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Comment by epapsiou | Hacker News Reader

This is so timely. I made this with a buddy of mine to help us figure out optimal allocation for stocks in a portfolio using Kelly. https://engine.oracled.com/

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Another word of caution. The Kelly Criterion depends on each event being independent. Lets say I'm told to allocate 50% to QQQ and 50% to SPY. Those may independently be correct, but since the NASDAQ and S&P are highly correlated, this wouldn't be the correct allocation. You've essentially allocated 100% of your portfolio to one probability, rather than 50% to two independent probabilities.

This is an obvious example. But really all stocks (or at least sectors) are correlated just like this. So other examples wouldn't be so obvious.

True. Correlations are not modeled in here. And the fact is once shit hits the fan all correlation converge to 1. This is not a tool for helping you with that. All it does is tells you - don't put more than x% in this stock. It answers a very specific question --- I like XYZ, how much should I buy?

There are many assets and securities that are inversely correlated with the stock market like gold or inverse ETFs.

> The Kelly Criterion depends on each event being independent.

That's not quite true. The Kelly criterion (generalised to portfolio selection) requires the joint distribution of outcomes, which captures all correlations.

Taking somewhat recent historic outcomes as representative of the joint distribution of outcomes (this effectively becomes the Cover universal portfolio), I'm guessing the Kelly criterion would suggest something like 50 % cash and 50 % equity, if those are the only two options.

How does kelly criterion apply to sizing portfolio positions? From what I understand trying to use it in the stock market is a fools errand.

Options Implied probabilities gives a way to understand what market is pricing volatility at. Given the option price, it is not hard to get the probability distribution. There is not judgement here. Just plain Math. Here is some explanation - https://engine.oracled.com/FatKelly

Be careful using this formula too naively. Predicting tomorrow's expected return is quite difficult, though predicting tomorrow's expected volatility is doable.

I have no idea how this website works, could you explain?

The probabilities are calculated using options market. Options (and risk neutral distribution) gives you the market implied probability of stock going up/down and by how much.

It’s telling me I should short SPY and go long GameStop and AMC… Sounds suicidal to me.

This is beta hedging, it works on the assumption that when SPY performs positively, your risky basket will outperform SPY, but if there is some systemic risk-off event, your SPY short will at least dampen if not fully cover any losses made in your risky basket

Good day, you lose -0.5% on SPY but gain +2% on AMC

Bad day, you maybe gain 0.5-1%% on SPY and lose -2% on AMC

But this is only true if expected returns and beta are constants, right?

Ha yes. We had same reaction. But it is what the market is pricing probabilities at. And if you see the returns market has been right so far. We are also skeptical. But numbers don't lie. I think it is a good way to size how much to buy if you really want to buy GME. Don't put all your money in but limit it to 10% as Kelly suggests

There's rumors/fears about SPY dipping from the next CPI report, could be causing options/sentiment to lean downwards in the short term.

Some estimates end up being negative, is that intentional? E.g AAPL.

Yes that happens when vol skew are a certain shape. I think better use this link. Gives a better understanding of what is happening

https://wiki.oracled.com/

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