Everything’s A “Derivative”
May 12, 2010 5 Comments
A lot of commentary on “derivatives” seems strange to me because it is premised on the idea that there’s a hard and easy-to-draw line between what’s a “derivative” and what’s not. Supposedly, to folks who want to (even more highly) regulate if not ban “derivatives”, among financial instruments there are things that are okey-dokey and they are very, very easy to delineate from those dangerous, scary things that are “derivatives”.
I disagree. Maybe it’s just the mathematician in me, but I think virtually all financial arrangements and transactions – at least, all those which don’t literally involve you standing there face to face with someone, handing over actual cash, and receiving a good or service at that exact time – could be considered “derivatives”, it’s just that some are special cases that are simple enough that they confuse people into thinking they’re not “derivatives” when they are too.
What is a “derivative”? Wiki seems to call it “an agreement between two people or two parties – that has a value determined by the price of something else”. So, like, everyone agrees that a stock option is a derivative; its value depends on the price of something else (namely, the stock). Add FX options, volatility swaps, CDS, CDOs, etc., things which are obviously derivatives. But people seem to imagine the list ends here, with the scary stuff and the acronyms. Surely it doesn’t include normal stuff our grandpas looked at with their newspaper-stained fingers, like stocks.
But guess what? A stock is also a “derivative”, at least if you believe the Merton model in which a stock is said to be a call option on a company’s assets. At the very least, a stock’s value surely depends on things like a company’s assets and earnings – why else do people look at P/E ratios? But what are a company’s assets? Surely among them will, as well, be some “derivatives” (stuff that has a value determined by the price of something else). Like if the company has a 12-month contract with some other firm to be their exclusively sprocket supplier at a fixed price-per-sprocket – the value of that contract will surely depend on the price of sprockets (if their contract is struck at $10 per sprocket, but sprocket prices shoot up to $20 three months from now, suddenly that contract is not as valuable to them). Maybe they hedge that out using sprocket futures – more “derivatives”. And what is the price of sprockets anyway? Surely it depends on supply and demand; supply could depend on whether sprocket suppliers are in good health or bad, which depends on their assets (which could include “derivatives”); demand could depend on whether people have jobs, which could depend on other derivatives; or it could depend on the price of steel and other raw materials for the sprockets, which depends on steel futures (more derivatives!)….you get the point. Trying to chase each “derivative” to its supposedly pure, unrefined, free-range, organically-grown, non-derivative root can, sometimes, be a fool’s errand.
Derivatives are also often just convenient ways of splitting out and parsing and understanding the value of assets one would normally think of as straightforward, vanilla assets. A floating-rate bond can be thought of as, whether or not this is how it is constructed, a fixed-rate bond (nice, safe finance) plus an interest-rate swap (a DERIVATIVE). Or, for an example closer to home, do you have a mortgage? Just a simple, normal, 30-year-fixed mortgage? Well then you, my friend, are almost certainly involved in the nasty, high-stakes, high-finance game of DERIVATIVES. After all you almost certainly have purchased, as part of your mortgage contract, a difficult-to-value and completely non-vanilla DERIVATIVE called a (gasp) Prepay Option – that is, the option (but not the obligation) to prepay the principal of your mortgage early, whether by just paying down principal faster than scheduled on your own volition, refinancing (i.e. finding a new mortgage that will pay off this one), or selling the house (finding someone else to take out a mortgage that pays off yours). The value of this prepay option depends on, most prominently, the prevailing mortgage rate (which can depend on things like the prices of TBA agency mortgage bonds, which can depend on the price of a 10-year Treasury, or on whether the government is buying up mortgage bonds, or on the political winds, or all of the above…). If your fixed rate is 5% and current mortgage rates are 7%, then your Prepay Option is probably not a very valuable option, but if rates come down, its value can shoot way, way up (time to call Ditech?). On the flip side, you also (at least in most states) have an embedded Default Option – that is, the option to ‘walk away’ from your mortgage and hand your house over to the bank in its stead and let them try to sell it. The value of that option depends on home prices; if they sink below a certain level, and you start to owe more on your house than it’s worth, the Default Option starts to look really in-the-money to some people.
And you know what’s funny, far from being some esoteric financial gibberish that only sniveling French Goldman-Sachs-working spoiled-brat business-ecole a-holes understand, all homeowners understand these things quite well. Normal boring middle-class folks across the country know about the prepay option and its dependence on the mortgage rate, follow the prepay option’s implicit valuation regularly, and intuitively understand whether it’s in-the-money or not. Similarly, they (only too well, in the past three years) understand the Default Option, i.e. the concept of how much ‘equity’ they have in their house, and whether they are ‘under-water’ – concepts that can’t be reckoned other than as derivatives of home-prices. So let’s face it, if we’re being honest, a huge percentage of Americans play around in derivatives. They just might not think of it that way.
