My first RI!

I brought this up here a few weeks ago but I thought it was worth expanding on. Our exhitit of badeconomics:

BIS says there are $1 quadrillion in derivatives right now on earth. The last time there was this much in derivatives was before 2008. The banks made sure they can take your money if they crash in the last budget bill passed by U.S. How much is $1,000,000,000,000.00? If one dollar = one second. one million dollars = 12.5 days one billion dollars = 30 years one trillion dollars = 30,000 years one quadrillion dollars = 30 million years When derivatives collapse, you will finally understand that sea level and earth temperature rises will be the least of your worries, unless a resilient high pressure block parks its ass over the mid-west this summer. Because if it does, world starvation will begin. Don't forget that the U.S. government sold off its grain reserves in the last recession.

Admittedly this comes from /r/collapse, so I feel almost mean picking on this (the other post I made was criticizing Bloomberg News for misusing the figure we're going to talk about). Also apparently agriculture will collapse in 50 years. But I wanted to talk with you about derivatives, because I worked with them for 6 years and I find them endlessly fascinating.

The Biggest Number You'll Ever Hear

One thing that is true about this (and perhaps the only thing) is that the notional value of the world's derivatives is probably the single largest money value you can meaningfully talk about in finance and economics. The world's total debt, for perspective, is about $200 trillion, or 2.86 times global GDP.

If you google "derivatives quadrillion" you will get a lot of posts from people sharing our friend's view with varying degrees of breathless panic that the sheer size of this number will bring down the global economy. (Saying that it will end civilization, though, is new to me.) This quadrillion figure purports to be the notional value of the world's derivatives, and our friend is kind enough to cite the BIS, the Bank for International Settlements. The BIS is an international financial institution predating the IMF and World Bank sometimes called a "Central Bank's Bank" because it, well, settles international finances. If you've heard of the Basel Agreements (such as Basel III), which are at the core of international financial regulation, the reason they're called "Basel" is because the BIS lives in Basel, Switzerland.

Anyway, one thing the BIS does is count up all those derivatives. You can see the BIS data here. Indeed, you will see an eye-wateringly large number there: $552 trillion notional value for the world's derivatives (again, compare that with $200 trillion in global debt). That is down from $710 trillion in 2013 but a far cry from one quadrillion dollars.

That $552 trillion figure refers to OTC (over the counter) derivatives. There is another variety of derivatives - "listed" or "exchange-traded" derivatives. The BIS calculates an additional $63 trillion open interest in listed derivatives. Open interest is a comparable figure to notional value for listed derivatives.

If you don't know what OTC and listed derivatives are, don't worry, the difference is an important part of our story that we'll get to.

The BIS excludes certain types of popular listed derivatives from this total for some reason, including the kind of derivative that most people have heard of: stock options. The Office of the Comptroller of the Currency (OCC) [http://www.occ.treas.gov/topics/capital-markets/financial-markets/trading/derivatives/dq415.pdf](provides reports) on US derivatives exposure: out of $181 trillion in notional value US derivatives, $3.4 trillion are stock and commodity derivatives, so we aren't missing much.

I've Got a Notion Of A Notional

So what is notional value and why is it coming to kill you?

Financial derivatives are about being derived from something. The something is called the underlying of the derivative. Roughly, the value of that underlying is the notional value.

There are many fancy variations of derivatives, but there are three basic kinds: forwards, options, and swaps. The simplest one is a forward contract, which is just an agreement to buy something at a certain price at some point in the future. I'll give the same example I gave a few weeks ago:

Say we have a forward contract for one barrel of oil. This agreement says you will buy a barrel of oil for $30 from me in three months. The notional value of this contract is $30. If oil ends up costing $31 when the contract is due, you are able to pay $30 for something worth $31. The value of the contract then is...not $30 (the notional value), not $31 (the spot price), but...$1.

At the time the contract expires and you have to pay for the oil, this contract is just a coupon for $1 off on a barrel of oil. You're still obligated to pay $30 for the oil, but the derivative itself is only worth that $1 coupon.

If you had wanted just the option (not the obligation) to pay, you could have bought...an option. I won't get into options because this is already really long although options are way more fun.

I Just Wanna Sit Back And Unwind (My Forward Contract)

You might say, "Well, Sporz, fine - the contract itself is worth $1, but I'm still obligated to pay up $30 (notional value) for the oil. So it's still relevant?"

Yeah, and if you actually do hold it to maturity, you have to accept delivery of that barrel of oil and pay. But there is a way to get out of it and just pocket your $1 without actually getting a barrel of oil: Sell the contract. In fact, sell it back to the person who's giving you the oil for that $1 that it's worth (who will just rip it up, what's the point of delivering oil to himself?) Now there's no $30, just that $1 that changed hands - and nothing to do with the notional value!

"Sporz, that's insane!"

It is a little convoluted but it works. It works so well that the vast majority of contracts are unwound this way.

