Money market rates

Floating-rate notes (FRNs) are Eurobonds that have their coupon levels reset periodically, with reference to a money market rate. For dollar-denominated assets, this is LIBOR (the London Inter-bank Offer Rate) as determined by a group of 16 reference banks. The mechanism is run by the British Bankers Association (BBA). The BBA also supervises LIBOR fixings in a number of other currencies. For euros, the most common reference rate is EURIBOR, as determined by a reference group of around 50 banks chosen by European Banking Federation. In both cases, most issues are priced off of the three-month rate, although one-month and six-month rates are also used. 

In debt capital markets the yield on a domestic government T-bill is usually considered to represent the risk-free interest rate, since it is a shortterm instrument guaranteed by the government. This makes the T-bill rate, in theory at least, the most secure investment in the market. It is common to see the 3-month T-bill rate used in corporate finance analysis and option pricing analysis, which often refer to a risk-free money market rate. 

The reference rates that have been used for the floating rate in an interest rate swap are various money market rates. The most common in Europe is EURIBOR. EURIBOR is the rate at which prime banks offer to pay on euro deposits available to other prime banks for a given maturity. There is not just one rate but a rate for different maturities. For example, there is a 1-month EURIBOR, 3-month EURIBOR, and 6-month EURIBOR. 

In that case, the investors borrow at the money market rate. They... 

For the strategy employing forwards, contracts are bought, where r is the daily return (or instantaneous money market rate) and T the maturity term in days. The start forward price sF=X, and the payoff on expiry... 

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. 

For risk-free investments, such as U.S. Treasury bills, the required return (as a percent of the capital invested) is determined by supply and demand in the money markets. If the going risk-free interest rate is 5 percent per year, for example, an investor who puts up 100 expects to get at least 105 back next year. From another point of view, 100 promised for delivery next year is worth only 95.23 today, because the investor could take that 95.23, invest it in a risk-free security, and have the 100 a year hence. Not having access to the 95.23 today essentially deprives the investor of the opportunity to invest at the going interest rate. 

In this section, we describe the relationship between the price of a zero-coupon bond and spot and forward rates. We assume a risk-free zero-coupon bond of nominal value 1, priced at time t and maturing at time T. We also assume a money market bank account of initial value P t, T) invested at time t. The money market account is denoted M. The price of the bond at time t is denoted P t, T) and if today is time 0 (so that t > 0), then the bmid price today is unknown and a random factor (similar to a future interest rate). The bond price can be related to the spot rate or forward rate that is in force at time t. 

The continuously compounded constant spot rate is r as before. An investor has a choice of purchasing the zero-coupon bond at price P(t, T), which will return the sum of 1 at time T, or of investing this same amount of cash in the money market account, and this sum would have grown to 1 at time T. We know that the value of the money market accoxmt is given by Me If M must have a... 

Before we come to that, however, we wish to describe the spot rate and the money market account processes. In Equation (4.4), under the particular condition of the maturity point T as it tends towards t (that is t), the forward rate tends to approach the value of the short rate (spot rate), so we have... 

The money market account is also described as a Wiener process. We denote by M(t, t)=M (f) the value of the money market account at time t, which has an initial value of 1 at time 0 so that M(0,0) = 1. This account earns interest at the spot rate r(f) which means that at time t the value of the account is given by... 

The expression for the value of the money market account can be used to determine the expression for the zero-coupon bond price, which we denote as P(t, T). The money market account earns interest at the spot rate rit), while the bond price is the present value of 1 discounted at this rate. Therefore, the inverse of Equation (4.8) is required, which is... 

The no-arbitrage condition is set by defining the price of a zero-coupon bond that matures at time T in terms of an accumulation factor B(t) which is the value of a money market account that is invested at time 0 and reinvested at time t at an interest rate of r(t). This accumulation factor is defined as Equation (4.31) ... 