The classical way to understand a derivative is its payoff profile. These are just graphs designed to show how a derivative’s value (y) depends on the underlying’s price (x). Anyone who took Derivatives 101 got very used to understanding these little diagrams with bent lines or inverted triangles on them. So like here’s a picture of an equity call option payoff – its worth (y) is 0 if the stock price ends up being somewhere on the left (i.e. x is low), but has an increasing value to the right (if the stock lands higher than a certain level – the ‘strike’ – then the option has value, and the higher the stock price ends up, the more the option will end up being worth).
Similarly, here’s a possible payoff shape for the Prepay Option you homeowners all have, where x = current mortgage rates; if rates are low (x = to the left) then your option has value, and the lower rates are, the more valuable it is (i.e. the more you have to gain from refinancing), but if rates are above a certain point the option is worthless. (Note this option is also an American rather than European option, since it can be exercised at any time, so in a sense it’s even more complicated than a stock option):
So why do I say that everything’s a “derivative” then? Well what about this payoff:
This payoff is just y=x, i.e., the value of something is the price of that thing. This is just the payoff of a spot transaction, i.e. a transaction done then and there, for a price. If the price is 50 the value is 50, if the price is 100 the value is 100, and up and up. This seems like a silly, roundabout way of saying something obvious, but the point I’m trying to illustrate is that this is (or at least, can be thought of as) just a special case of all those nasty, complicated, French-seeming things we call “derivatives”. It’s not as if it’s a whole different animal after all.
Let’s say you go to Circuit City and see a large-screen TV you like. They offer it at $500 and you think that’s ok so you buy it. That’s a ‘normal’, safe, healthy transaction that doesn’t need Congressional oversight right?
Or is it a “derivative”? After all, maybe we should think of what you’re really doing at Circuit City as entering into a forward contract at the strike price of $500 to have some guys in a truck deliver it to your house probably later that afternoon. So that’s a derivative! Its value depends on the value and likelihood of that delivery. What if there’s traffic, and the guys use more gas than expected – your side of the contract gained value, Circuit City lost. Or maybe you don’t have it delivered but they still have to get it from the stock room while you wait. Maybe they take longer than expected to find it, using up your (valuable) time – your side of the contract lost value. These are all derivative considerations that affect the value of this seemingly simple, spot transaction.
On the flip side, notice the store’s side of the transaction: they haven’t actually taken money from you, they just swiped your credit card and got your signature. This effectively creates a supplemental agreement to existing contracts that they and you had with your credit-card company: they now have a piece of paper (or electronic equivalent) from you with “$500″ written on it that (the credit-card company promises) they can deliver to your credit-card company and receive $500 cash in return – in other words they have a put. That’s a derivative! It has counterparty risk (what if the credit-card company declares bankruptcy?), legal risk (what if you dispute the transaction or decide to sue them or the card was stolen?) and a tiny bit of interest-rate risk (since they won’t actually get the $500 cash till a bit later…). Your credit-card company, in turn, has a complicated hedge contract with you in which you promise to repay whatever they have paid out on your swipes, either right away or with interest, and with penalties that can kick in according to certain rules, etc. The interest-rate on unpaid balances is probably fixed (and high, of course) so that’s interest-rate risk which they surely hedge with swaps. The overall rules governing repayment are quite complicated and depend on lots of things. And your credit-card company obviously has counterparty risk – you might go delinquent, or not pay at all. So surely that’s a derivative too!
So you see? Buy a TV at Circuit City and you’re a nasty, despicable derivatives trader.
Now my point is not that I really think it makes sense to call this transaction a “derivative”. The simplest explanation is the best, and all. The above complicating factors aside, surely the payoff on such a transaction is still pretty much the straight diagonal line diagram above – if the TV costs $500, Circuit City’s end of the deal is pretty much worth $500 to them, more or less, and you’re pretty much out $500, more or less. Sure. It’s pretty much just a spot transaction. But…well, not quite, is it? There are complicating factors, it’s just that they don’t affect the valuation from that straight line all that much. So while a pure spot transaction is executed right away, and has that straight-line payoff, many if not most real-world transactions are not pure spot transactions. They’re DERIVATIVES.
It’s just that some derivatives are close enough to idealized, perfect spot transactions that the difference can be ignored. But this is a difference of degree, not kind. So if you really want Congress to ban or closely circumscribe all “derivatives”, you are either speaking very loosely or you’re talking about far more transactions than you realize. In the real world, the value of almost everything depends on the value of other stuff. This is because we are so interconnected, efficient, and wealthy, and is not a scary fact or one that can be wished away or regulated away at all. Or at least, it shouldn’t be.