One structured note that has received negative publicity in the past is the inverse floater. For example, the large quantity of inverse floaters held by Orange County California in its investment portfolio exacerbated the damages that it incurred when interest rates rose in 1994. An **inverse floater** is a floating-rate instrument whose interest rate moves inversely with market interest rates.6 In a typical case, the rate paid on the note is set by doubling the fixed rate in effect at the time the contract is signed, and subtracting the floating reference index rate for each payment period. Suppose the coupon on a five-year, fixed-rate note is 6.5%. An inverse floater might have a coupon of 13% − LIBOR6, with the rate reset every six months. In general, an inverse floater is constructed by setting the payment equal to *nr* − (n − 1)LIBOR, where *r* is the market rate on a fixed-rate bond and *n* is the multiple applied to the fixed rate. If interest rates fall, this formula will yield a higher return on the inverse floater. If rates rise, the payment on the inverse floater will decline. In both cases, the larger *n* is, the greater the impact of a given interest rate change on the inverse floater’s interest payment.

Issuers, such as banks, can use inverse floaters to hedge the risk of fixed-rate assets, such as a mortgage portfolio. If interest rates rise, the value of the bank’s mortgage portfolio will fall, but this loss will be offset by a simultaneous decline in the cost of servicing the inverse floaters used to finance the portfolio.

The value of an inverse floater (e.g., 13% − LIBOR6) is calculated by deducting the value of a floating-rate bond (e.g., one priced at LIBOR6) from the value of two fixed-rate bonds, each with half of the fixed-coupon rate of the inverse floater (e.g., two 6.5% fixed-rate bonds).7 Mathematically, this valuation formula is represented as

where *B(x)* represents the value of a bond paying a rate of *x.* That is, the value of the inverse floater is equal to the sum of two fixed-rate bonds paying a 6.5% coupon minus the value of a floating-rate bond paying LIBOR6.

At the issue date, assuming that 6.5% is the issuer’s market rate on a fixed-rate bond and LIBOR6 is the appropriate floating rate for the borrower’s creditworthiness, the market value of each $100 par value inverse floater is $100 (2 X $100 − $100) because the fixed-rate and floating-rate bonds are worth $100 apiece.

To take another, somewhat more complicated example:

In effect, an inverse floater is equivalent to buying fixed-rate bonds partially financed by borrowing at LIBOR. For example, the cash flows on a $100 million inverse floater that pays 13% − LIBOR6 is equivalent to buying $200 million of fixed-rate notes bearing a coupon of 6.5% financed with $100 million borrowed at LIBOR6.

The effect of an inverse-floater structure is to magnify the bond’s interest rate volatility. Specifically, the volatility of an inverse floater with a payment structure equal to *nr* − *(n* − 1)LIBOR is equal to *n* times the volatility of a straight fixed-rate bond. The reason is that the floating-rate portion of the inverse floater trades at or close to par, whereas the fixed-rate portion—given its structure—changes in value with interest rate fluctuations at a rate that is *n* times the rate at which a single fixed-rate bond changes in value.

6 The interest payment has a floor of zero, meaning that the lender will never owe interest to the borrower.

7 The object is to ensure that there are as many principal repayments as bonds (otherwise, if we priced a 13% coupon bond and subtracted off the value of a floating-rate bond, the net would be zero principal repayments—the principal amount on the 13% coupon bond minus the principal on the floating-rate bond).

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