129: Victor Haghani – Optimal Bet Sizing—Lessons From a Biased Coin Flip Experiment

Chat with Traders is brought to you by Trade the Pool. Did you know that every decade the market reinvents itself? Online brokers opened the doors, mobile apps made trading seamless, and commission free trading erased barriers. Now a new era has begun. Meet, trade the pool, limited risk trading. And now you also have unlimited time to reach the profit target. From now on, your trading risk is capped. and your trading opportunities are limitless.

Trade the pool funds home-based stock traders with up to$200,000 in buying power. That means you can trade larger positions and scale your strategies without risking your own savings. It's time to trade with more capital, making it truly worth your time and effort. Ready to trade the pool? Click the link in the description and join the stock trading revolution today.

Are you ready to get serious about trading? Then join Tasty Trade, Investopedia's best platform for options trading in twenty twenty six. Options, futures, and more. Tasty Trade has everything you trade all in one platform. Get low commissions, including zero commissions on stocks. So you can keep more of what you earn. Trade smarter with advanced charting tools, a pre-built strategy selector, risk analysis tools, and more features. Visit Tastytrade.com slash.

Tasty Trade Inc. is a registered broker dealer and member of FINRA, NFA, and SIPC. Podcast. What's going on?

Welcome back. Thank you for listening in. Now, to introduce my guest of this episode, his name is Victor Hagini. Victor began his career at Salaman Brothers in nineteen eighty four, starting out in a research role before joining their prop trading desk. In 1992, Victor left Salomon to become one of the founding partners of long-term capital management.

LTCM was an incredibly successful hedge fund. Some years, while using a lot of leverage, the fund would return over 40% until 1998 when LTCM failed in a spectacular fashion. Causing the Federal Reserve to step in and organise a bailout in order to prevent the possibility of a collapse in the global financial system. Victor took a ten year sabbatical after the dust settled, and in twenty ten he founded Elm Partners, which is an active index investing fund.

Victor mentioned to me that he didn't want to spend too much time discussing LTCM, but if you're interested to find out more there is plenty of info online and I've linked to a couple resources in the show notes which can be found at chatwithraders.com slash one two nine. But we did spend quite a bit of time on something I thought was very interesting, which is optimal bet sizing and how bet sizing alone can drastically alter outcomes over a large number of bets or trades, if you will.

Much of this discussion is in reference to an experiment Victor carried out, with some involvement from Edward Thorpe, on the patterns of how sixty one participants would bet on a biased coin with real money. You can find a link to the paper which was produced afterwards also in the show notes. Last thing, the sound quality isn't superb, so I do apologize, but I'm sure, hopefully, your ears will quickly adapt. With that being said, here is my guest for episode 129, Victor Hagini.

I read somewhere, I'm not sure how true it is, but your father was also a trader. Yeah, my father uh was a trader. He wasn't a trader in financial in the financial markets, but he was a trader in uh in the import export business, more that than an entrepreneur, but he was a he was also an entrepreneur and a businessman. Uh, okay, okay, that makes sense. So did he have any influence on you getting into trading? I mean, what got you into trading?

Well no, he did not have any influence on me getting into tr Trading. What got me into trading was John Merriwether and his team um asking me to join uh their trading group on the floor. I I had joined research at Solomon Brothers in fixed income research and after a few years of doing research they invited me to become a trader. I didn't I had no idea uh uh about it or uh didn't know if I would be I mean it w it wasn't something that I was planning on doing. Um my father though did

Influenced me to join Solomon Brothers. I had an offer from JP Morgan and Solomon Brothers, and I said, Dad, which one do you think I should take? I said the JP Morgan one is paying about forty percent more. And he said, sort of crazier place where if you do well you can go further. Which one is more bureaucratic? And I said, Well, JP Morgan's definitely more bureaucratic and he said, Well, go for the Solomon one then. You know, go go in there and have some fun. And he was right.

Now we won't spend too much time on this because there's some things that I definitely want to get into conversation with you about, but just give us a quick rundown on what you were doing at Solomon Brothers and then for anyone who, you know, is unfamiliar with you. Bring us up to speed on the long term capital management situation and then we'll get into some other topics which I think are quite interesting. So yeah, just give us a short rundown on your background in this industry.

