Derivatives

Several words that start with D have become terms of opprobrium recently. Many have argued that debt and derivatives bear much of the responsibility for the current recessions in many countries. Some fear that depressions could follow.

Depressions may or may not be in store. But times are bad enough now and excessive debt and reckless use of some derivatives clearly deserve much of the blame.

Most of us have direct experience with debt. You give me money now and I promise to repay you later with interest. Of course it is not always this simple. The bewildering complexity of some debt instruments can boggle the mind. But at least the fundamental idea of debt is familiar.

In contrast, you may think that you have never bought or sold derivatives and have little or no notion about their good and bad features. What are they? Are they really needed? If they are malevolent why not just outlaw them?

Here is a starter course. I will have more to say in future posts.

Wikipedia defines financial derivatives as follows:

Derivatives are financial contracts, or financial instruments, whose values are derived from the value of something else (known as the underlying).

I was brought up to take umbrage when an adjective ("underlying the ...") morphs into a noun ("the underlying"), but this usage is too pervasive to ignore.

The Wikipedia definition is a good start, but let’s make it a bit more general:

 A financial derivative is a contract in which one party promises to make a payment to another party in the future, where the amount to be paid is based on the value of something else (known as the underlying) at the time.

Even this is not broad enough but will do for now.

Here is a graph of an example that appeals to many investing for their retirement years.

 

Your neighborhood bank manager, who looks a bit like the actor Jimmy Stewart, comes to you with the proposition summarized in this graph. The x (horizontal) axis shows the value at the end of the year 2010 of $100 invested today in Standard & Poor’s 500-stock index.  The y (vertical) axis shows the amount that you will receive at that time from the bank. When the time comes, the value of the hypothetical investment in the S&P500 will be computed and marked on the x-axis. Then the point on the curve directly above it will be found and the height (y-value) determined. This is what you will be paid.

 Pretty attractive, isn’t it? If the market goes up, you will get more. If it goes down, you will get $100. In finance-speak you get upside potential and downside protection. All you have to do is add your signature to the contract already signed by the bank.

 But wait. What do you have to pay for this contract?  More than $100 of course. Perhaps $110. So you could lose money, but no more than $10 out of your initial investment of $110.

 This sounds good to you, so you pay the money and sign the contract. You have just purchased a derivative. The payoff (shown on the y-axis) depends on the value of an underlying (shown on the x-axis) in the manner shown by the red curve.

 Not so fast. Recall that the red curve shows you the amount that the bank has promised to pay. Somewhere in the fine print in the contract there may be an indication that under some conditions they might pay less. Perhaps it should have said “we promise to pay you no more than …” 

 The possibility of receiving less than promised gives rise to what is known in the trade as counterparty risk. In this case the bank is your counterparty. If they were to go out of business before the end of 2010 or force you to get partial payment from a bankruptcy court, your actual payoff would be below the red curve.

 Here is a more realistic picture of what this derivative might pay you. 

You could end up below the curve. In fact, you might end up with a payoff of zero – most likely in a situation in which security markets, including the U.S. stock market, had fallen like rocks.

All this can be summarized in a formula:

The symbol x represents the final value of the underlying. For emphasis I have put a tilde (squiggly line) over it to indicate that its actual value is not known with certainty before the payoff date. The symbol y represents the value of the payoff, which is also uncertain today. The symbols f(..) represent a function, which relates the promised payoff to x.  In this case, it is the red line in our first figure – it shows the relationship between the underlying (x) and the promised payoff.

 The final term. e,  is the amount by which the actual payoff y falls short of the promised payment f(x). Since it is generally uncertain before the payoff date, I have put a tilde over it as well. If you are lucky, it will equal zero. If not, the value of e will be positive and the payoff lower than promised.

 This derivative has two sources of risk. Absent clairvoyance, you don’t know for sure what x will be. Moreover, you don’t know whether e will be zero or positive and, if the latter, how big it will be. The first is underlying risk; the second is counterparty risk.

 The press has gorged on stories of derivatives gone bad and I will reflect on some of them in future posts. Sometimes when you take risk you lose. But that doesn’t mean you should avoid risk at all costs. As we will see, a sensible approach to lifetime finance involves taking some risks and avoiding others, with or without derivatives.