Ask A Banker: What's A Derivative? : Planet Money I will tell you what a derivative is, but I will take a while to get there, and you may feel cheated. That is okay. If you want to understand derivatives, you must learn to live with uncertainty, and also with feeling cheated.

Ask A Banker: What's A Derivative?

Not just an empty suit.
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Hi! Remember me? I was a banker. Now I am a guy who answers your questions, when I'm not writing for Dealbreaker. You can send questions to with "ask a banker" in the subject line, or ask on Twitter (@planetmoney).

A bunch of questions last week were about what I actually did as a banker and why I left. These are good questions but to get to them we need to make a brief (not brief) stopover at another question, because what I did was "sell corporate equity derivatives," and that perhaps leaves you no more informed than you were before. So let's take the question reader Mike Kelly posed in a comment on my previous post:

Q. It would be nice if you wrote about derivatives. The term gets used a lot in the media but is seldom explained in a way that is understandable outside the financial industry.

I am glad you asked! You may end up less glad. I will tell you what a derivative is, but I will take a while to get there, and since I won't use words like "put option" or "synthetic CDO" you may feel cheated. That is okay. If you want to understand derivatives, you must learn to live with uncertainty, and also with feeling cheated.

In your finance textbook, if you have one, which I hope you don't because I'm just making this up, a derivative is defined as a contract whose payoffs are determined by reference to the price of some underlying variable. Derivatives, which include options, futures, forwards and swaps, allow levered and/or nonlinear bets and ...

... and let's start somewhere else.

There is a world. That world will have a future, and that future is uncertain. There are different possible states of the world, and different things will happen to you in those different states. If it's cold this winter, you will be sad, or perhaps happy if that's what you're into. If it rains tomorrow, you will get wet. If you take an economics course, you will start to talk like this.

If you are a company or an investment fund, the outcomes that you care about can pretty much be reduced to money: if it's cold this winter, individual workers and managers might be happy or sad, but the company has no feelings. The company just has money. If it's cold this winter, the company might have more money, if it's an oil company, because people will buy more oil to heat their homes. Or it might have less money, if it's in the agriculture business, because its crops will freeze. Or it might have the same amount of money, if it's, like, Facebook or whatever.

One thing you can do is graph future states of the world versus the amount of money you will have in those states. So for instance here is the money that an oil company will make this year (y-axis), graphed against the temperature this winter (x-axis):

The world is not this simple. Matt Levine hide caption

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Matt Levine

This is a simple chart but you should see immediately that it's wrong, or at least not right.

Of course you can't predict how much money an oil company will make just by knowing the weather: there are many other things going on.

You can make your graph better - make it a more useful tool for understanding future states of the world - by including more factors. For instance, oil companies make more money when people drive more, and people drive more when they have jobs to go to. So high unemployment is bad for oil companies, and unemployment is uncertain. So you can think about how much money the company makes against two uncertainties: the temperature, and the unemployment rate.

Two uncertainties plus how much money the company makes leads to a three-dimensional graph. NOTE: You can totally skip over the following ridiculous three-dimensional graph, which I just made up.

Ignore this graph. Matt Levine hide caption

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Matt Levine

This is better – incomprehensible! but otherwise better - but it still goes only a very little way towards capturing the actual world.

The unemployment rate itself depends on lots of other things, all of which are uncertain - interest rates and government policies and corporate innovation and the growth of China's economy. And each of those things can interact with each other in uncertain ways; the future path of China's economy could well influence corporate innovation, which in turn could affect interest rates.

On top of all that, there's the stuff we haven't even talked about yet. The oil company's rigs could blow up, say, or everybody could start driving electric cars to their jobs producing solar panels that bring down the price of oil.

Imagine building a million-dimensional graph. Each input - all of the axes but one - is some fact about the world whose future value is uncertain: the temperature this winter, the population growth in China, the price of corn, the number of homes built in Utah, the amount of rainfall in Tuscany. Each of these inputs is uncertain, and each can have an effect on the others. The output - the last axis, call it the "height" of the graph - is the amount of money that your company will make given any set of values for each of the other 999,999 axes. The higher the graph at any point, the more money you make at that point. Higher - more money - is better.

You can't build that graph. You can't visualize a million dimensions (this screen is crowded enough with three), you can't think of all the uncertainties in the future that might matter, and you can't figure out how much money you'll make in every state of those uncertainties. I just wanted to tell you about it because everything in the financial world is an attempt to catch a flickering glimpse of that graph. That graph is the thing, the Platonic form. Stocks and bonds and hedge funds and derivatives and everything else are the shadows, the imperfect methods of approaching the thing. If you want to make all the money in the world, go make that graph.

If you had that graph the next thing you'd ask yourself is: how do I think the world will be? If you're sure that it will be cold this winter, then you might think that our oil company will make more money. That's great, if you're the oil company, or its shareholders. If you're not a shareholder of the oil company, though, maybe you should buy some shares: they'll probably go up in value if it's cold*.