Okay, sure. Yeah, so by way of background, uh you know, as I mentioned, I started at Solomon in fixed income research and then after a few years was invited to join the ARB desk, uh the government uh government ARB desk or proprietary trading desk run by John Meriwether that was kind of in the center or uh a prominent

um player in the book Liars Poker. Um and uh I I was the youngest uh trader on the desk and learned from uh all these other great people and became very very close to um to everybody and it became my family and so uh when a few of them, in particular John, left Solomon Brothers in nineteen ninety two. to uh start LTCM. Uh I had just gotten married, decided that I would like to stay with my uh with my

colleagues and mentors and friends. So I left uh I left Solomon Brothers um in uh late ninety two and I uh and and then after a while I gave it some more thought and joined with John

um and my other partners as one of the uh founding uh a partners at at LTCM. And then I moved to London with my wife because I had I had been in London before for school and university and I set up our London office and eventually had a a an excellent partner in the office, Hans Hofschmidt, and we ran all of the trading that we were doing in uh in sort of the European sphere.

And uh and then when Solomon sorry when LTCM failed In uh nineteen ninety-eight, I was one of uh probably a minority of partners that stayed to work for the thirteen bank consortium that took over our portfolio. and we liquidated it for them over the course of a little more than a year. And then I stayed a little bit longer to um to help my friends uh get get a successor hedge fund started called JWM Partners.

And um I forget the exact year, but I took a sabbatical and then which turned into a ten year sabbatical. around two thousand and one, two thousand and two, um which then eventually led to me founding Elm Partners, which I've been uh running for the last five years, which is kind of a um, you know, a big reverse of direction from very active investing at at LTCM to what we call active index investing, which is a much more passive, long only approach.

where we charge just uh we where we charge clients twelve basis points to help them to get efficiently invested in ETFs and index funds.

I know we don't want to get bogged down in this and we want to keep things moving, but The long term capital management situation was a very interesting event. For someone listening to this podcast who wants to find out more information about that and wants to kind of read up on that just out of, you know, curiosity and just interest.

Where should they go? I know there's a lot of information online and that sort of thing. I'm not sure how much of it is accurate. I mean, is there any credible resources which you'd suggest someone turn to if they're interested in finding out more about what really happened? Absolutely. So so the problem is that um the the problem with the writing about LTCM is that it was it was such a big news item that authors and researchers felt that they needed to write about it right away.

So the most popular book following uh LTCM is the Roger Lowenstein book called When Genius Failed. You know, it's it's a good read. It's a good read and and um you know it's it's it can't possibly be a hundred percent accurate, but it gets a lot of the facts of the situation correct.

But the problem is that it was written in such close proximity to the event that it it it really doesn't have the perspective um w where there's so much more valuable insights to be drawn that you would get In looking back at this um

You know, after fifteen years or so, and particularly after the um financial crisis of oh eight. So Nobody is really gonna write a book about L T C M uh, you know, that's a fresh look at it, say in two thousand and ten, looking back at that, you know, that's that's uh You know, from so long ago. So unfortunately that doesn't really exist. So the Lowenstein book, there's another book by a gentleman named um Oh, I just had his name in my mind. Uh Dun Dun

Dunbar. Yeah, yeah, Nick maybe Nick Dunbar. That was another book written at the time that came out just before Roger's book. So those are okay, you know, in terms of laying out what happened at the time. Those are decent and and Roger Lowenstein's a they're both good writers, so they're well written books. Sort of the most uh I would say, you know, to really get a uh a much better idea of the whole thing though, I would suggest buying the Harvard Business Study

Harvard Business School case study by Andre Perold, P-E-R-O-L-D. Uh so Harvard Business School did a case study on L T C M and so they collected a lot of facts and it's very concise. Um, and uh that's where I would really go to to try to get more directly at the facts and save yourself a few hundred pages of reading. So the Harvard Business School case study. I think those are really the best um resources for

trying to take a look at what happened. But you know, as I say, the best thing would be for somebody to write a book now reflecting on it, because I think that it I I think that the lessons to be learned from it are are different than they felt in the aftermath. Okay, okay, excellent. And I mean I'm sure as we get talking you'll probably draw on some of those lessons as we go. So um I appreciate you sharing those few resources.

