Reset date

Index duration is usually equal to the time until the next reset date, whereas spread duration is equal to a modified duration of a bond paying fixed coupon, with same coupon payments and time to maturity. Therefore, conventionally floaters have lower index duration and higher spread duration. 

Moreover, duration will be influenced by the floater s stmcture. In fact, the choice of the reference rate affects the duration depending on how much volatile the index is. The lower the frequency of couptm payments, the greater the price sensitivity between reset dates. Thus, while floating-rate notes have a lower price sensitivity to a change of the reference rate, fixed and floating-rate notes both have a price sensitivity to changes of credit spread reflecting the issuer s creditworthiness. A shift of the credit term structure will determine the decline of the bond s price. 

There are several features about floaters that deserve mention. First, a floater may have a restriction on the maximum (minimum) coupon rate that be paid at any reset date called a cap (floor). Second, while a floater s coupon rate normally moves in the same direction as the reference rate moves, there are floaters whose coupon rate moves in the opposite direction from the reference rate. These securities are called inverse floaters. As an example, consider an inverse floater issued by the Republic of Austria. This issue matures in April 2005 and delivers semiannual coupon payments according to the following formula ... 

Thus far our coverage of valuation has been on fixed-rate coupon bonds. In this section we look at how to value credit-risky floaters. We begin our valuation discussion with the simplest possible case—a default risk-free floater with no embedded options. Suppose the floater pays cash flows quarterly and the coupon formula is 3-month LIBOR flat (i.e., the quoted margin is zero). The coupon reset and payment dates are assumed to coincide. Under these idealized circumstances, the floater s price will always equal par on the coupon reset dates. This result holds because the floater s new coupon rate is always reset to reflect the current market rate (e.g., 3-month LIBOR). Accordingly, on each coupon reset date, any change in interest rates (via the reference rate) is also reflected in the size of the floater s coupon payment. 

The discussion is easily expanded to include risky floaters (e.g., corporate floaters) without a call feature or other embedded options. A floater pays a spread above the reference rate (i.e., the quoted margin) to compensate the investor for the risks (e.g., default, liquidity, etc.) associated with this security. The quoted margin is established on the floater s issue date and is fixed to maturity. If the market s evaluation of the risk of holding the floater does not change, the risky floater will be repriced to par on each coupon reset date just as with the default-free floater. This result holds as long as the issuer s risk can be characterized by a constant markup over the risk-free rate. 

Note it is the differential risk annuity that causes the floater s price to deviate from par on a coupon reset date. Specifically, if the required... 

We will illustrate this process using a hypothetical 4-year floater that deliver cash flows quarterly with a coupon formula equal to 3-month LIBOR plus 15 basis points and does not possess a cap or a floor. The coupon reset and payment dates are assumed to be the same. For ease of exposition, we will invoke some simplifying assumptions. First, the issue will be priced on a coupon reset date. Second, although floaters typically use an ACT/360 day-count convention, for simplicity we will assume that each quarter has 91 days. Third, we will assume initially that the LIBOR yield curve is flat such that all implied 3-month LIBOR forward rates are the same. (We will relax this assumption shortly.) Note the same principles apply with equal force when these assumptions are relaxed. 

The second methodology uses market data on actively traded interest rate caps to form an estimate of a and O. An interest rate cap comprises q caplets, where q is the number of reset dates. Each caplet corresponds to the rate at time and provides payoff at time An interest rate cap provides insurance against adverse upward movements in floating-rate obligations during a future period. An interest rate caplet provides the cap holder with the following payoff ... 

A constant maturity swap, or CMS, is a basis swap in which one leg is reset periodically not to LIBOR or some other money market rate but to a long-term rate, such as the current 5-year swap rate or 5-year government bond rate. For example, the counterparties to a CMS might exchange 6-month LIBOR for the 10-year Treasury rate in eflFect on the reset date. In the U.S. market, a swap one of whose legs is reset to a government bond is referred to as a constant maturity Treasury, or CMT, swap. The other leg is usually tied to LIBOR, but may be fixed or use a different long-term rate as its reference. 

Note that the swap PVBP, 425, is lower than that of the 5-year fixed-coupon bond, which is 488.45. This is because the floating-rate bond PVBP reduces the risk exposure of the swap as a whole by 63.45. As a rough rule of thumb, the PVBP of a swap is approximately the same as that of a fixed-rate bond whose term runs from the swaps next coupon reset date through the swap s termination date. Thus, a 10-year swap making semiannual payments has a PVBP close to that of a 9.5-year fixed-rate bond, and a swap with 5.5 years to maturity has a PVBP similar to that of a 5-year bond. 

Typically, the cap rate is compared with the indexed interest rate on the rate-reset dates—semiannually, for instance, if the reference rate is sbc-month LIBOR. The cap actually consists of a strip of individual contracts. 

Generally, the reference rate for FRNs is LIBOR, the London interbank offered rate—that is, the rate at which one bank will lend funds to another. The interest rate is fixed for a three- or six-month period, at the end of which it is reset. If, say, LIBOR is 7.6875 percent at the coupon reset date for a sterling FRN paying six-month LIBOR plus 0.50 percent, the FRN will pay 8.1875 percent for the following period, and interest will accrue at a daily rate of 0.0224315. 

Because the future values for the reference index are not known, it is not possible to calculate the redemption yield of an FRN. On the coupon-reset dates, the note will be priced precisely at par. Between these dates, it will trade very close to par, because of the way the coupon resets. If market rates rise between reset dates, the note will trade slightly below par if rates fall, it will trade slightly above par. This makes FRNs behavior very similar to that of money market instruments traded on a yield basis, although, of course, the notes have much longer maturities. FRNs can thus be viewed either as money market instruments or as alternatives to conventional bonds. Similarly, they can be analyzed using two approaches. 

The simple margin formula may be adjusted to take into account changes in the reference index rate since the last reset date. This is done by replacing the price in (131) with an adjusted price, defined using either (13.2a) or (13.2b) which assume semiannual coupons. 

Loans have less uniform terms than bonds, varying widely in their interest dates, amortization schedules, reference indexes, reset dates, maturities, and so on. How their terms are defined affects the analysis of cash flows. 

At certain times, the simple margin formula is adjusted to take into account any change in the reference rate since the last coupon reset date. This is done by defining an adjusted price, which is either ... 

CPI is the next coupon payment (that is, Cis the reference interest rate on the last coupon reset date plus... 

The swap payments are usually quarterly or semiannual. On the interest-reset dates, the underlying asset is marked to market, either using an independent source, such as Bloomberg or Reuters, or as the average of a range of market quotes. If the reference asset obligor defaults, the swap... 

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