58: Ignore Investing's Mathematical Underpinnings at Your Peril

up until like fourth grade. And then as soon as it like hit the level of like where I actually had to do work and couldn't just do stuff in my head, I just like I just totally became very average. So I went from being really good at math to really mediocre very fast. But I do really love math, and I do really like doing a sort of math in my head and think about math and stuff like that.

So I think I have a love hate relationship with math, Like I find it very very difficult to do and is probably my most hated subject, but conceptually I think it's really interesting and statistics. I was actually quite good at UM, so I like thinking about math ideas I hate actually doing the math. I mean, I think I think we're probably in the same boat on this one. Okay, well, we're going to talk about maths, and yeah, we're not going to do do math because that would be the

world's most boring podcast ever. But we are going to talk about mathematical ideas and specifically how they applied to investment and markets and finance. And we have a very cool guest who is probably better better able to talk about math and investments than just about anyone else. Yeah,

that's right. So, anyone who's ever heard of long term capital Management, you know that there was a quant there co founder called Victor Hagani and basically was hugely instrumental in the founding of that firm and is a mathematical expert of the highest order, I suppose you would say, right. And so these days there's so much interest in like algorithms and computers and quantitative finance and stuff, and there of course really ahead of the curve on a lot

of these ideas, and now there's much more interest. So we're going to talk about the connection between math and finance and particularly some important mathematical concepts that investors should understand. Maybe we'll get an LTCM questioned in there too. Who knows. Let's bring in Victor Hagani. Like I said, he was at l T c M, but he is now the CEO of ELM Partners, which is basically a portfolio of low cost index and exchange traded funds. Victor, thanks so

much for joining us. Thank you very much for having me so. Victor. We actually brought you on after reading a paper that you did, UH basically about what coin tossing and the probabilities involved in coin tossing? Can each us about investment? Can you tell us about that paper?

So it came out of an experiment that that I did with the colleague of mine UM who I worked with at Ellen Partners, Rich Dewey, and we had heard about some research that was that had been done involving coin flipping and how people UH managed situations where they were given a favorable odds kind of investment opportunity. And I know we can't remember it with with these things, sometimes you can't quite remember where the ideas come from.

But we decided to do this experiment where we would UM give gives depends some some real money and allow them to flip a coin that was biased to come up six likely to come up heads tails, and we told them that to begin with, and we gave them half an hour to flip to bed as much of their starting as they wanted. And at the end, however, were much money they had left in their bank, we would pay them up to a maximum amount of two

and fifty dollars. And what we found was that UM our participants, who were pretty quantitatively quantitatively trained UM young men and women, didn't do very well and they didn't kind of get some of the basic concepts of UM decision making under uncertainty or the they didn't quite get the independent nature of the flips and the fact that it just made sense to keep betting on heads to debt you know, some modest constant proportion of how much they had in their bank at any point in time

on heads and so UM. Yeah, it was, it was. It was really interesting to think about, you know, how people were we're having trouble with that, and you know, to give us some ideas for trying to help with UM with education as well. On on that, on that topic, explain real quickly the exact mechanics they were supposed to play. They had twenty five dollars and they were supposed to bet, what explained to us what the nature of the bet is, and then what did the lessons show about mistakes that

people might or might not make when they invest. Sure, so the you know, the exact mechanics of it were that, you know, we told that the people to come for a lecture and uh, and then we asked them to get out their laptops and to play this game. So we gave them twenty five dollars that turned up on their screen and their banks and their bank accounts or their bank roll, and then they could bet up to the on the flip of a coin, and they could

do it repeatedly. Some people flipped the coin three hundred times in the thirty minutes that they had and if they won the slip, then their bank roll would go up and and and vice versa. And however much they were left with at the end, we actually told them and we did pay them as a check or cash, which was you know, especially for a bunch of college students, which were the majority of our subject. You know, it

was very welcome. And the two d and fifty dollar maximum that we were going to pay them, uh, we only told them that if they got close to it, so we told them that there was a maximum payout to begin with, but it was only when they got to a point where they could reach the two hundred and fifties. So if they had two d and twenty five dollars in their bank account and they were betting thirty dollars on heads, we would say, by the way,

the most will pay you is two fifties. So you might want to do see your best from thirty dollars to twenty five dollars, because there's no point in winning two hundred and fifty five dollars. We won't pay you that. The most surprising thing, uh, in a way, was the fact that people would relatively frequently bet on tails, um, you know, even though we told him it was likely