Yeah, yeah, no absolutely. I mean we're all we're all a product of our experiences. So yeah, uh L L T C M was probably one of the biggest experiences, certainly was the uh certainly by far was the biggest business experience of my life.

Now, Victor, you first came onto my radar. You know, obviously I was familiar with the whole uh LTCM thing, but You first came onto my radar recently when you produced a paper. Now that paper was based on um an experiment, an experiment about a biased coin flip.

I'm not gonna try and explain what the paper was about, I'm gonna leave that up to you. Um, but I'd really like to talk about this. I I thought it was quite an interesting experiment. So just to begin things, what was the premise or idea of the experiment? Well, we uh we wanted to investigate how uh quantitative, financially trained people would approach wagering on a biased coin with real money. So we set up an experiment uh where we went out and ultimately tested sixty one subjects.

Where we gave them twenty one dollars, we gave them a computer program that had a biased coin that you could flip by pressing a button. We told them that the coin was biased, sixty percent to land on heads, and it was. And we told them that however much money they had at the end of thirty minutes, we would pay them that money out, uh, subject to a cap, and the cap they would find out about if they got close to it. So flip away for uh for a half an hour.

And within a half an hour, uh f you know, some people who flipped quickly were able to flip three hundred times. Um and you could flip any amount of the twenty any amount of money that you had in your bank account at uh you could wager on the flip of the coin uh down to a one cent increment. So that was it. That was the experiment. Okay, and how much would the participants make if it landed on I presume it was probably heads that paid out the sixty percent and then

Tales was the the losing side. How much would they win or lose for each, depending on which side it landed? No, so the coin was biased. So the coin would would land on heads sixty percent of the time, but the payout would just you would win or lose whatever you bet. So if you bet if you started off and you bet four dollars and it came and you sorry If if you bet four dollars on heads and it came up heads, you would win four dollars. If it came up tails, you would lose four dollars.

You could also bet on tails. Um you might say, why would somebody do that? But people bet a lot on tails. We told them it was sixty percent heads and and it was. But still uh people sometimes bet on tails. So you could bet on either side that you want. That was one of the things we were curious about.

And uh the payout was a one to one payout, but you had a sixty percent chance of the coin landing on heads. Uh, okay. I get it. So I mean that's that seems quite bizarre. Why did people bet on tails? I mean, especially if there was a much greater probability of it landing on heads. Why did people pick tails?

Well, we conducted some interviews afterwards, and the two biggest reasons that we found were one was um that and this is a well-documented uh bias that people have, is that they kind of feel that things that are random aren't random, that there's predictability in random things, right? So after a so people after a string of heads, like if there were four heads in a row,

They would be more likely to bet on tails. They couldn't resist. It was like, wait, there were four heads in a row. It's gonna be tails next. And there's a whole, you know, there's There's papers and papers written on the every one of these biases in in the literature. So that's been documented before. The other one, which was really interesting, which I got from my mom. So my mom wasn't in our sample, but I let her I I had her do the the uh experiment, but we I didn't count her in there.

And I said, Mom, you know, you you bet on tails sometimes, you know, why'd you do that? And she said to me, You know I know that I should never bet on tails. I understand that. That never should bet on tails. It's 60% heads. But you know It was just so boring and I couldn't help myself. So I think that this boredom is really important. Um it's a really important um aspect of of of what of what goes on. You know, that just sitting there and and just betting as fast as you can on heads.

is is boring and um and that's a bit of a problem for some of us. Yeah, yeah, that's that's an interesting point.

So, you know, once you conducted this experiment, what sort of results did you see? Like how did how did the group perform? Well people did uh I mean, especially given that these were, you know, m you know, math students, finance students, MBA students. um venture capital investors and um investment managers, you know, that's kind of described all of the backgrounds of the people. About a third of the people went bust.

