Given that there's no magic on Wall Street, you may wonder how an issuer can sometimes walk away with a big cash payment just for signing the contract for an interest rate swap.

There's no hocus-pocus involved. The key questions line up this way: How does the firm setting up a swap decide its terms and price? And how does the firm manage to make a profit?

The swap is really no different from other products offered by financial firms, but the valuation is more complicated. Breaking down the transaction into its components reveals the value.

For example, with short-term rates low, more municipalities are considering selling variable-rate bonds. Investment bankers suggest a synthetic transaction that uses a swap to achieve the same goal.

In the synthetic transaction, a municipality would sell fixed-rate debt and then enter a swap. A Wall Street firm, acting as the swap counterparty, would pay the municipality a fixed rate and the municipality would pay the firm a floating rate.

With short-term floating rates currently well below long-term fixed rates, the municipality could receive a sizable payment on the swap. It might pay the counterparty the rate on the Public Securities Association's municipal swap index, about 2.40% this week, while receiving a fixed rate of about 4.15%. That's a net gain of 175 basis points.

What's the catch?

The catch is that floating rates float. The municipality has no guarantee that the PSA Index will always be less than the 4.15% fixed rate it must pay.

The firm that agreed to the swap did not pull the 4.15% fixed rate out of the air. In fact, the rate is based on the firm's cost to hedge the transaction plus a bid-ask spread. The firms derive the hedging cost from the forward interest rate curve.

One simple way to consider the value of a swap is to compare the transaction with o nary bond trades. In a fixed-to-floating swap, the firm is, in effect, issuing to the municipality a fixed-rate bond. The municipality is, at the same time, issuing the firm a floating-rate bond with an identical maturity and principal amount.

In the swap, of course, the two parties never actually exchange principal amounts. The principal amount, also called the notional amount of the swap. is used only to calculate the interest payments.

The firm is trying to put a value on the floating-rate bond that it is receiving from the issuer. It will then offer a fixed-rate bond of almost equivalent value, minus its bid-ask spread.

To value the floating-rate bond, the firm turns to the forward interest rate curve.

Forward rates are a projection of the current interest rate yield curve. The forward rate reveals the rates that would be needed in the future to allow an investor in one bond maturity to get a return equivalent to the one an investor in another maturity would get.

For example, if the market yield on a one-year bond is 6% and the yield on a two-year bond is 8%, a firm can calculate the one-year rate for one year from now. That calculation would provide the so-called forward one-year rate.

The calculation attempts to find the rate in one year for a one-year bond that would give an investor the same return as an investor who bought the two-year bonds.

The owner of the two-year bond will receive two payments of $80 for each $1,000 invested. The owner of the one-year bond will receive one payment of $60 for each $1,000 invested and then will have to roll over the investment into another one-year bond.

The forward rate is the rate that the one-year investor would have to receive to gamer the same return as the two-year bond investor.

After one year at 6%, for example, an investor would need another year at 10% to equal the return of the two-year bond paying 8%. So the one-year forward rate, one year from now, would be 10%.

On the swap, the side receiving the fixed rate is comparable to the investor holding the longer maturity bond with a single rate. The side receiving the floating rate is comparable to the investor in a series of shorter fixed-rate bonds.

On a two-year swap, a firm might offer to pay a fixed rate of 7.90% in return for floating payments based on the one-year rate. The 7.90% comes from the 8% rate available on a two-year bond, minus a bid-ask spread of 10 basis points. The one-year rate, the floating rate on the swap, is 6%. But the forward one-year rate is 10%.

That means the market expects the one-year rate to rise above the fixed rate that the issuer has just locked in. The firm can take advantage of this expectation by buying bonds, futures, or forwards or by entering other swaps.

By buying other instruments, the firm hedges its risk on the swap. If rates do not move as expected, it will have to continue paying out on the swap but its hedge transactions will pay a profit. If rates do move as expected, the swap will turn in the firm's favor but the hedging transaction will lose money.

If everything comes out equal, where's the profit? In the bid-ask spread. If the firm is perfectly hedged, it will still make a profit from the 10 basis point spread.

A firm may not always be perfectly hedged. Carrying unhedged swaps could lead to bigger profits or bigger losses.

But in the end, the pricing issue is complicated by each firm's particular situation. Firms will not quote identical terms and prices for similar swaps.

A firm's profit goals or previous swap transactions could alter its swap prices. Supply and demand factors in the swap market also affect pricing. And one firm may set aside greater reserves against possible defaults than another firm.

The lesson for issuers is simple. Issuers should always call several dealers to ensure that the price and terms they are being offered are "on the market."

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