Fat tails in life and in your character

I recently wrote something about copulas. I actually wrote my undergrad thesis on using copulas to price bivariate index options. At the time, I knew about fat tails—the idea that large returns, especially negative ones, often fall outside the standard deviations that a normal distribution would imply. I saw a glaring problem: if tails were fat, then not only was volatility being unobservable a problem (there is no way to know for sure how volatile an asset is at any moment, but you can estimate it), but,  the state-of-the-art methods we used to estimate it, i.e. standard deviations and variance, we’re not good enough. Also, what happens when you need to deal with that asset returns that might follow different distributions? Like if you were pricing options with more than one underlying asset.

These problems bothered me for a few months as I expected to encounter them when I became a practicing quant. But then I found Umberto Cherubini’s “Copula Methods in Finance”. Talk of perfect timing. In that book I discovered copulas and was immediately fascinated by how elegantly they seemed to solve these problems. Their mathematics felt a bit too good to be true-almost like a magic trick.

Fat tails are a big problem in financial modeling. They mean that whenever you have a vol estimate say a 3-month standard deviation, you are always underestimating how bad things can get.

Back when I was freelancing, I was engaged on a project that used Vine copulas to optimize the so-called ‘crack’ spread (nothing to do with cocaine, I promise). A crack spread, also called a refiner’s spread, is a position in commodities where you are long oil, and short gasoline and heating oil. This is the natural position of any functional oil refinery. Refineries have to buy oil, refine it and then sell gasoline and heating oil. Not on paper like most traders but the physical commodities. They must take and make the deliveries on the futures contracts. Optimizing this spread—knowing how much of each to buy at any moment—is crucial to the ongoing concern of an oil refinery because it directly affects their operating expenses. Failure to optimize it can lead to huge losses. That’s exactly what happened when oil prices dropped in March 2020—a lot of oil and gas companies, a majority of them refineries, went bankrupt. They typically fund their operations with debt, and all of a suddenly they had bought oil at the highs and couldn’t sell their gasoline and heating oil because of Covid lockdowns and had to pay back loans with interest in the meantime.

Most refineries naively hedged this spread. They either buy some fixed pre-determined amount based on how they view things in the near-term, or they estimate hedge ratios by regressing the crack using say 6-month returns, perhaps using the same to estimate volatility to set upper and lower bounds on how much to buy or sell. This tells them how much operating margins to maintain, and they then go to a bank and take out a loan if they have insufficient cash. When shit hit the fan in March i.e. oil prices dropped significantly and volatility went through the roof, they were like fish out of the water. What they needed were models that incorporated fat tails. In the project I worked on, we showed that Monte Carlo simulations of oil prices based on Vine copulas would have given better hedge ratios and vol estimates—better than even GARCH (1,1)’s.

I’m not saying this to scare you, but to illustrate that you need to be aware that if you are using standard deviations for vol estimates: (a) you are using past returns, and that says little about the future, and (b) fat tails aren’t accounted for—in a risk event, you will likely see a bigger drop that you imagined. Always be aware of that as you set your stop losses.

Anyway, I’ve been thinking lately about fat tails in real life. There are of two kinds: the things you never imagine can happen to you, and the things you think you would never do.

You often hear people say things like: “I would never do that!” or “Me? Never” Well, the thing is, most times you just don’t really know. You’ve just never been in those circumstances. Usually, it’s when you hear a story about such-and-such person who did such-and-such thing. Then you think: “That nuts. I’d never do that”

Take being conned for instance. I don’t know if you know about the pig butchering scam; it was famous during Covid. Some guy somewhere far away  pretends to be this gorgeous man or woman online. They initiate what looks like a random or mistaken message, and they present themselves as very successful. You start talking and slowly they get you to fall madly in love with them, and then you ask what they do, and they tell you about their investments. At some point, they encourage you to invest in crypto or whatever other asset class. They give you the name of the platform they use, and you set up the account. You put a lot of money into it, and watch it grow with their advice and guidance. You put more and more money in, maybe even withdraw some of it a few times, and then one day, you log in… aaaaand it’s gone! All of it. You hear about such a story and you think: “that would never happen to me.”

It can. It can happen to you because you are human. You think you can’t be dupped but you can. You’ve just never found yourself in the conducive circumstances for such a thing as the pig butchering scam, but you would fall for some other scam even now. So the truth is actually that you don’t know. It’s the fat tails problem.

