Odd Lots - 58: Ignore Investing's Mathematical Underpinnings at Your Peril

Episode Date: December 9, 2016

What's the optimum amount of money you should bet on a particular outcome? The answer is dictated by mathematics, yet plenty of people still go against the laws of numbers and probabilities when it comes to investing. This week, we speak with Victor Haghani, CEO of Elm Partners Management and the co-founder of the collapsed hedge fund Long-Term Capital Management, about the most important mathematical concepts for investing. We also discuss the pros and cons of quantitatively led finance.See omnystudio.com/listener for privacy information.

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all investing is subject to risk vanguard marketing corporation distributor. Hi, and welcome to another edition of the Oddlots podcast. I'm Tracy Alloway. And I'm Joe Wisenthal. Joe, I got to ask, when you were at school, were you good at math? So it's really funny that you should ask that because, so my dad is a physics professor. Oh, that's right. And he started me on math training when I was very young.

And I was really good at math and really good at mental math and super good at multiplications 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 like really good at math to really mediocre very fast. But I do really love math and I do really like doing sort of math in my head and thinking 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 it was probably my most hated subject. But conceptually I think it's really interesting. And statistics I was actually quite good at.

So I like thinking about math ideas. I hate actually doing the math. Does that make sense? I think we're probably in the same boat on this one. Okay. Well, we're going to talk about maths. And math ideas. Yeah, we're not going to 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 apply to investment and markets and finance. And we have a very cool guest who is probably 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 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 they were, 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 question in there, too. Who knows? Let's bring in Victor Higani. Like I said, he was at LTCM, 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, basically about what coin tossing and the probabilities involved in coin tossing

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

But we decided to do this experiment where we would give – some real money and allow them to flip a coin that was biased to come up 60% likely to come up heads, 40% hailed. And we told them that to begin with. And we gave them a half an hour to flip to bet as much of their starting $25 as they wanted. And at the end, however much money they had left in their bank, we would pay them up to a maximum amount of $250. And what we found was that, um, that, our participants who were pretty quantitatively trained young men and women didn't do very well. And they didn't kind of get some of the basic concepts of decision-making under uncertainty or they didn't quite get the independent nature of the slips

and the fact that it just made sense to keep betting on heads to bet some modest constant proportion of how much they had in their bank at any point in time on heads. And so, yeah, it was really interesting to think about, you know, how people were having trouble with that and, you know, to give us some ideas for trying to help with education as well on that topic. So explain real quickly the exact mechanics. They were supposed to play. They had $25 and they were supposed to bet what?

Explain to us what the nature of the bet is. And then what did the lesson show about mistakes that people might or might not make when they invest? Sure. So the exact mechanics of it were that, you know, we told the people to come for a lecture. And then we asked them to get out their laptops and to play this game. So we gave them $25. That turned up, you know, on their screen in their bank account or their bank roll. And then they could bet up to the $25 on the flip of a coin.

could do it repeatedly, some people flipped the coin 300 times in the 30 minutes that they had. And if they won the flip, then their bank roll would go up and vice versa. And however much they were left with at the end, we actually told them, and we did pay them, especially for a bunch of college students, which were the majority of our subjects, you know, was very welcome. And the $250 maximum that we were going to pay them, 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 250. So they had $225 in their

bank account and they were betting $30 on head. We would say, by the way, the most will pay you is $250, so you might want to reduce your bet from $30 to $25 because there's no point in winning $255. We won't pay you that. The most surprising thing, in a way was the fact that people would relatively frequently bet on tails. You know, even though we told them it was 60% 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 flipped it a number of times, they still felt, and particularly after a string of heads.

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 numeracy to ever bet on tails, even to think that some like the past streak of flips is any bearing on the next flip. Yeah, it is, but it's just it's like this deep-seated need that we have, you know, to sort of see a story and random thing. It's very, you know, given that like half of the people did, you know, half of this subject at some point bet on, on, on, uh, tails, and like 30% of them bet on tails a fair amount of the time. So there's something kind of deep-seated in there. My mom – I had my mom do 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, you know, it's interesting. We did another experiment following up on this, this famous interview question about family planning that if you, you know, that if you're going to, 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 thought of

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 expected number of boys being equal to the expected 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, they were, some of them were, you know, some of them were even mathematicians at one of the universities where we did it, and some of the subjects were also professionals, investment professionals that had both, you know, a lot of math and econ and finance training. So they understand it, but I think there is this sort of, there's something deep-steed 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 is not a lot of fun. I mean, think about if you're sitting there flipping a coin for half an hour, and you're just trying to bet 15% of your bankroll 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 no limit is more fun, is more exciting. It's a little less mathematical and more sort of

based on emotion. They are more inclined to lose. 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 few people, 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 the change in interest rates or something. Right. So it's sort of fighting that urge to be that fighting the urge to be active is difficult in a lot of different context.

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 was 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 have said something like that as strange as it may. 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.

