cash position. So it would be close to impossible to accurately determine an outcome distribution with these unknowns.
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*This was as polite as I could come up with. Saying that the number was pulled out of your ass would denigrate asses from which more accurate numbers have been pulled.
It seems you did some internet searches to try to come up with answers, and instead you post stuff like "Kelly Criteria".
You started with the assertion that calculating kelly ratios is not possible for parallel (i.e. not sequential) investments, which is absurdly not true.
From Wikipedia:
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The Kelly criterion maximizes the expected value of the logarithm of wealth (the expectation value of a function is given by the sum, over all possible outcomes, of the probability of each particular outcome multiplied by the value of the function in the event of that outcome).
The above definition obviously includes parallel investments, as they aggregate to a distribution of outcomes (e.g. returns), each with a respective probability. It does not get much simpler than that.
I have never seen the words "Kelly Criteria" recorded anywhere in relation to investing. I think you just made it up.
I could go on refuting your post but I don't see the point.