Funds Investing

Once the swap transaction is completed, changes in market interest rates will change the payments of the floating-rate side of the swap. The value of an interest rate swap is the difference between the present value of the payments of the two sides of the swap. The three-month LIBOR forward rates from the current Eurodollar CD futures contracts are used to (1) calculate the floating-rate payments and (2) determine the discount factors at which to calculate the present value of the payments.

To illustrate this, consider the three-year swap used to demonstrate how to calculate the swap rate. Suppose that one year later, interest rates change as shown in Columns (4) and (6) in Exhibit 25-9. Column (4) shows the current three-month LIBOR. In Column (5) are the Eurodollar CD futures prices for each period. These rates are used to compute the forward rates in Column (6). Note that the interest rates have increased one year later since the rates in Exhibit 25-9 . As in Exhibit 25

the current three-month LIBOR and the forward rates are used to compute the floating- rate payments. These payments are shown in Column (8) of Exhibit 25-9.

In Exhibit 25-10, the forward discount factor is computed for each period. The calculation is the same as in Exhibit 25-6 to obtain the forward discount factor for each period. The hprward discount factor for each period is shown in the last column of Exhibit 25-10.

In Exhibit 25-11 the forward discount factor (from Exhibit 25-10) and the floating- rate payments (from Exhibit 25-9) are shown. The fixed-rate payments need not be recomputed. They are the payments shown in Exhibit 25-5 for the swap rate of 4.9875%, and they are reproduced in Exhibit 25-11. Now the two payment streams must be discounted using the new forward discount factors. As shown at the bottom of Exhibit 25-11, the two present values are as follows:

Present value of floating-rate payments $11,459,496

Present value of fixed-rate payments

$ 9,473,392

EXHIBIT 25-10 PERIOD FORWARD RATES AND FORWARD DISCOUNT FACTORS ONE YEAR LATER IF RATES INCREASE

The two present values are not equal, therefore, for one party the value of the swap increased while for the other party the value of the swap decreased. Let’s look at which party gained and which party lost.

The fixed-rate payer will receive the floating-rate payments. These payments have a present value of $11,459,496. The present value of the payments that must be made by the fixed-rate payer is $9,473,392. Thus the swap has a positive v^alue for the fixed- rate payer equal to the difference in the two present values of $1,986,104. This is the value of the swap to the fixed-rate payer. Notice that when interest rates increase (as they did in the illustration analyzed), the fixed-rate payer benefits because the value of the swap increases.

In contrast, the fixed-rate receiver must make payments with a present value of $11,459,496 but will only receive fixed-rate payments with a present value equal to $9,473,392. Thus the value of the swap for the fixed-rate receiver is —$1,986,104. The fixed-rate receiver is adversely affected by a rise in interest rates because it results in a decline in the value of a swap.

The same valuation principle applies to more complicated swaps that we describe later in this section.

Duration of a Swap

As with any fixed-income contract, the value of a swap will change as interest rates change. Dollar duration is a measure of the interest-rate sensitivity of a fixed-income contract. From the perspective of the party who pays floating and receives fixed, the interest-rate swap position can be viewed as follows: long a fixed-rate bond + short a floating-rate bond. This means that the dollar duration of an interest-rate swap from the perspective of a floating-rate payer is simply the difference between the dollar duration of the two bond positions that make up the swap; that is,

dollar duration of a swap = clonal^, duration of a fixed-rate bond

— dollar duration of a floating-rate bond

Most of the dollar price sensitivity of a swap due to interest-rate changes will result from the dollar duration of the fixed-rate bond because the dollar duration of the floating- rate bond will be small. The closer the swap is to the date that the coupon rate is reset, the smaller the dollar duration of a floating-rate bond.

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