to be heads. You know, even though in general, you know, heads was coming up more frequently for most people, you know, after they have flipped a number of times, they still felled them, particularly after a string of head So like if they got four heads in a row, they were then more likely to bet on tails. Not everybody. That seems like a deep failure of numerousy to ever bet on tails, even and to think that something like the

past streak of flips. Is any bearing on the next flip, Yeah, it is, But it's just that it's like the deep seated need that we have, you know, to sort of see a story and random thing. It's very you know that given that like half of the people did you know, half of these subjects at some point bet on tails, and like thirty percent of them bet on tails fair amount of the time. So there's something kind of deep

seated and there my mom. I had my mom through the experiment and we talked about it afterwards, and she said to me, I know that I should never bet on tails, but I just couldn't resist. So she knew it, she knew it didn't make any sense, but she just

couldn't resist. And it was interesting. We did another experiment and following up on this, this the same as interview question about the family planning that if you uh, you know that if if in a if you're going to in a society, if if everybody wants to have a girl and so they keep having children, each family has children until they have a girl, does that change the

expected number of boys and girls? And most people feel that it does, even though when father as a coin flip, you can kind of see that they're independent, and you know that there's nothing there's really nothing much you can do to change the expect number of boys being equal to the expect number of girls to any finite horizon.

So the point of those types of experiments is essentially that the optimum investment strategy is dictated by maths, right, and yet we choose to ignore it for whatever reason because we instinctively don't understand probabilities, or there's some emotional thing going on. Yeah, I mean I think people, you know, understand it. I mean like our subjects were really quantitatively trained.

I mean they understood all of this, you know, there they were some of them were even mathematicians that at one of the universities where we did it, and and U some of and some of the subjects were also professional investment investment professionals that had both know a lot of maths and econ and finance training. So they understand it. But I think there is this sort of there's something deep seated that that sort of comes up and steers

us off the path. And so you know, it's kind of like quite a lot of specific training is probably what's needed to get people to be disciplined, and you know, to be disciplined, it's not a lot of fun. I mean thinking about you're sitting there flipping a coin for half an hour and you're just trying to get of your bank roll on it and keep betting on head.

It reminds me of reading about professional poker players who know that they can make a steady profit playing limit poker, which is a very mathematical, no, very little bluffing version of the game of poker, but they're just bored out of their minds when they play it. So they no limit is more fun and more exciting. There's it's a little less mathematical and more sort of based on emotion. Uh, they are more inclined to lose, Like you know, these games,

these sort of sure things are not very enjoyable practices. Yeah. Yeah, Well, and think about index investing, right, I mean kind of the most you know, the most boring thing you could do is to take all of your savings and to put it into two index funds. You know, very few people really do that, and very you know, very few

people do that and stick to it. I mean, people will do it and then they sort of will come back and feel that they need to change it because you know, there was an election, or there was a change in interest rates or something. So it's sort of fighting that that urged to us. That fighting the urge to be active is difficult in a lot of different contexts. We're all suckers for a sense of control. Let's talk about a different mathematical concept that's incredibly important to investing

and that is compounding. This sort of I forget who said it. Maybe it's like Einstein, someone famous said something about compounding or being one of the most powerful forces on earth. Yeah, I think that they say Einstein may said something like that. As strange as it me. Yeah, I don't know why he would have been talking about it, but I think he did say something about it for whatever reason. Um, what don't people understand? What is it?

Why is compounding such an important concept to understand? And what do people what do people get wrong about this? Well? You know, I think that you know that in these sort of investing things or mass things in general. You know, one of the things that really gets us is nonlinearities, you know, as things that are not proportional, and compounding is one of those things. So, um that the growth of your money doesn't kind of go up in a

straight line. It goes up in this exponential line. It starts off growing slowly, and then as it gets bigger, it's growing faster in terms of the amount of money by which it's growing, I mean, the rate of growth, let's say, stays the same. And and so you know, when you start to look at relatively long periods of time, which are the kinds of periods of time that are relevant to us in terms of building savings for retirement or or uh, you know, our our our sort of

personal security longer term, or for our family or our kids. Um, you know, those long term horizons are important, and and compounding and small effects really magnify out there. So you know, the one that we always that we can hear a lot about, right, is sort of the effect of fees.