There are many things you say ‘can’t happen to you’ or ‘you can’t do’ but you would be surprised. One of the best pieces of advice I ever got about such things is that whenever you hear such stories, assume it can happen to you, or that you would do the such-and-such thing. It expands your empathy. In fact, you should do this for all the things you think fall in the above two categories. Think you can never be homeless? Maybe, but imagine if you did. Think about the circumstances that would put you in that situation. Think about how you would behave. Think about how you would get out of it. Mind you, you will still not be using a big enough imagination, but it’s a step in the right direction.

For one, the very belief that something like being conned can’t happen to you makes you more vulnerable to it, but also, exercising this kind of empathy gives you a different perspective on people in general. You always hear these stories of people doing weird shit on the bus or the train, and you are rightly disgusted by them. But sometimes, if you find out how they got to such a place, it would make a lot of sense why they are the way they are. There are many other examples of when you need to use this kind of empathy. For instance, we humans have a natural tendency to ignore the bad things in society. You hear a story of a burglary in the neighborhood, but is wasn’t your house so you don’t care much. You know who cares? Older people. They know about fat tails in life. They wanna know where, who, and what happened. They empathize a lot, and then they take extra precaution. You might think it’s overkill and maybe it is, but better safe than sorry.

Think a lot about the things you say you would never ever do. When I left for college, I told my cousin that I would never ever smoke weed. You know what happened on day one? I smoked weed with my neighbor. Why? Simply because of peer pressure--the need to fit in and be perceived as cool. And I liked it for a while despite the paranoia, but later realized it wasn’t for me, so I stopped. But while I was smoking weed for those few weeks, I questioned who I was becoming. I felt I had betrayed myself. “This isn’t me!”, I thought to myself.

When you say you’d never ever do something, you are ill equipped to deal with yourself when you end up doing it. You feel like a bad person, you don’t know who you are anymore and messes up your psyche. As long as you are human, you can do anything else a human can do. That is a good thing to remember. Fat tails.

It’s not all bad; there’s a positive side to it too. You hear stories of people winning the lottery, of finding the love of their life, of achieving their dreams, and you don’t imagine it happening to you. So you never buy the lottery ticket, you never ask out your crush, and you don’t pursue your dreams. And then you never know what could have been. Most people are content to live that way but then you miss out on a lot of great things. I’ve heard that when you get older, you regret more the things you didn’t do than the things you did and failed at. Generally, it is better to try. Try your hardest, and if you don’t make it, you can live with no regrets.

Every now and then life will throw you a curve ball. You don’t need to live in fear of it happening. When it does, you will be able to deal with it. But it’s coming. Fat tails.

We generally don’t think about fat tails when we plan things. Most people plan like so: they think of a goal, and then they think about how they will get from A to B. But things rarely go how we thought they would. I’ve recently learnt that that is the wrong way to plan. What you need to do is get in the habit of thinking about all the details and minutiae. To plan well, you first need an infallible vision, and then you need to be flexible on the details. Think deeply about what things will come up and how you will deal with them. It’s a lot more work, but you will more often that not achieve your goals.

We quants need that in finance too. Do a sensitivity analysis, include more variables. Do a scenario analysis, include more scenarios. I once heard a story that illustrated the risk management culture at Goldman Sachs. One time when there was a blackout in NYC due to hurricane Sandy, the only building that was lit was Goldman’s headquarters. Why? They had the same information as everyone else—hurricane Sandy was coming—but they actually prepared for it. Their culture encourages them to think about different scenarios and plan for contingencies. That is the correct way to manage risk.

Young traders don’t understand that they will experience fat tails in their trading. If you trade in the financial markets, at some point in your career, you will experience the mother of all losing streaks and the mother of all single-trade losses. It can’t happen to you right? It can and it will. Be prepared for it. But so is the other extreme; trade long enough and you will experience the craziest lucky streak of your life.

I got the idea for this post when I was thinking about how George R.R. Martin writes his characters. Most of his characters have a fatal flaw, and a redeeming quality. Little finger, for example, is one of the most helpful people you would ever come across, but he is also a master manipulator who can easily ruin your life. We are all like that: light and dark. It’s what makes love so great. When you love someone, you love all of them—good and bad. That is unconditional love. You want to be involved with people who will love you this way, and you want to love yourself this way too. You need to because not many will. A good way to deal with your dark side is to find out all the things you are capable of and then be in a position to choose not to do those things. Atheists usually get this question thrown at them: “If you don’t think God exists, why aren’t you out there doing X, Y or Z”. They simply respond that they chose not to. You want something similar; you know what you are capable of, but you are able to choose not to be that way. Otherwise you will have a weak character, and in the right (wrong actually) circumstances, you will find yourself doing the very things you swore you could never ever do.