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Interest payments on a standard floating-rate note adjust from period to period to reflect changes in a money market reference rate. The market for floaters started in the 1970s when interest rates began to rise due to “inflation creep,” as it was called back then. Fixed-income bonds, which were seen to be boring compared to the excitement of the stock market, finally became interesting. Interest in bonds arose because conservative, buy-and-hold investors experienced losses, at least in terms of current market value, when yields to maturity went up. Floaters, first issued by commercial banks, were offered to investors as a way of “preserving capital value,” meaning that they transferred interest rate risk from market value to future cash flows.

Consider a 10-year, floating-rate note making quarterly interest payments of 3-month LIBOR plus 0.50%. LIBOR is set at the beginning of each period, and the interest payment is made in arrears at the end of the period. In practice, the rate typically is set two business days prior to the start of the period. Although there might be a cap or floor on the interest rate, thereby setting a maximum or minimum payment, here we deal only with “straight floaters” that have no such embedded options. So, if 3-month LIBOR turns out to be 1.50%, the annual interest rate for the period is 2.00%. The interest payment for the quarter will be about $0.50 per $100 of par value, depending on the number of days in the period. Most FRNs use an actual/360 day-count in the U.S.; actual/365 is used in many other markets.

Notice that while the money market reference rate varies, the margin over LIBOR is fixed at 50 basis points. That's the key to understanding the market value volatility (i.e., duration) of the floater. LIBOR, the standard reference rate for U.S. dollar-denominated FRNs, captures macroeconomic factors (e.g., expected inflation, monetary policy, and general business conditions). Students are often surprised that one of the most important interest rates in the U.S. financial market is determined in London, not in New York. Moreover, most of the commercial banks that are surveyed each day to set LIBOR are not even headquartered in the U.S. The margin on the FRN, like the spread over the benchmark yield on a fixed-rate bond, captures micro- economic factors (e.g., credit risk of the issuer, liquidity, and taxation).

As long as this floater's “correct” margin continues to be 50 basis points, meaning no change in credit risk, liquidity, or taxation, the FRN will trade at par value on each coupon payment date. The 10-year floater is then the financial equivalent of rolling over a series of 40 short-term time deposits, each paying three-month LIBOR + 0.50%. Each time deposit is initially like a 3-month zero-coupon money market security having an annual Macaulay duration of about 0.25.

The usual presentation of the interest rate sensitivity of floaters makes the assumption of repricing at par value on each payment date. That is, the duration equals the time remaining in the coupon period. However, assuming no change in credit risk or liquidity severely limits our analysis. Although that assumption might be reasonable for government floaters, the U.S. Treasury has just started to issue FRNs in January of 2014. Most floating-rate notes in existence have been issued by financial institutions that can and do experience downgrades in their credit ratings (and even upgrades once upon a time). The liquidity of these FRNs can also change over time. Fortunately, we can use some bond math tools to build valuation models for floaters that do not necessarily reprice at par value. From those models, we can derive expressions for duration.

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