What don't people understand? Why is compounding such an important concept to understand? And what do people get wrong about this? Well, you know, I think that in these sort of investing things or math things in general, you know, one of the things that really gets us is non-linearities, you know, things that are not proportional. And compounding is one of those things. So 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 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, you know, our sort of personal security longer term or for our family or our kids, you know, those long-term horizons are important and compounding and small effects really magnify out there. So, you know, the one that we always, that we hear a lot about, right, is sort of the effect of fees, you know, that if you're compounding at a 5% return because you're paying 2% fees or if you're compounding at a 7% return, that what you wind up with at the end is not proportional to 7 over 5, right? But that 7 winds up giving you a lot more at the end because it's, you know, it's one point. 0.07 being raised to a power divided by 1.05 being raised to a power. So, you know, everything kind of

gets magnified by by compounding. And so, you know, you get a lot of, you know, like another thing that, you know, sort of similar to fees is taxes. So if we can invest in a way where we don't pay tax until the end of our investment horizon, 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, like, you know, an example of that would be, let's say that you have an investment that has an 8% rate of return, and let's say tax rates are 50%, just to make the math simple. Well, after 30 years, if you were, well, if you're paying tax every year, then you're 8% return, like a 4% after tax return. So if you have a, if you have $100,000 and you're investing it, you're, you're,

then after tax, that $100,000 has grown to $324,000 after 30 years at this 4% rate of growth, half of the 5%. But instead, you're deferring your tax to the end, then you're growing at 8%, right, because you're not paying any tax on it. But at the end, you have to pay 50% tax on all your gains. And when you do that, you wind up with close to double the money after 30 years. You wind up with like $550,000 and almost a 6% instead of a 4% 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 of compounding. What's your favorite financial formula for investing?

Like if you had to choose one. I don't know. I guess, you know, one of the simplest ones, one that's been on my mind lately. I don't know if it's – I think if I had more time to think of it, I find a better one, but it's been on my mind a bit is what's known as Sharp Equality from a paper that William Sharp, the Nobel Prize winner, wrote in the early 1990s. I think the paper was called like the aristotic of active investing. And in that, he just made the very simple. statement that the return on the average actively managed dollar has to equal the return of market minus fees on the active stuff. And that comes about because the market return is must equal a weighted average of the returns of the passive and active segments of the market.

So if the total market return is the same as the indexing return of the passive part, then, you know, it's sort of like, you know, if two equals one plus one, then two minus one equals one is kind of, you know, I guess I suppose a way of seeing it. So it's a very simple, it's kind of like in physics, the idea of the conservation of energy. And, you know, so what do the practical ramifications of that from an investor standpoint, this sort of, I get, and 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, that we have to believe that there's some other active strategy. strategy that's losing money. And we have to be able to identify, you know, why and and who that's likely to be, you know, that if we're, that if we think that we're making, going to make money, we really have to be sure of who we're making the money from. And it's not really coming from. It's like a zero some game, essentially. Yes. Yes. You know, within that space, I mean, at least to, you know,

I think that it needs to a first approximation. 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. It reminds us as Bill Sharp, who is a really cool guy. I think it's a really useful one to remember. Oh, I promised a potential LTCM question. So I guess 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 the 1980s. And some people have connected LTCM's 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 mathematics in finance. For me, the really short answer is that the leverage, you know, my LTCM experience is just,

made me not want to use leverage explicitly in any sort of investment strategy, you know, for myself or anybody that I would be trying to help. You know, leverage has its place in our financial system. It has its place perhaps within the investment community. But personally, you know, that that was, you know, that was the primary cause of the problems at LTC. And so for me, anyway, I mean, I know the arguments for risk parity, 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 to 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 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 very useful. That they're a way of us, you know, thinking that if we, in one of my colleagues once said that, think about just the yield to maturity of a bond. Think about that as a model.

So, you know, at some point in time, yield to maturity didn't, wasn't really used. So people used to talk about the price of a bond. They've talked about the current yield, the coupon divided by the price, and then people started to 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. Implied 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 these models, are a useful way of decomposing things into more intuitive quantities that we can use in our decision-making. So I think that math in finance is useful for sure. There's no doubt about that. But when we start to try to optimize things too much using math, when we try to get, you know, trying to become too optimal. and following, you know, sort of narrow mathematical rigor too far is extremely dangerous, right? So it's sort of the, you know, 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 common sense would tell you probably don't make taken to an extreme. I think that math, that sort of mathematical outcomes can lead us to the dangerous. places sometimes. But 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 listeners will have learned a lot from this. Thank you. Well, thank you very much. It was 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 audio, which I think would be tough. I mean, I sympathize with the coin tossers. Because if you think that a coin toss has a 50-50 chance of coming up heads or tails, then if you get five in a row, well, I suck at probabilities. No, I mean, I get like, like, no, there is something in your gut. Like there's something you've got. 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 50, 50 coin and say it came up 20 times in a row, you might think that it's going to be heads forever because then it's like broken another way. But that is really fascinating. And like, you know, like I said that the poker comparison. Right. It's like, it's not fun. Like if you, sticking to rules, it's like, yeah, everybody knows we should. just put our money in a bond index fund and a stock index fund 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 something big is happening or if the model doesn't seem to be performing, you kind of have to step back. and go, wait a second, what's going on? Or just the intuition that a model, you're taking a huge risk. Right. Even though if you're leveraging 30 to 1, and obviously, as Victor pointed, or much bigger 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.

Yeah. Quantitative finance. Fun. 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, sort of assessing where things are and the idea of like implied volatility being a sort of unified way. Or yield to maturity.

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 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 Wisenthal. You can follow me on Twitter at the stalwart. And I'm Tracy Allaway. I'm on Twitter at Tracy Alloway. Thanks for listening.

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