A third of the people went bust, flipping a biased coin in their f that's in their favor. about a third of the people or a little bit less than that reached the maximum the payout which was two hundred and fifty dollars. So a bunch of these, I mean in a lot of cases, these kids, you know, it's like going into uh

you know, one of the London universities and a bunch of these these guys are around and I'm paying them all out, you know, like two hundred and fifty uh dollars, you know, for sitting for flipping a coin for half an hour. But so it was really interesting. So about twenty percent of the people

hit the cap of two hundred and fifty dollars or tenx, thirty percent of the people went bust. The other fifty percent of the people averaged about eighty dollars. Everybody altogether averaged about ninety dollars. And this is really suboptimal because a very simple kind of rule such as I will just bet fifteen percent of my stake on every flip and bet heads would give you upwards of a ninety five percent chance of hitting that

two hundred and fifty dollar cap. So very suboptimal behavior. I mean the the uh what was it like ha uh just under half of the people bet on tails more than five times. I mean that was kind of crazy that that there was so much tails betting. Um and we and we said, you know, as I think more than five times. So I think I I mean I might have bet on tails once just to see what would happen. Like if I bet on tails.

Would it say, you know, you've just won you know, you've won, you know, that you d you that you stepped out of the box and bet on tails and now you're a winner or something. You know, I might have bet on tails once for a dollar. But you have but like forty, fifty percent of the people bet on tails more than five times. So um really interesting. I I I love this coin flipping stuff. It's great. Yeah. So

You said I I think if I heard you correctly, about a third of people went bust. They went bankrupt. They lost all their money. What were the reasons that led participants to go bust? Like did they just bet everything on one flip? Was it

Well ul uh ultimately they had to do that, right? I mean the only way you can go bust and I mean there's two ways to go bust really. Either you you know you sort of bet you y either you make a voluntary choice to bet everything, or you get down to having one cent left. And then you can't bet anything less than one cent. And so you have to bet the one cent and if you lose your bust.

But basically everybody just voluntarily sort of bet their whole stake at some point and um and and were and they were out. And normally what would happen is they bet their whole stake bef uh just after they had lost betting more than they should have been betting. So it was kind of like, you know, you had

you know, fifteen dollars in your bank account and then you for some reason you bet seven dollars, you know, maybe you were following a doubling down strategy. So you bet seven dollars on heads and now you had eight dollars left.

And you're like, Oh gosh, you know, I gotta get back up there so you bet so maybe you you know, you would bet a small amount for a while, then you know, you're not really going anywhere. So then you'd say, Okay, I you know, I've got nine dollars, I'm gonna bet four dollars, now you've got into five dollars. Then you bet two and a half dollars. You lose that, you're down at two and a half dollars.

And then, you know, you're like, How am I gonna get out of here? And you just start betting pretty heavily as a fraction of the two and a half dollars and you know, all of a sudden you're at fifty cents and you're like, All right, you know, the only way I'm gonna get out of here is to just bet my fifty cents And get five heads in a row or something, you know, which is

I don't know. Well uh we didn't we did not uh we should have interviewed the uh people who went bankrupt more, but um but they didn't really want to talk about it much. They were kind of out of their Pretty quickly. I can understand. I can understand. I mean they were I mean we we did we did have a rule. We said you cannot leave this room

Until the half an hour is over. So we were afraid that sometimes, you know, you would get this thing where somebody would say, Geez, I got two dollars in my bank. I just gotta I just wanna go out and make a phone call I wanna get out of here and have a coffee, so I'm just gonna bet the thing and and leave. So we said, No, no, you gotta you so we made everybody sit in the room. So even if you went bust, you had to just sit there until the half an hour was over.

Now you made an interesting comment before. You said something like If participants had of just bet fifteen percent of their bank roll on each bet, they would have had a ninety five percent chance of hitting the money cap or the the payout, um the max payout, which was I think two hundred and fifty dollars. So Where does that fifteen percent come from? I guess we're now kind of getting into optimal bet sizing, but yeah, how did you arrive at that fifteen percent?