You know that, Um, you know that if you're compounding at a five percent return because you're paying two percent fees, or if your account compounding at a seven percent return, that what you wind up with at the end is not proportional to seven over five, right, that that seven winds up giving you a lot more um at the end because it's it's you know, it's it's one point oh seven being raised to a power divided by one

point oh five being raised to a power. So you know, everything kind of gets magnified by by compounding, and so yeah, you get a lot of you know, like another thing that you know, sort of similar to sees as taxes. So if we can invest in a way where we don't pay tax until the end of our investment horizon, um, you know, we wind up with a lot more money than if we're paying the same rate of tax on

our growth every year that we go along. So um, like you know, an example of that would be let's say that you have a uh an investment that has an eight percent rate of return and let's say a tax rates or fifty percent. Just to make the mass simple, Um, Well, after thirty years, if you were well, if you're paying tax every year, then your eight percent return duringly like

a four percent after tax return. So if you have a if you have a hundred thousand dollars and you're investing it, then after tax, that hundred thousand dollars has grown to three four thousand dollars after thirty years at this four percent rate of growth. Half of the five but it's instead you're deferring your tax to the end. Then you're growing at eight percent right, um, because you're not paying any tax on it. But at the end

you have to pay tax on all your games. And when you do that, you wind up with clothes to double the money. After thirty years, you wind up with like five fifty thou dollars and almost a six percent instead of a four percent rate of return. So that stuff really kicks in over these long horizons and is important. You know, small differences wind up being big differences because

it's compounding. What's your favorite um financial formula for investing? Like, if you had to choose one, UM, well, I don't know. I guess, uh, you know, one of the simplest ones one that there's been on my mind lately. I don't know if it's and I think if I had more time to think of it, I find a better one,

but it's been on my mind. Of that is is what's known as Sharp equality, from a paper that William Sharp, the Nobel Prize winner, wrote, um in the early it was I think the paper was called like the Aristhetic of Active Investing, And in that he just made the very simple, uh statement, that the return on the average actively managed dollar has to equal the return of market minus minus fees on the active stuff, and that comes about the market return is UM must equal a weighted

average of the reach end of the passive and active segments of the market. So if the uh, if the total market return is the same as the index thing return of the passive part, then you know, it's sort of like, you know, if if two equals one plus one, then two minus one equals one is kind of um. You know, I guess I suppose the way of seeing it.

So it's a very simple. It's kind of like in physics, the the idea of the conservation of energy UM and you know, so what are the practical ramifications of that? From an investor standpoint? This sort of I get it sounds like an identity essentially, what do the how does that manifest itself practically in terms of making investing decisions? Well, it just helps us a lot in terms of thinking

about what we're doing when we choose active strategies. That for an active strategy to be working for us UM that we have to believe that there's some other active strategy that's losing money and we have to be able to identify, um, you know why and who that's likely to be. You know that if we're that that, if we're if we think that we're making you're kind to make money, we really be sure of who we're making the money from. And it's not really it's some game essentially, yes,

you know, within that space. I mean, at least too, you know, I think that at least to a first approximation, it's the it's a valid identity. I mean, there's some caveats and so on that people would bring into it, but I kind of like that. It's simple. Um. It reminds us of Bill Sharp, who is a really cool guy. I think it's I think it's a really useful It's really it's a really useful one. Um to to remember.

Oh um, I promised a potential l t c M question. Um, so, I guess like one of the other things we've observed in markets recently is the rise of smart beta, but also risk parity strategies, and some people have likened risk parity to the old black shoal portfolio insurance of THEES, and some people have connected l t c MS collapse with black shoals. So I guess I'm just curious how you feel about risk parity and how you feel about

the downsides of math addicts in finance. For me, the really short answer is that the the the leverage, you know, my ltc M experience has just made me not want to use leverage, um explicitly in any sort of investment strategy. Uh, you know, for myself, for anybody that I would be trying to help. Um, you know it. Leverage has its

place in our financial system. It has its place perhaps within the investment community, but personally, um, you know, it was that that was you know, that's that was the primary cause of the problems at ltc M. And so for me anyway, I mean, I know the arguments for risk parity, UM, you know, it may well be that the aversion to leverage by people like me is what makes using a moderate amount of leverage a good idea.