Perhaps you're not sure that it will be cold. Let's say you think that most likely the temperature in the Northern U.S. will average about 30 degrees this winter, but there's a chance it could be as warm as 60. And let's also say you're the oil company. You will probably make a lot of money (if the average temp is 30 degrees). But you have a chance of making a lot less money (if it's 60). That's just fine. You don't have to do anything about that.

But you could, if you wanted to. You might not want to risk making less money – maybe you took out a loan and you need at least a certain amount of money to pay it back. So you could do something that will make you less money in the cold-winter case, but more money in the warm-winter case. (Everything in life has trade-offs.) In other words, you'd smooth out your outcomes a bit. Like this:

This is a hedge. Matt Levine hide caption

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Matt Levine

This is called "hedging."

How do you hedge? Well, one thing you can do is just bet that it will be warm. You could make a bet where I pay you a quarter of a million dollars for every degree over 40, and you pay me a quarter million for every degree under 40. That would give you the outcome above. You'd need to find someone else to bet with you, though; I am unlikely to be good for it.

Another thing you can do is find something correlated with a warm winter - that is, something that goes up in value if it's warm. Let's say agriculture companies will make a lot of money, and their stock prices will go up, if it's warm this winter. Oil companies don't often buy agriculture stocks but there's no reason they couldn't. It might be a nice hedge**.

Hedging is one way to change the shape of the graph: you smooth the graph, making it less bad in bad cases at the cost of making it less good in good cases. There are other ways to change the shape of the graph. One is just doubling down: making the graph better in good cases and worse in bad cases. (Again: tradeoffs.) If you're an oil company, you make more money as oil prices go up. But if you're really confident that oil prices will go up, that might not be enough for you. Why not make even more more money if oil prices go up? Why not, say, buy another oil company?

Your imaginary chart is million-dimensional, and you are just one person or oil company. So you think about some of the axes that you can predict accurately - and about some of the axes that you can't predict accurately, but that worry you, because how much money you make is strongly tied to them. If you are a farmer, you can't really predict the weather with much certainty, but your livelihood is tightly bound up with the weather, so you spend time thinking about the weather.

The ones you can predict, you predict - as traders say, you "take a view." If you think the price of oil will go up, you buy oil stocks. If you think Facebook's stock will go up, you buy Facebook stock. If you think there's gold in them there hills, you buy the hills and start digging. You change the shape of the graph to make you more money in the states of the world that you think will come true.

The ones you can't predict, but that keep you up at night - those you hedge. You flatten the graph in the scary places, so you can get back to sleep.

Changing the shape of the graph is in some loose sense the business of the financial system, particularly the big investment banks, which are sometimes thought of as "dealers in risk." "Risk" here means the shape of the graph: hedgers come to dealers to flatten their graph by buying hedges (or "reducing risk"). Speculators come to dealers to steepen their graph by "putting on risk."

Where do you get risk? Well, most of it comes from things that exist in the world. If you think house prices will go up, buy a house. If you think gold prices will go up, buy gold, or mine it. If you think Chinese people will buy more cars, start building cars and selling them to China.

And if you think Facebook stock will go up, buy Facebook stock. A subset - a small but important subset - of "things that exist in the world" is the group of things called "securities." These are just stocks and bonds, which we've talked about a little before. Companies and governments finance themselves by selling securities, and people then go buy and sell them because they think that good or bad things will happen to those companies and governments.

Securities are important because for the most part they are pretty easy to buy and sell, so they let you change the shape of your graph without drastically altering your life. If you think a lot of Chinese people are going to buy cars, but you don't feel qualified to start building cars, you can just go buy some shares of Ford stock. Because Ford will probably make more money if lots of Chinese people buy cars***.

But you can also get that risk from things that don't exist in the world. Instead of buying oil, or oil company stocks, you could go to your friendly risk dealer and say, "I think that the price of oil will go up. But I don't want to buy oil because, where would I put it? I just got a new carpet and, you know, oil. So I just want you to give me money if the price of oil goes up."

The dealer will agree to give you money if the price of oil goes up. In exchange, you will give the dealer money now, or maybe instead you'll just agree to give him money in the future if the price of oil goes down. You enter into an agreement that just changes your graph directly, without the intervention of things that already exist in the world.

This is called a "derivative."

A derivative is a contract – that is, not something previously existing in the world – between a risk dealer (an investment bank, often, or a commercial bank or insurance company or an options exchange) and a customer. The contract will have different payoffs in different future states of the world. It is entered into because the customer wants to change his risk profile. The customer wants to change the shape of his graph by the amounts of those payoffs in those different states.

There are technicalities of course. There are "linear" derivatives, like forwards and futures and swaps, that change your graph in ways that look like straight lines. There are "nonlinear" derivatives, like options, that change your graph in ways that curve or kink. There are "exotic" derivatives, which, basically, have more curves and kinks. Incidentally, Wall Street more or less charges by the curve and kink, so exotic derivatives are more expensive than options, which are more expensive than linear derivatives.

