Raw Transcript: How Kelly Criterion Affects Trading Allocation Strategy

Market Measures is our weekday research segment where we test trading concepts with real market data. Today we break down the Kelly criterion and why position sizing matters as much as strategy if not more. Stay tuned to discover how sizing mistakes can limit growth and how the Kelly criterion with real options examples helps you avoid them. Kelly's criterion is is an interesting it's an interesting mathematical uh >> theorem. Yes. Yeah. It actually applies. So when I when I started trading it was all about my poker history and trying to like translate poker strategy to the options world. And it was always like you know f pick your spots bankroll management high probability trades etc etc. But the Kelly criterion is actually something that comes up a lot too in the poker world in terms of like expected value, that kind of thing, implied value, expected value. So Kelly criterion is super important to understand from a conceptual basis. Um, and we'll dive in >> the growth formula from April 25th, 2025. The Kelly criterion helps determine the optimal fraction of capital capital to allocate in order to maximize long-term growth while reducing the risk of ruin. So a simple definition Kelly equals maximize growth and control risk through proper sizing based on edge applied uh implied value expected value that kind of thing. Next slide please. So the formula is expressed as F= P minus Q over B where F is the optimal capital percentage to allocate. P is the probability of profit, Q is the losing probability uh or the probability of loss and B is the net odds received or the amount one per dollar bet. Uh >> Q is also equal to one minus B. >> Y what I'm saying? >> Yep. Yep. So, just probability of profit and then the probability of loss ultimately. >> So, now that we've got that math stuff out of the way, uh, let's dive the last time I saw a formula. >> It's always funny whenever I'm looking for a formula, I always ping Dr. Jim. I'm like, "Hey, can you give me a formula for this?" He's like, "Oh, yeah. Here you go." Uh, let's use iron condors as as an example. So, $100,000 portfolio strategy one lot iron condor probability of profit 85% which brings your probability of loss to 15%. And the net odds of 20% for example $3 premium versus $1,500 buying power. So, the result Kelly recommends allocating 10% of capital for optimal long-term growth with virtually no risk of ruin. Um so risk of ruin can also be stated as how your bet size uh run out 100 times thousand times if it's too large. If your bet size is too large you don't allow yourself the ability to absorb variance against you. So that's we talk about this all the time like that's embedded in this in this segment here. Uh let's move to the next slide and we can dive deeper. So the sample portfolio should expect to see a 25% final profit after 100 trades with zero chance of depleting the capital. So again 10% allocated uh the mean final value 125k so 25% expected gain average draw down 37%. So this is a this is a good uh call out here that even though you're expected after 100 trades to make 25% your average draw down is still a pretty large number with 10% allocated. So and this is kind of a multiple multiple effect where if your allocation's too high that average draw down is going to really drag down as well. rune rate uh projected to be zero and uh you know the full Monte Carlo simulation 100 runs I know Monte Carlo traditionally is usually a lot more so like 5,000 10,000 uh simulations which gives you it gets you closer to that expected value right the more you run something the more you account for the tails in your favor and the tails against you and uh I think that's a good way to think about this like if you're entering a new trade or you're making an adjustment. If I run this a thousand times, do I feel good about what I perceive the results to be? And if the answer is yes, you're likely in a positive expected value situation. Uh, and I think that comes with like price extremes and things like that. But from a a straight up formula standpoint, 10% uh with the strategy in place, here's your expected mean return. >> It's pretty damn good. I mean, 25% profit on trades, zero. It really the the ruin rate is the most important thing. We we see this all the time. It's harder to trade small and smaller accounts, but at the end of the day, like if you're throwing on four or five trades and you're using all your buying power, like it's only a matter of time before things turn into ruin because you can't absorb the volatility of a tariff situation and like literally anything. And even this year, we're up 20% this year. The previous years it's we're up 20 30%. Within that annual return, there's still super volatile periods like we had a VIX of 60 this year. Yep. >> We just forget about it. Yep. >> Because we have, you know, the near-term memory, short-term memory. Uh, next slide, please. >> If we keep the success rate at 85% but change the odds, the optimal Kelly allocation will also change. Higher odds support larger, more aggressive position sizing. So if we uh look at uh 15% 20% and 25% odds your Kelly is going to uh ultimately go from 15 to 25. So the mean return if your odds are lower shift negative average draw down is significant rune rate is significant and this is just on a a 5% change. So, uh, I think when you look at a lower percent odds of of making money, that's when you need to really size down to account for the fact that you're taking more risk by way of a lower probability of profit. where if you have a higher odd probability to make money on this this simulation, you can use more of that uh allocation ultimately because you have significantly more uh winners versus losers. So, this goes back to this segment we talked about earlier, the question we we answered earlier of like you're going to always have losers. If you do 100 trades, 200 trades, 300 trades through a year, you're going to have losing trades for sure. But if you can turn those losing trades into lesser losses or scratches, it makes a massive difference as you can see here in your year-end results or your projected year-end results. >> I mean, it's amazing how different it is. >> Yeah. And another another call out here, this average draw down. So, we looked at the 20% odds, 10% allocation, average draw down of 37%. Slightly higher odds and more than double the allocation. You basically double your average draw down. So still have to understand that even in a you know 25% allocation situation you're going to have draw downs uh that are still pretty pretty high. Last slide please. Takeaways. Kelly provides a mathematical framework for optimal position sizing and many traders use fractional Kelly 25 to 75% to reduce volatility. option strategies fit Kelly well because probabilities and payouts are known before entry. Uh, and I think the biggest the biggest takeaway for me from a defined risk standpoint is just matching up your probabilities. Like I know we looked at this the other day. If I'm