Well well first of all, as I was saying, there's kind of a whole range that works pretty well in this particular problem. Like if you were betting anything from like eight or nine percent up to about twenty percent. you'd have a really, really high chance of hitting that um that cap. Kind of the magic number in a way, the there's there's sort of this magic number which is known as the Kelly number, the Kelly criterion, which maximizes your

rate of growth of wealth, um, named after John Kelly and, you know, lots of books and everything written about that. That that fraction would actually be twenty percent. But, you know, given that this game has a cap you know, that probably you would want a bit less than that Kelly number. The s the optimal solution to this game is really complicated. Um but these approximations or heuristics are fine. I mean you just have to have the insight

that you wanna bet some you know, you wanna be betting some fraction of your bank on the bets. And you also, if you know that there's a cap, you wanna have some idea, you know, you wanna have some prior of what the cap could conceivably be. I mean you know, I mean I think any Um, you know, sort you know, the common sense would tell these guys that I'm not gonna walk in and do this experiment and pay somebody a million dollars if they make a million dollars, right?

So, you know, whether it's two hundred fifty dollars or fifty dollars or a thousand dollars, you know, these guys should know that You know, that's kind of gonna be the range of this cap, you know, that it just wouldn't be credible that I would go in there and be paying these guys, you know, if they if they got on a roll that I would pay them a hundred thousand dollars, right?

Yeah, and when I read the paper, I I think it stated in the paper that if someone had have used optimal bet sizing with um these sort of odds The payout, um, after flipping a coin for thirty minutes could have been I think it was well over a million dollars. It might have been way over. How much was it? Yeah, so um exactly. So if this game had been uncapped, so one thing that people had no appreciation of is just how incredibly valuable this game would be uncapped.

So so if this game were uncapped, then the expected value and and this is this is gonna be in I think this is kind of an interesting thing to dwell on a little bit more, the expected value of the game would be about three million dollars. In other words, if you flip the coin Uh three hundred times. And every time you bet twenty percent on it, that would be like a four percent return on every flip. And a four percent return over three hundred events, you know, is like um

over a hundred thousand. And so that's where you get to the three million dollars. from the twenty five starting point. So that's the expected value, which I think, you know, n none of the participants really, or virtually none of the participants appreciated. But then it's kind of interesting because you get into this question of so how much would you pay? Let's say that let's say that somehow, for some reason, somebody offered you this game uncapped, as unlikely as that would be.

But somebody for some reason, you know, you got to play this game uncapped, just as a thought experiment. What would you pay to play the game? Right? You would say, Well well it's it's worth three million dollars. Should I pay a million dollars to play the game if it's got an expected value of three million dollars? Well the answer is um no. I mean that that the way to figure out how much you should be willing to pay to play the game is that you need to bring in

a uh a function of your own risk aversion. You need to bring in a utility function. And this is so interesting. It goes all the way back to Daniel Bernoulli And uh all this work that was done, I don't know, what four hundred I four or five hundred years ago, the St. Petersburg paradox is about a game It's about a game of chance similar to this one that has an expected value equal to infinity, but people are only willing to pay like ten dollars to play it. Because the expected utility of the game

has a a value equivalent to ten dollars. Now I know that I'm going really fast here, uh you know, etc. Sort of you know, there's a bunch of short pieces on our website that that talk more about this, but probably people also have learned this at uh, you know, in in uh you know, in in um finance or economics classes if if they've taken those. But it's so interesting because that expect that difference between the expected value

And the expect the the dollar value equivalent of the expected utility is so huge. So in this game, the expected value uncapped would be three million dollars. But you know, we could we you you could imagine somebody who's, you know, sort of normally risk averse um being willing to only pay ten, twenty, thirty thousand dollars to play the game, depending on their risk aversion. And so

Because and and the way to think about that is where the real value of this game is coming from is when you're getting a lot more you know, that's very skewed. If you get a lot more heads than the expected number of heads, you know, it becomes a bonanza. So and I've got a little bit more to say on that, but let me ask let me stop there so you could give me a little more direction, but I've got something that I want to explain on that more as well.

Feel free to do so. I mean, I was gonna ask about how this ties into financial markets, so I think that might take us on another tangent. If you wanna finish off any further comments you have yet, feel free to do so. Okay, so what I'd like to say is that you know one of the really key Things that this that this research makes us think about is is investment sizing, is trade sizing, and is risk management, all the same thing. And what's so interesting here to me is

Let's think about the sixty-fourty coin for a second again, right? So I said, well, the Kelly uh optimal bet is twenty percent, right? Well, what's the what's the strategy that gives you the highest expected value of the game. Right,'cause I said Kelly gives you the highest expected growth rate.