You know, That's what some people that are proponents of risk parity would argue that it's an inefficiency that a bunch of people like me now are averse using leverage. But I'm averse using it. I don't. So I'm not a fan of risk parity because I'm sort of you know, I just don't want to. I don't feel that I need to use leverage to get better quality returns. I think that the returns afforded by the marketplace without using leverage, and the risk attached there too, is all sufficient for me.

And then I can go to sleep and not worry about having to reduce exposures because my leverage is causing me to do that. What about financial formulas in general and maths in investing, what are the downsides? Well, you know, models used in investing are are very useful. That they're they're a way of us um you know, thinking that that if we in one one of my colleagues one said that, uh, think about just the yield, yield to

maturity of a bond. Think about that as a model. So, you know, for a while, you know, at some point in time, yield to maturities didn't wasn't really used. So people used to talk about the price of a bond.

They talked about the current yield the coupon divided by the price, and then somebody and then people started to use yield to maturity or yield to worse more, Well, yield is just a much more useful thing to use and thinking about comparing different bonds with each other, implies volatility is a more useful way of thinking about comparing

stock options to each other. There's nothing kind of magical, It doesn't tell you what to do, but it's just a more useful that that these models are a useful way of decomposing things into more intuitive quantities that we can that we can use in our decision makings. So I think that um, you know, math in finance is

is useful, for sure, there's no doubt about that. But you know, but when we start to try to optimize things too much using math, when we when we try to get um, you know, trying trying to become too optimal and following you know, sort of narrow mathematical rigor

too far, is extremely dangerous. Right. So it's it's sort of the you know, you you come up with a whole portfolio of different investments and you look at an optimization of that, and it tells you to do things that that common sense would tell you probably don't make sense to do. So taken to an extreme, I think that that math, that sort of mathematical outcome can lead us to uh, the dangerous places sometimes. But that's that's

a great question. I wish I had more time to think about it and give you a better answer to it. That's a great answer, And Victor Hagani of ELM Funds really appreciate you coming on. Fascinating conversation, looking forward to reading and learning more about some of these concepts, and I think uh listeners will have learned a lot from this. Well, thank you very much as a pleasure, Joe, was that

mathematical enough for you? I think that was just like the sort of a perfect level of mathematical sophistication while being able to understand the concepts without actually having to attempt to do math over the over audio, which I think would be tough. I mean, I sympathize with the coin tossers because if you think that like a coin toss has a fifty chance of coming up heads or tails, then if you got five in a row, well I

suck at probabilities. I mean I get like, like you know there is something in your gut, like like you're something like that's exactly right, Like you really have to sort of sublimate your intuition and your feelings about how things work. Although then the question is like if you had a coin and say it came up twenty times in a row, you might think that it's going to

be heads forever because then it's like broken other way. Um, but then it's really fascinating and like you know, like I said that the poker comparison, it's like it's not fun. Like if you're sticking to rules and it's like, yeah, everybody knows we should just put our money in a bond index fund, in a stock index fund or and leave it there. But it's really tough to be disciplined

about these sort of rules and investing. Yeah. But conversely, you know, as LTCM to some extent demonstrated, it can't all be maths, right, Like the models sometimes need to be used with human judgment, even though they're useful in

many ways. If if something big is happening, or if the model doesn't seem to be performing, you kind of have to step back and go way to second what's going on, or just the intuition that a model you're taking a huge risk, even though if you're leveraging thirty to one and obviously, as Victor pointed, or much much bigger and some at some points and as Victor pointed out at this point in his career, he doesn't have any interest after that experience in sort of applying leverage

to finance at this point connotative finance. On his point about models, I did think that was really interesting, which is that you don't necessarily want to over determine what markets are going to do for models, but that models can provide a lot of insight just in sort of like, uh, sort of assessing where things are, and the idea of like volatile implied volatility being a sort of yeah, like the fact that all these things are in fact models that help you sort of compare one thing to another.

I never thought of that because it's everyone uses it, right, we don't even think of them as models. Yeah, all right, Well that was a fun discussion. That was great. Let's say goodbye goodbye everyone. Thank you very much for listening. I'm Joe wisn't Thal. You can follow me on Twitter at the Stalwart and I'm Tracy Alloway. I'm on Twitter at Tracy Alloway. Thanks for listening. Year to E