selling an at the money spread and I'm not collecting 50% of the width, I'm not selling the at the money spread because an at the money spread is a 50/50 probability. if I'm not collecting 50% of the width of that spread reflecting a 50% probability, that's not a great trade to make. So, just understanding those kind of things, like if you're at the if you're uh one standard deviation away and you're collecting one/ird the width, that's pretty standard. But when you have these situations where there might be skew affecting premium on both sides, if I'm expecting a 50% probability and I'm not collecting 50% of that width, it's a no-go for me. And that's that's just from this. Like that's literally mathematically from this but applied to real life trading. >> Yeah. It helps you realize when trades working are well in your favor potentially or when not to force trades. Yeah, I >> agree. >> 100%. >> That was a quick one. Rapid fire. >> Wait, what? >> Um, >> got one. >> Another one. We got a bonus. >> Another one. >> We got a bonus. What to expect after a 10% decline from March 28th, 2025? Um, what what would you expect after a 10% decline? Uh would after a 10% decline, I expect the market to be higher six months later. >> Bingo later. That's it. That's the show. >> Uh >> I've seen these things before. >> Yeah. Yeah. Let's dive in. Uh frequency of 10% drops in the S&P 500 within 1 month is uncommon for a 10% drop. Historically, it takes an average of 25 days for the first 10% correction in any 30-day period. Uh and you know these are these dots are there but this is over a from when I was in high school to now period like this is a long time. So 10% drop we've got a handful of them and they do happen. They they will happen. They will continue to happen even though we're in this crazy bull market. Like they will continue to happen. >> I traded in all of these. >> Yeah. It's nuts. It's wild when it does happen cuz in your mind you're like the world is ending. The markets don't matter anymore. Everything's going to zero. Well, I know we're talking about the frequency attention 10% drops and what I just said is true, but we I think the best thing to think about as we go through these slides is >> um sizing, right? Because the 10% drop can turn into a 15 to 20% drop. And that's what we're always scared of. That's why we don't jump all the way in sizing. >> Yep. Uh and this speaks directly to the year-long trade in MEES. Like you have to be able to withstand any variance. And that's the problem that a lot of people run into is they they want to they believe that there won't be a 10% drop in whatever year they're trading it in and they size up to account for a lack of a 10% drop and eventually it's going to happen. So if you know that eventually it's going to happen and you account for it now by staying super small, it's just a a totally different world that you're in, especially in the S&P where it's it's very predictable in the sense of like these things are going to happen, but over time they've always recovered. So, if you can account for that, you're in a whole another ballpark in terms of uh future trade expectations. Next slide, please. When we analyze the 30-day window after the first 10% market drop, we found that in 32% of occurrences, the market fell even further. Only two occurrences, 11% saw the price rally all the way back to pre-drop levels, both happening in 2008. Interesting. The average return during the 30-day period was less than 1%. All these findings indicate that the market recovers from these large drops much more slowly than it moves south. So the old adage uh escalator up, elevator down. Y >> there you have it. Uh it's just hard to time when that elevator is going to drop. >> Mhm. >> Um so yeah, interesting to see that within that 30-day window, only two occurrences, both in 2008, which just goes to show how wild 2008 was. uh takes a longer time, but the longer the longer you go out on the horizon, the higher the probability that that has recovered because we're sitting at all-time highs or close to it now. Next slide, please. Everything starts to improve when the duration ex is extended. As we just stated, we find the markets show higher chances of recovery after 2 months, although still only less than half of the events saw a full recovery after 3 months. But still these are high percentages in terms of if you see a if you see a 10% correction full recovery in 90 days almost 40%. A full recovery is a big recovery. Uh and if you have a if you think about it mathematically if you have a 10% correction to the downside that's almost a 20% correction back up from the new price point. So that's pretty substantial when you think of opportunity. >> Yeah. It's what we saw this year. What 20 almost 20% correction downside of more than 40 to 50% higher in a couple months. >> Mhm. Next slide, please. Uh it took less than a month to rally back 50% of the original price. Makes a lot of sense. This is much quicker than expected. There's only one occurrence that it took longer than 6 months to recover 50% which was in 2022. Uh, and that makes sense too because 2022 between 2020 and 2022 was co and that was the time that I saw extended volatility being heightened. Like that was when VXX, UVXY, the VIX, like all of those things were popping and we were elevated with 25 to 30% implied volatility. That was the time where uh the president would take the stand and markets would fly around at 4:00. Like it was crazy times. >> Yeah. >> I remember literally like me, Nick, and Kevin would get on a Zoom call for those press conferences, crack a beer cuz everyone was just at home and we would just watch them and watch the markets go like fly around. It was crazy. >> It was wild. I mean, because again, it was all determined on what was going on with with CO, etc. >> Yep. Last slide, please. Uh recovery speed 100%. It took about three months to fully recover from all the losses. Uh partial recovery recovery is more realistic early on. Uh but maintaining some negative delta and selling premium at high IV may help before full recovery occurs. Um but at the same time like if you know that the median is 3 months for a full recovery, I'd rather lean bullish in those situations. Like you can still sell premium on both sides for sure. Uh, but this is the this is one of those adjustments that I'm personally making in the sense of like if you believe this to be true going forward then into these drops like you probably want to pick up some some delta even just a little bit or at least have a plan to offset delta to the upside if you do get that quick recovery. You can keep shifting things higher and uh trade that new range for sure. Yeah, I try to pick up longer deltas in these type of situations at least a month maybe maybe two months out because again it takes some time and you never know. This study was done says March 28th 2025 whole lot going on then if I could have talked to those people I'd be like hold on just wait for another two weeks but we don't have that ability. That's why sizing matters.