# Bond crash/course: Swaps

Suppose I own a bond that promises to make certain interest payments. Suppose you own a bond with the same face value and maturity. Want to trade?

This is the basic idea behind the interest rate swap. The question only makes sense, of course, if the interest promised by our respective bonds is different. Maybe mine is denominated in dollars and yours is in Euros. Or maybe mine pays a fixed coupon and yours pays a variable coupon.

Terminology: If a bond’s coupon varies depending on future events, the coupon is said to be variable or floating. The math for pricing such bonds is more complicated than what we have discussed so far, but all of the concepts we have seen still apply.

Why might you and I want to make such a trade? Oh, all sorts of reasons. For example, recall that bonds with identical face values and maturities can have different durations. Many entities wish to hedge against interest rate risk; that is, to create a portfolio where the duration of their assets matches the duration of their liabilities. So it is possible for both of us to wind up with better-hedged portfolios by trading bonds of different durations.

Or maybe we just have different opinions about where the dollar and Euro are heading. Differences of opinion make a market.

Now, since the face values and maturities of our bonds are equal, we do not actually have to trade the bonds. We can simply enter into a contract where I give you my interest payments, and you give me yours. Hey, come to think of it, we do not even need to own the bonds. We can simply pretend to own them, and enter into a contract where I pay you the interest on my hypothetical bond and you pay me the interest on your hypothetical bond.

Such a contract is called an interest rate swap, or simply a swap. The face value of the hypothetical bonds that we exchange is called the notional value of the swap.

Are such contracts commonplace? Yeah, you could say that. According to the Bank for International Settlements, as of December 2008, the total outstanding notional value of all interest rate swaps was $328 trillion (with a “tr”). For comparison, Terran planetary GDP is$60 trillion. Of course, GDP represents real stuff, while notional values of swap contracts are just “notional”. But this does provide some sense of the scale.

The most common kind of swap, called a vanilla swap, is an exchange of a fixed coupon for a floating coupon that is based on LIBOR. (Follow the link if you want details on LIBOR. What matters is that it provides a variable benchmark roughly corresponding to “current interest rates”.) The entity making the fixed-rate payments (and therefore receiving the floating-rate payments) is called the payer. The entity receiving the fixed-rate payments (and therefore making the floating-rate payments) is called the receiver.

The way these contracts generally work is that the receiver offers a certain variable rate, and then the payer decides what fixed rate to offer in exchange. The rates are such that the Present Value of both streams of future payments are identical at the time the swap is created.

For example, you might come to me and ask to receive fixed-rate payments in exchange for payments of 3-month LIBOR every six months. I would compute the Present Value of your offer — which math I will omit because I do not fully understand it — and then offer a series of fixed-coupon payments with the same Present Value.

Then we just agree on a notional amount, and we are off to the races. What happens if interest rates change in the future? Well, my payments are fixed, but yours are not. If interest rates should fall in the future, you (the receiver) will be happy, because the payments you have to make will go down. If interest rates should rise in the future, you will be sad, because those same payments will go up. And I will be happy when you are sad.

But recall that bond prices and bond yields move opposite to each other. If you own a bond, you are happy when rates fall, because the market price of your bond goes up. So being a receiver on a vanilla swap is lot like owning a bond. Contrariwise, being a payer on a vanilla swap is a lot like shorting a bond.

We already have a name for how an instrument’s value fluctuates with interest rates: Duration. My last two paragraphs are saying that the receiving side of a fixed-for-floating swap has positive duration, while the paying side has negative duration.

I think that is enough to digest for one sitting. If you want more, see the PIMCO Introduction and/or the Wikipedia page.