Derivatives 101: 10

Reasons are more interesting than facts; and always outnumbered by them. Pundits incessantly tell us we are living in an Information Age, and they are probably right. Information is something more than mere data -- is, in effect, a filtration of it -- but it is nevertheless some way short of what really matters, which is understanding.

Derivatives markets are an accretion of historical arbitrariness, and almost everything they do is steeped in idiocy. There are often reasons for the idiocies -- eg, to do with tractability of computation in the pre-electronic age -- but that doesn't make them any less stupid now, and it often feels like the real reason things work in a particular way is basically protectionist: it's job security through obscurity.

Detour for a moment into the lunatic world of Imperial measures: inches, feet, yards, fathoms, furlongs, chains, rods, poles, perches, more varieties of mile than you can shake a stick at -- and that's just one dimension. Arbitrary distances related by arbitrary ratios, each with a different use. These things may develop for good reasons or they may be just happenstance, but once in use they effectively become a private language, a cryptosystem -- and a currency. There is value in their peculiarities because learning how they work is hard; hard in that annoying, pointless, nitty-gritty way that involves little or no understanding. Hard as in hard facts. If, say, the King taxes his subjects on the basis of the acres they farm, there'll be money in knowing what the fuck an acre is.

Financial markets are exactly like that.

Newspapers like the Wall Street Journal and the Financial Times print daily market information in excruciating detail, in an age when no-one who actually has any reason to care about any of it is going to wait around for the dead tree version, out of date before the ink dries. Irrespective of the route by which the numbers are received, people pore over and analyse them endlessly and hope to bend them to their wills -- and these people are morons, even the unbelievably clever ones¹.

Let me be clear: numbers are not boring. Numbers are fun and fabulous, a deep and powerful language through which to understand things. But these numbers are the dullest, deadest kind of fact, mere grit in the well-oiled workings of the world; and the way they are bandied as news to the uncomprehending masses is one of those things one must pit a lot of beauty against in those moments one seeks to justify living.

Fortunately, there's a lot of beauty out there to pit.

All of which is simply by way of a preamble.

Obviously, I have no idea how much you've understood of this whole Derivatives 101 malarkey; to be honest, I'm not entirely sure how much I've understood myself. What I do know is that you've only been exposed to a vanishingly small fraction of the facts of the case. The devil, as they² say, is in the details.

Well, grab yourself a long spoon, sunshine -- it's time to sup, albeit briefly, with the devil.

The two basic types of option are call -- an option to buy something -- and put -- an option to sell it. Options exist for a fixed term, so they have an expiry date. If they can only be exercised on that date then they are termed European options; otherwise, they are American. European are easier to model, because there's just that one decision point. As it turns out, for call options there is no practical difference between the European and American versions, because it is never optimal to exercise a call option early. Puts are another matter.

Writing options is riskier than buying them, because as a buyer the most you can lose is what you spend in the first place. You have no subsequent commitment, only opportunity. You place your bet and watch the horses run. As a writer³ you are much more exposed. Writing a put commits you to paying the strike price on demand; which, at least, is a fixed potential loss. Writing a call commits you to a theoretically unlimited downside: if the price of the underlying goes through the roof, that's pretty much what you'll lose⁴.

There are all sorts of fancy variations on these basic options, each in its own way diminishing the pretence that the process is about choosing to buy or sell some real thing and, instead, making more obvious the fact that what is happening is simply the placing of bets. For example, binary options are just a straight gamble on the asset price at expiry: if it's one side of the strike price, you get nothing; if it's the other you get a fixed sum.

Barrier options add an interesting wrinkle, because they don't just depend on what the underlying price is in the end, but on how it got there. A knockout option, for example, works just like a normal one except that if the underlying price reaches some specified level at any time before the payoff, the option is void. Knock-in options, contrariwise, are void if the price doesn't reach that level before payoff. There might, conceivably, be several barriers in sequence, in different directions, and so on. Investing in one of these things is basically to say something like "I bet the price is going to go up to $10 next week, drop to $5 the week after, and finish up about $12 at the end of the month." Ideal if you happen to be dropping by from the future in your time machine or have an unusually high-resolution crystal ball.

Derivatives are not restricted to pigs -- which, in our casual abuse of terminology here, stand for both commodities and equities. There are also a wide variety of interest rate derivatives and credit derivatives. Both of these are to do with the dynamics of debt, the former trading on loans that go according to plan, the latter on the potential for default.

One of the simplest fixed income⁵ derivatives is the interest rate swap, which basically exchanges the interest on one loan for the interest on another. Obviously, at least one of these interest cash flows must be unpredictable, or else the swap would make no sense: who would swap a guaranteed income of 5% for a similarly certain 4%⁶? But as long as there is some indeterminacy involved, you've got yourself a bet.

Interest rate swaps are so ubiquitous that the "interest rate" part is almost optional -- they are often just called "swaps". But they aren't the only swaps in town. Another very common swap is the credit default swap or CDS, which is an explicit exchange of cash for credit risk: one side receives regular known cash payments, while the other gets paid off if a particular loan (ie, bond issue) defaults. It's a kind of insurance.

There are lots of more complex cases, such as basket CDS (or more generally nth-to-default instruments), where the insurance applies to a bunch of loans and pays off if some predetermined number of them default. These things are some of the many mechanisms financial institutions use to pool risks⁷.

Another very common way in which derivatives insinuate themselves into the fixed income world is through embedded options and related bond contract details. Which is to say, opportunities for one side or the other to vary the terms of a loan.