Um I said the game is only worth an expected utility terms, you know, ten to forty thousand dollars, maybe more, depending. But what's the optimal strategy to follow if you were not risk averse at all? You had no risk aversion. And you were just trying to sort of get the highest expected value from the game. The answer is that you bet 100% of your money on every flip. And you do that for three hundred flips. Now, you know, I think that that is

that that you know just a moment's reflection tells you that that is a ridiculous strategy. You have you have almost a hundred percent chance of winding up with no money left over because you're going to lose the chances that you don't lose money on three hundred that you don't come up tails in three hundred flips is pretty close to zero. It's like one of those crazy small numbers. But that's the highest expected value for the game, right? Because well, that that's what it is.

Now, what if we said instead of betting this sort of Kelly optimal fraction, if I said to you, well, look, this is a great game. Forget about Kelly. Let's just bet 50% of our bank on each flip. Well if you do that. The expected value of the game is much, much higher than it is by betting 20%, because you're betting more on a favorable flip.

Okay? But what's the problem with that? Well the problem with that is that you can see that so first of all in terms of expected gain, right? I said to you that if you're betting 20%, your expected gain for each flip. is four percent, right? Sixty percent of winning a dollar uh minus I'm sorry, sixty percent of winning twenty cents because you l let's say that you have a dollar of wealth and you're betting twenty cents.

Uh that's the 20%. So it's 60% of 20% minus 40% of the 20%, and that is um 4%. So you make four percent expected return on each flip. But if you're betting fifty percent of your wealth on each flip, then the expected gain per flip is actually ten percent, because you have a sixty percent chance of making uh fifty cents and a

40% chance of losing 50 cents and that adds up to a 10% return. So that means that after 10 flips, your expected gain is to be at a multiple of 2.6 times your starting point, or after 100 flips. you're up four you're you've grown your wealth expectation to fourteen thousand. But but

Think about this for a second. Let's say you're taking ten flips like that, and things turn out exactly as you expect, which would be what six heads and four tails, right? Well Let's think about first you go the four let's think about that as being four heads Four tails and then two more heads. So what does that look like, right? Well, when you make fifty percent of your money, that's great. Your dollar f dollar grew into a dollar fifty. But then when you lose on the next coin

You've lost 50%. You're down at 75 cents. So do that up and down four times, right?

and you're down to having about 30 cents left over. Jeez, that's terrible. But then you win twice in a row because we said six heads and four tails. But the result of winning twice in a row after that is you've just grown back up to 0.7. So In the case where you go up six and down four in any order, if you get six heads and four tails and you're betting 50% of your wealth, you're going to wind up losing 30% of your wealth.

Isn't that crazy, right? That's the sort of downward drift in the median value. And so if you do that a lot, you're going to be if you do that a hundred times, you're going to wind up with like zero leftover, zero point oh three or something like that. And What's more is that if you think about it in sort of any kind of normal utility sense, you'll see that betting fifty percent is a negative expected utility investment to make.

And so therefore we shouldn't do it. It's a bad thing. You would be better off. So if somebody came to you and said, Here's a sixty forty coin, the only thing is you have to bet fifty percent of your wealth on it, what would you do? Any normal person should say, Hey, uh I'll pass. Thank you very much and sort of move on. So You know, I think this whole bet sizing thing is is so important. It seems so sort of simple and it seems like it's secondary to the idea of identifying a good investment.

Um, we do need to identify good positive return investments. That's critical, but we also then need to decide how big to be in them. And I think that, you know, one of the great lessons from LTCM is is is about trade sizing. You know, if if we had had if we had had a third of the positions that we had, you know, the things would have been different. So I'll stop there. Yeah, I I think if anyone's getting lost in this, which is quite easy to do.

Check out the paper. I'm gonna link to the paper in the show notes, so it'll be at chatwithstraders.com. Might make some of this a lot clearer. If you are getting lost, if you're following along, that's even better. But um yeah, I'll link to the paper in the show notes. Are you ready to get serious about trading? Then join Tasty Trade, Investopedia's best platform for options trading in 2026.