The traditional approach to yield curve fitting involves the calculation of a set of discount factors from market interest rates. From this, a spot yield curve can be estimated. The market data can be money market interest rates, futures and swap rates and bond yields. In general, though this approach tends to produce ragged spot rates and a forward rate curve with pronounced jagged knot points, due to the scarcity of data along the maturity structure. A refinement of this technique is to use polynomial approximation to the yield curve. 

The fitted spot curve can differ considerably if yields on short-term repo are included. The effect is shown in Figure 5.7, which is reproduced from Anderson and Sleath (1999). Note that this is a short-term spot curve only the maturity extends out to only 2 years. Two curves have been estimated the cubic spline-based yield curve using the repo rate and without the repo rate. The curve that uses repo data generates a curve that is much closer to the money market yield curve than the one that does not. The only impact is at the very short end. After about 1 year, both approaches generate very similar curves. 

The repo market has allowed the hedge fund to borrow in sterling at a rate below the cost of unsecured borrowing in the money market (4.95%). The repo market maker is overcollateralised by the difference between the value of the bonds (in ) and the loan proceeds (2%). A rise in USD yields or a fall in the USD exchange rate value will adversely affect the value of the bonds, cansing the market maker to be undercollateralised. 

A DNT option is a path-dependent digital option. The digital characteristic means that payment at maturity is not dependent on how much the option is in-the-money instead, the payout, if made, is fixed at the outset. The path-dependent characteristic means that market rates throughout the lifetime of the option are monitored, not just on the maturity date. If, at any time, the nnderlying market rate touches (trades at or through) the barrier levels, this triggers the payout at maturity. 

The two major European derivatives exchanges, Euronext-LIFFE and their German-Swiss competitors Eurex, offer options on interest rate futures that cover a wide spectrum of maturities. Eurex and Euronext-LIFFE both offer options on their money market futures, 3-month EURI-BOR contracts. Contracts which have the European Interbank Offered... 

Another key feature of a bond is its term to maturity the number of years over which the issuer has promised to meet the conditions of the debt obligation. The practice in the bond market is to refer to the term to maturity of a bond simply as its maturity or term. Bonds are debt capital market securities and therefore have maturities longer than one year. This differentiates them from money market securities. Bonds also have more intricate cash flow patterns than money market securities, which usually have just one cash flow at maturity. As a result, bonds are more complex to price than money market instruments, and their prices are more sensitive to changes in the general level of interest rates. 

Floating-rate bonds, often referred to as floating-rate notes (FRNs), also exist. The coupon rates of these bonds are reset periodically according to a predetermined benchmark, such as 3-month or 6-month LIBOR (London interbank offered rate). LIBOR is the official benchmark rate at which commercial banks will lend funds to other banks in the interbank market. It is an average of the offered rates posted by all the main commercial banks, and is reported by the British Bankers Association at 11.00 hours each business day. For this reason, FRNs typically trade more like money market instruments than like conventional bonds. 

Quoting annualized rates allows deposits and loans of different maturities and involving different instruments to be compared. Be careful when comparing interest rates for products that have different payment frequencies. As shown in the earlier examples, the actual interest earned on a deposit paying 6 percent semiannually will be greater than on one paying 6 percent annually. The convention in the money markets is to quote the applicable interest rate taking into account payment frequency. 

Given these assumptions, the YTM can be viewed as an expected or anticipated y Adi. It is closest to reality when an investor buys a bond on first issue and holds it to maturity. Even then, however, the actual realized yield at maturity would be different from the YTM because of the unrealistic nature of the second assumption. It is clearly unlikely that all the coupons of any but the shortest-maturity bond will be reinvested at the same rate. As noted earlier, market interest rates are in a state of constant flux, and this would affect money reinvestment rates. Therefore, although yield to maturity is the main market measure of bond levels, it is not a true interest rate. This is an important point. Chapter 2 will explore the concept of a true interest rate. 

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