Lending and borrowing are tricky things. As a borrower, the last thing you want is to be locked into a draconian interest rate for your entire life. As a lender, you'd really prefer not to have your money tied up in loans that are earning a lot less than people are willing to pay. But loans are a time-based proposition and the future is, as we've observed repeatedly, unknowable. So, in the absence of such impossible foreknowledge, the parties negotiate terms; and they may try to keep their options open.

A callable bond is a loan that the issuer (ie, the borrower) can buy back (repay) at specified points in its life. A puttable bond is one that the lender can sell back (demand repayment of) at similarly specified points. Those points are options; they exist only in the context of the particular bond contract, but they are options nonetheless. They have an underlying -- the interest rate at which the money might be borrowed/lent differently when the opportunity comes around -- and they have a value, modifying the value of the bond in which they are embedded. Callable bonds give more leeway to the borrower, so they decrease the bond value; puttable bonds offer freedom to the lender, and so increase the bond value⁸.

And so on.

I could probably blither on about this nonsense forever -- have I even mentioned Asian options, or convertible bonds? Monte Carlo simulations or Value at Risk? -- it's a parthenogenetic enterprise, creating itself from the void to spiral out into infinity. But like Zeno's Achilles I'd be on a hiding to nothing. If you took this stuff seriously you wouldn't be reading my delirious rantings⁹, and if you didn't, well, the jokes ran out ages ago.

A slow retreat might be more apt than a hard finish, the dwindling discussion becoming more and more about less and less, but then again we're all about the non-linear here, so--

---

[1] And some of them really are unbelievably clever. Imagine where we might be if those geniuses had applied themselves to something worthwhile instead of the watery gruel of finance. I found myself, a few days ago, at a lunch outing with my colleagues, constructing good arguments for our business as socially responsible, trying to prove that we aren't evil. And they really are good arguments, a few tiny echoes of which have even made their way into one or two of these Derivatives 101 postings. Economics is not a zero sum game. It's entirely possible that the world would be better served by its smartest inhabitants applying themselves to the dismal science than to the other, prettier ones. But it is such a wretched enterprise, and so much of it is driven by greed. Things like insurance and pensions are without question a Good Thing, textbook demonstrations of how we can be better together than apart -- of how cooperation beats defection -- but the people who run the money for insurance companies and pension funds often seem to be drawn from the ranks of the most selfish, avaricious, amoral vermin alive, and if they aren't, someone else in the process will be. Is the whole business a vicious edifice with peripheral benefits, or is it an ultimately virtuous enterprise despite the bad apples? I have no idea, but I'm happy to be leaving it for something cleaner.
[2] Those bastards.
[3] Wallow, I urge you, for a moment, in the marvellous synonymy of this jargon: to write, in the context of options, is to be a bookmaker. Doesn't the English language make you proud?
[4] A point to understand here -- and, for all that it may seem a mere detail, rather important to everything we've been discussing -- is that you don't need to own an asset in order to sell a call option on it (or buy a put). If the option happens to be exercised, you can buy the asset at that time and sell it on -- you just have to be prepared to take a significant loss. If you do own the asset, then a call option written on it is termed a covered call. The loss in this case is less direct -- you don't have to actually part with the cash -- but just as real: were you not already committed to selling for the considerably lower strike price Y, you could have sold it for the current enormous market price X.
[5] Fixed income is one of those terms bandied about all over the financial arena that -- even though there is a vague literal justification -- doesn't remotely express what it really means. What it really means is usury -- as distinct from active shareholding. In the latter, I give you a sum of money to start a company, which we then jointly own in some degree and share the profits or losses accordingly; in the former, I lend you some money and expect you to pay it back in full, with interest, according to some agreed conditions. The conditions might be simple -- I lend you $100, you pay me back $110 in a year's time -- or complicated -- I lend you $100, you repay me at $10 each month for a year, but in six months you can give me $55 and we'll call it square, but if you don't you can instead borrow another $100 under these same terms, but if you don't do that I can demand $10 extra at month ten to close out the loan, and so on -- but it's always a loan, and I don't have any direct interest in what you do with it. The income from a loan is notionally fixed because the terms are agreed upfront -- hence the phrase -- but (in the words of Tom Baker's Doctor) this is life, nothing's sure. Income least of all. (One notable way in which fixed income investments differ from equities is that they have legal priority in the case of bankruptcy: creditors get paid before shareholders. The taxman, of course, gets paid before either, as do, in theory, employees.)
[6] Well, you might if one was considerably riskier than the other, but that would be trespassing on the territory of credit derivatives.
[7] Another example, at least potentially, of non-evilness. Mortgage-backed securities are a case in point. Lots of people or (more typically) institutions put money into a fund, from which other people are given loans to buy homes they could not otherwise afford. The interest on the loans goes to the investors, but they also share the risk of both default and prepayment. That is, the possibility that the loan will be repaid early, thus depriving the investor of the interest they were expecting. As so often with this stuff, prepayment risk is difficult to feel much sympathy for at the level of individuals -- so you got your money back too soon, big deal! Invest it again, if it means that much to you -- but at an institutional level it can be an issue. If the pensions of thousands are relying on other thousands not to repay their mortgages early, who has the moral high ground?
[8] These value differences must be compensated one way or another, and this is usually reflected in the coupon, which is indeed what we see in practice: the more freely a loan operates, the more interest we pay. Credit cards are a textbook example: your flexible friend. Murderous neighbourhood loan sharks work within the same framework, but a lot of other profoundly depressing factors come into play there.
[9] You'd be reading this and maybe this or some of the many others of their ilk.
Posted by matt at August 14, 2006 01:36 PM