Stocks, options, futures, and more. Tasty Trade has everything you trade all in one platform. Get low commissions, including zero commission on stocks. so you can keep more of what you earn. Tasty Trade is packed with advanced charting tools, backtesting, a pre-built strategy selector, risk analysis tools, and more features to help you trade smarter. See equities and derivatives with high trading volumes, dividends, upcoming earnings reports, and more with their pre built watches.

Or create a custom watch list to keep an eye on the companies and sectors that matter to you. Manage your positions with speed and precision using Active Trader Mode one click trading and smart order tracking. Plus Tastytrad's Stellar Trade Desk team offers live support during trading hours if you need it. Visit Tasty Trade dot com slash chat for more info. KC Trade Inc. is a registered broker dealer and member of Finra, NFA and SIPC.

Have you ever watched a stock explode and thought, if only I had the capital? or sat on the sidelines because your account balance felt too small to matter. Good news With Trade the Pool's limited risk platform, you don't need millions or even thousands to start trading the US stock market. Bypass the PDT and tap into over twelve thousand US licit equities. From penny stocks to big caps, ETFs, even the newest IPOs, and short anything you like, with zero locate or hard to borrow fees.

Start your evaluation, get funded with up to$200,000 in buying power so you can go big without risking your own savings. And now you can also have unlimited time to reach the profit target. It's a game changer. Not ready to trade yet? Trade the pool offers a free demo and educational resources. practice on live data, master the platform, and build confidence risk-free before you even pay a cent. Click the link in the show notes to start trading with Trade the Pools Capital.

Now this is all very interesting, but I guess the real question is what can we learn from this as traders? Like where can we get a biased coin in financial markets? Well, the the clearest place to get in my opinion, the clearest place to get a biased coin in the market is uh is beta.

That's the to me that's the clearest place to get it. Is that the stock market, um, not only that that there's both reason to believe that the stock market will give us a return above the risk free rate We can verify that on a uh on an ex ante basis by looking at uh corporate earnings, corporate dividends.

and making some relatively straightforward assumptions about the future uh future outcomes. So without looking back at the past at all, I think that we can look at equities and uh convince ourselves that equities should and do have a positive uh expected return above the risk free rate or above inflation. Unfortunately, it's a pretty bad sharp ratio compared to what we really want, right? So, you know, I think that it's it's a bit like a sixty forty coin uh toss.

But with a lot more hair on it than the coin has. So that's one place that we can get, you know, other related sources of beta, uh similar sources of beta out there. You know, we can also get um that that sort of positive uh biased coin from those. So I mean, you know, not only is our global equities uh likely to have a risk premium going forward, but also, you know, real estate and other related things. But um Once you move away from that, Aaron, it gets really tough.

But but you know, I mean there's there's lots of but you know, there's lots of I mean there's relative value you know, there's a lot of relative misvaluation in the world out there, so you can put on Uh I mean I I I don't really follow it anymore, but you can put on trades, you know, buying uh

in the fixed income world and different places and find these good relative value trades. I mean the problem is that You know, I think that the the distributions of those trades are really difficult in the sense that they tend to have these big negative fat tails on the on the downside.

Yeah. I mean I guess one of the the big takeaways from this sort of this experiment is just showing how position sizing can have such a huge effect. on your your outcome, you know, after however many flips or however many trades, um, you know, after doing something many times over. I know one of the people who helped you with this experiment was Edward Thorpe. What sort of comments did he have and what was his input on this experiment?

Well, I would say that his involvement in it was uh first uh inspiration that that he uh uh that that Uh everything he's done, everything he's uh uh uh uh uh communicated to people sort of inspired us in this direction. And then after we had done the experiment and after we had written it up, we sent it to him to get his comments and he had helpful comments for us.

And he had um even even better than that, he was like very encouraging and he really liked it and he's and he's talked about it uh to some of his um followers as as well. So that's um his involvement in it.

I listened to a talk you gave, I think it was at uh the transfer wise office, um and it must have only been the other week. I came across it on YouTube and I noticed it was it'd only been online for about uh for a few days. One of the things you said uh during that talk I found rather interesting, especially given that you have worked with Ed Thorpe, you said I don't know if you can beat the market and I think this kind of ties into what we're talking about.