You may be wondering why you would bother doing this if you didn't actually want to buy or sell oil. One answer is that you could be just speculating on the price. The other is if, say, you're an airline that wants oil, or an oil producer selling oil - you get the ability to fix the price ahead of time rather than worrying that, when you need oil the price will be sky high or rock bottom. This reduces your risk substantially. A lot more oil producers would be bankrupt now if it weren't for these handy little hedges. This is why derivatives are so important and valuable and how they can make the world safer.

"But I still need oil!"

Yes, but not oil in Cushing, Oklahoma.

Back To The Future (Contract)

"Why are we in Oklahoma, Sporz?"

So, a forward contract like the one we made is an over-the-counter (OTC) derivative. OTC derivatives are nifty because you and I get together, decide on a custom price, and a custom location for delivery. The problem is that this is expensive (we're hammering out a very custom contract and I am a very expensive banker), you're dependent on me still being in business when the contract is due (I may be very expensive, but I also could be very incompetent), and if you want to get out of it, either I'm feeling nice, or you have to find someone else to take this very special contract and that can be hard. People still do this sometimes (Pemex, the Mexican national oil company, hedges using OTC oil derivatives) but you can see some problems.

Futures contracts are closely related to forward contracts. The difference is that they are listed derivatives - instead of calling me up and hammering out this very custom contract, you go to a big exchange, like the New York Mercantile Exchange (NYMEX) and buy the contract there.

The contract is completely standardized: the oil (West Texas Intermediate) gets delivered on specific dates, and at a specific place (Cushing, Oklahoma).

"But I want oil in Ohio."

The price of oil in Ohio is going to be pretty close to what it is in Oklahoma. (The difference is called basis risk). But close enough. So you close out your NYMEX contract and pocket your $1 and pay about $31 in Ohio for oil. Net, you still managed to pay $30.

The benefit is: Because the contract is standard, many people want to buy and sell them, so you shouldn't have a hard time getting out if you want. Also, you aren't contracted with me specifically. If you want to buy, and I want to sell, the exchange will contract with us both. Your counterparty isn't me, the incompetent banker who might disappear tomorrow, but with the entire pool of buyers and sellers at the exchange.

The other thing is margining and daily settlement. Obviously the exchange doesn't want to pick up the tab for me being a deadbeat if I can't pay in three months for that $31 barrel of oil. So I have to keep some amount of cash in a margin account at the exchange to cover me. Each day, the contract is settled as if I had closed it - if the price went up, I have money taken out of my account. If the price went down, money gets put in from yours. If I don't have enough money in my account, I face a margin call#Margin_call). (Awesome movie) by the way, you should see it - ironically there is no margin call in it). If I don't make the margin call and top up the account, my position is closed immediately for being naughty.

"What does this have to do with notional values?"

It doesn't. It has to do with making derivatives safer (almost to the point of paranoia at times). So derivatives won't blow the world economy up like our friend thinks they might.

So, how big is it? Really?

So we've talked about the benefits of derivatives (being able to hedge risk), things that can make derivatives less risky (margining, daily settlement, and central clearing - we'll come back to those). And that notional value is not a good way to measure the size or risk of derivatives. So what is a good measure?

One way to think about it is, if we see that notional value can vastly overstate the size of a derivative (our $30 notional, $1 value forward contract again), we can think about the market value. Our forward contract has a market value of just $1.

It's also worth noting that notional value could (in rare cases) be less than the market value. If oil had risen to $90, the contract would be worth $60 - on a $30 notional. But this is rare and (for reasons I'll get to) statistically impossible for derivatives as a whole.

If we go back to our favorite BIS report you'll see a figure for "Gross Market Value" which is just $15 trillion rather than the $552 trillion for OTC derivatives. That's a huge difference, I don't have to tell you - $15 trillion is a big number but not nearly as mind-boggling as half a quadrillion. This is essentially the difference between the $1 and $30 values for our forward contract.

But it gets better. Let's look at our favorite OCC report, the one that talks about American derivatives.

We start with that $180 trillion notional, and there's a "Gross Positive Fair Value" (this is like "Gross Market Value") of $4 trillion. So, great the US's derivatives are a lot smaller than notional would suggest too.

But let's imagine that you're a bank now and you have lots of deals. Lots of these deals offset each other, though - one derivative I have with you might be worth $1M, the other might be worth -$500,000. If you or I go bust, it isn't $1.5M down the drain - just the difference, $500,000. This difference is net current credit exposure (NCCE).

That NCCE is just $500 billion for the US. So out of that $4 trillion worth of derivatives out there, there's enough offsetting going on that there's only $500 billion on the hook.

NCCE can change dramatically (It went up to $800 billion during the crisis) but it's pivotal to estimating the magnitude of derivatives as a potential economic risk.

You just make me wanna SWAP!

"So, Sporz, I was reading your favorite BIS report and I noticed you haven't talked the biggest part - $434 trillion in interest rate contracts. WHAT ARE YOU HIDING!?"

Calm down! I'm getting there!

The fun thing about derivatives is that they mix and match. You want a forward contract buying Euros intead of oil? You got it. An option on a commodity? Sure. An option on a future on a basket of options on a basket of stocks? Go nuts.