These things are all super important if you want to trade derivatives on Wall Street (or, more importantly, with Wall Street). If you do, I recommend that you go learn all about them and not read the previous 3,000 words. YOU'RE WELCOME.

But if you don't want to trade derivatives on Wall Street, there is no particularly burning need for you to learn about those things.

And that brings me to my question for you, Mike Kelly: If you don't want to trade derivatives on Wall Street, why do you want to know so much about derivatives?

Allow me a presumptuous guess.

While everyone's financial life consists of bumbling around changing the shape of their payoff graph in some more or less conscious way, the people who deal in derivatives - as dealers or as customers - are doing it particularly directly and consciously. If you build a lemonade stand, you probably do not scan the 10-day weather forecast and ponder historical correlations between temperature and lemonade consumption, because you are 8.

But if you build a global macro hedge fund trading eurozone sovereign CDS, you probably actually have a computer model that approximates the million-axis graph I talked about above. (Maybe you call it a "VaR model.") Each day you come to work and actually in so many words ask yourself questions like "what do I think will happen to Europe?" and "how much money will I make if what I think will happen, happens?" and "how much money will I lose if it doesn't?" and "should I do a trade that will make those numbers different?" And if the answer to that last question is "yes," then you most likely go trade a derivative.

Buying and selling derivatives means consciously trafficking in risk and uncertainty, in a relatively uncut form. This makes it interesting to people who don't buy or sell derivatives for a living, but who are curious about risk and uncertainty. These days, that is most of us. You may have heard of the "fear index," or the VIX, which reporters sometimes cite as evidence of the stock market's worries about the future. The VIX is basically just an arithmetic operation performed on certain derivative prices; it can't tell you how fearful you are unless you are buying and selling those derivatives. But the people who buy and sell those derivatives have been enshrined as our society's designated worriers about the future, and they're probably as good for that job as anyone else.

Similarly, lots and lots of people are worried that various countries in Europe will default on their debts. This is something that matters a whole lot to a lot of real people, not just derivatives traders. But the price of derivatives based on Portuguese or Greek debt (credit default swaps) is as good an indication as you can probably get of how worried the people whose job it is to worry about this are. So if you want to know how likely it is that Portugal will default on its debt, those markets are a good starting point.

So part of why you want to know about derivatives is because they tell you something important about the possible future states of the world. But there's another part. Because derivatives are a way to shift risk, they also have a tendency to hide risk, to move it from people who understand it to people who don't, and to allow too much of it to pile up in one place. And while everyone who trades derivatives is in some sense in the job of dealing thoughtfully with risk, some people are just bad at their jobs. This is why Warren Buffett has called derivatives "financial weapons of mass destruction."

This matters a lot, too. A simple model of the 2007-2008 global financial crisis is that a whole lot of people - German banks, Lehman Brothers, AIG - entered into lots and lots of derivatives that changed their graphs in basically the same way: they made lots of money if house prices continued to go up, and they lost many times more money if house prices dropped. They did this because they were confident that house prices would keep going up and so wanted to make money in that case, or because they were stupid, or both.

Obviously lots of people's graphs looked like that to begin with: everyone who had a house, and every bank who made mortgage loans, was better off if house prices went up than if they dropped. But the derivatives shifted some of that risk from people who understood and were able to bear it, to people who didn't understand it and blew up when the bad outcome materialized. And they also created additional risk: some people just went around betting each other that house prices would continue to go up, and those people also got blown up, magnifying the problem.

There are things to object to in that model but on the whole I think it's a good one****. And so you worry about derivatives because you remember 2007-2008, and you think that it might happen again, and you are afraid. Maybe you're right, I don't know. It's hard to know, isn't it? Maybe you should buy some derivatives, just in case.

Next time, maybe: What I did in banking, or, derivatives for regulatory arbitrage, or, why everything above was false.

*Unless everyone thinks the same thing. There is a deep and subtle mystery here. If everyone thinks it will be cold, then you will have to pay so much for the oil company's shares now that you won't make any money when your prediction comes true. It's not enough to know what the future holds: other people have to think otherwise. I could make a lot of money betting that the moon is not made of smoked Gouda, if I could find anyone to take that bet. But I can't. This is called the "efficient markets theory."

**For reasons mostly outside the scope of this column, the topic of hedging by oil companies - or other companies whose profits are tied to a volatile commodity, like gold miners - is actually full of interest. A very approximate thing you might say is "their shareholders don't want them to hedge, but their creditors do." A look at Figure 3 might give you a sense of why that might be. (Also, even more outside the scope: some oil companies do in fact own agricultural-ish companies because it turns out that lots of fertilizers are more or less made from oil byproducts. Appetizing!)

***Or they won't, I don't know. A possibly useful general disclaimer here: if you ever buy or sell a stock based on anything that I, or anyone else, say here, or anywhere else, you need to re-evaluate your life choices.

****Which is good, because it is a popular model. The version of it that I am waving at draws from Gary Gorton's work on the financial crisis, particularly his book Slapped by the Invisible Hand.