We'll have talked about uh prior to this as well. Would you mind just expanding on on that comment? Okay. Um tough question. Yeah, I don't think I don't well no, I'm trying to remember what I said and at the same time uh asking myself what I believe in this'cause I'm not sure that that's that's exactly what I said and and how it uh how it But um Well I believe that certain people can beat the market. I I definitely believe that certain people can beat the market. I'm very skeptical.

That investors can figure out who those people are in a positive, expected manner. So there are Um, you know, there are brilliant, uh rare people out there, relatively rare people out there who who can beat the market, um, as somebody who doesn't think that I don't think that I can do it uh or I don't want to try to do it. I don't think that I can find I don't think I can identify those guys

in a reasonable time uh to be able to allocate them money and and earn a uh an improved return as compared to a relatively passive form of investing. I think that's what I said to them. And I was talking to them about Uh the the um the paucity of uh or the lack of power of historical data

um to help us identify these things. I think that historical data, just as the I mean, I know it's very hackneyed uh when they you know, this saying of uh or this boilerplate phrase of past returns are not indicative of future performance. But when you do the numbers, when you think about the numbers from a statistical point of view, you'll conclude that um that past performance cannot really uh be indicative of future returns.

with the amount of data that we have on on different things. And actually I've just got a paper that we're going to post in the in the next couple of days um that's kind of on this topic. And again, it's using a coin. It's using a it's using the lens of coin flipping. to explain that. To give you a quick preview of one of the the opening of the paper says asks this question. It says, imagine that you have two coins.

Uh that you're t there are two coins presented to you and you're told one of them is a sixty forty coin and the other one is a fifty fifty coin. And you're asked how many times do you require you're gonna you're going to r request a certain number of times to see the coins flipped in parallel and count up heads and tails. How many uh times do you request to see them flipped?

So that you would have a ninety-five percent confidence in choosing the right coin or identifying the biased from the unbiased coin. people's intuition, all right, if they I mean if people sit down and and calculate it, they come to the right answer. But people's intuition is to give a relatively low number, like twenty or thirty flips. You know that in twenty or thirty flips you would get there. But the answer

is 143. And what that kind of means is that it takes 143 years to differentiate a uh an investment manager that's giving you a zero sharp ratio versus one that's giving you a sharp ratio of zero point two. And slicing the data up into weekly data or monthly data doesn't help at all. So um anyway, that's about half the paper I just gave you right there. So But hopefully you'll enjoy the other half of it when when you get to it. Yeah. And and when where will that be available when it comes out?

It'll be on our uh on our website and um you know by the way people can sign up to uh to to get our um our thought pieces as as we put them out there. You know, just go to the website and you can sign up and then we'll send you our blog pieces. But that'll be on our blog. Um and also on the Elm Labs uh website. And and hopefully in the next couple of days we're just trying to we're trying to make it interactive.

So we want to make it where you go there, we ask you the question, you put in your answer, then we talk about it, we ask you another question, and then talk about it some more. So we think that's kind of fun. Oh, okay. Good one. Very cool.

Are there any parting words of wisdom you'd like to leave with us? You know, anyone who's listening to this, Victor, anything you'd like to add to take us out? No, I I uh I I've really enjoyed this. I think um that I don't really have very much on the wisdom front. Um so um I hope you'll uh I hope you'll have me back sometime. I really enjoyed uh

um, you know, chatting with you and sharing sharing thoughts and experiences. I've thoroughly enjoyed this, Victor. I appreciate you coming on. So if anyone wants to find out more about you, ilmfunds dot com and are you on Twitter? No, I I guess I should I I'm hoping to do that soon. I haven't figured out Twitter yet. Um Sorry.

But I'm a little bit But I am uh I did do LinkedIn, so I've got Twitter ahead of me and uh and also Facebook is in my future, I think, or in the future of our company. But at the moment LinkedIn, but hopefully soon on Twitter. Okay. Okay. Very good. Well again, Victor, thank you for coming on the podcast. I've enjoyed it, man. Again, thank you. But rest assured there are more episodes of the channel. We'll catch you next time.