As you may know, interest rates are kind of important in finance. Like the oil price, interest rates move, and like people sometimes want to bet on the oil price or lock in a price that they find preferable to tons of risk, people want to do this with interest rates. A lot.

By any measure, interest rate derivatives are more popular than any other category of derivative. More popular than the rest of them combined, even.

So it's worth talking about them.

The characteristic feature of a swap is paying repeatedly for something. Our forward contract just had us pay once; a swap on oil would have me paying each month for a barrel of oil for say $30. (Like the forward contract, this is rare for crude oil - you'd rather buy a bunch of crude oil futures and pay those each month for that sweet, sweet Oklahoma oil).

A typical interest rate swap will have two sides - one will pay floating, the other will receive fixed. These are called the "legs" of the swap. The floating leg will pay every three months whatever the chosen interest rate is (say, 3 month LIBOR - yes, that LIBOR) The fixed leg will pay a fixed amount over the life of the swap. This is useful because if - say - you're being paid a lot of variable rates and worried they'll crash, you can trade that out for a known fixed rate and then you are safe and happy.

This is very common but swaps (like all derivatives) can get super fancy. Add in a few more legs, a collar, a call, some cross-currency risk, and now we're talkin'.

Interest rate swaps are important not just because of their enormous size, but because they are OTC. Like our original forward contract, these get sketched out between counterparties and are highly customized. In the past, these had some of the problems are forward contract had - you may find it hard to get out of this swap if you want to, and you're dependent on me, your sole counterparty, to pay up and if I don't show up then you are sad, lonely, and out of a lot of money.

Some of those things that make listed derivatives safer have been applied because of The Recent Unfortunateness to OTC swaps. There are now Swap Execution Facilities to, er, facilitate swaps. Specifically, swaps now have to be centrally cleared (kind of like the listed derivatives) which reduces dependency on a single counterparty. There are also margin requirements to make sure that the swap gets paid. This is intended to reduce the systemic danger of swaps blowing up.

So credit. Very risk.

Even if you've never thought much about interest rate swaps, you might have heard of credit default swaps.

These have a fun story. Swaps have been around in bulk since the 70s; options around the same time (thank you Black-Scholes); forwards are ancient. Modern credit default swaps were invented by a lady named Blythe Masters at JPMorgan in 1994 because they were worried that Exxon wouldn't pay a debt to them because of the Exxon Valdez disaster.

Credit default swaps (CDS) are usually described as insurance. They're called "swaps" in the name but they do not taste like swaps. The typical interest rate swap will see both sides make money at various points during the life of the swap (usually) and it will not be very much (remember - you make the difference between two different rates, which is unlikely to be very much). A CDS looks like this in that one side pays for protection ("protection buyer") and the other side sells it. The protection is on some debt some company owes (say, Exxon). As long as Exxon keeps paying its debts, the protection seller just keeps getting paid, and if everything is hunky dory, the protection buyer might never get paid back anything at all.

If things go pear-shaped, though, the protection buyer gets to cackle with glee and sell some worthless bonds for full price to the protection seller. Then the swap ends, and the protection seller is very sad.

One thing that makes this different from insurance is that I can't insure your house (unless I live there. Can I?) And I can't insure it multiple times hoping that it burns down.

"Well that's creepy."

Yep.

It's not quite as creepy as it sounds, though. For every "I hope his house burns down" there is an equal and opposite "I hope his house stays pristeen and perfect and only lightly singed." This is not academic - there are things like The Curious Case of the CDS and the Spanish Casino in which the company was made to technically default, trigger the CDS, and go on happily. It has been described as "objectively beautiful." It made The Daily Show.

No talk of CDS is complete without AIG, though. You'd think an insurer would have done better than insure the hell out of all the bad debt in the world, but that happened.

I bring this up not to bury CDS but to praise it. Derivatives are tools. They can be used for good and ill. The key is to make them good rather than throw out a potentially valuable tool.

The main challenge with CDS is that (unlike normal swaps) they have the potentially to blow up in a big way. For years you make a few pennies a month selling protection then one day you discover you've been protecting Lehman and then you are sad in a big way.

Since 2008 CDS was changed to be more standardized (helping you get out of one if you're in trouble). They now have to have fixed coupons (and, making them even less like normal swaps, there is an upfront payment to compensate) making them similar to one another. They also have margining and central clearing now. The goal here being entirely "Let's not let these derivative blow the world up, shall we?"

Oh, and Blythe Masters (inventor/popularizer of CDS) went on after inventing these things to prank the California energy market and is doing stuff with bitcoin now. Bon voyage.

So long, and thanks for all the derivatives

So this is incredibly long but I've had my thoughts on derivative percolating for a while and I wanted to illuminate some of it. So we covered how notional value vastly overstates the economic relevance of derivatives; we illustrated it with a forward contract; talked about how certain innovations in the listed market make derivatives less fragile; and discussed how those innovations have been applied to certain interest and credit derivatives since The Great Unfortunateness.

I do want an excuse to talk about mortgage backed securities and stuff because those are fun too.

"Wait, you owe me a barrel of oil!"

Dammit.