Fixed-rate bonds

For pricing fixed-rate bonds, the value is given by Equation (8.22) ... 

A fixed-rate bond pays fixed coupons during the bond s life known with certainty. Conversely, a floating-rate note ox floater pays variable coupons linked to a reference rate. This makes the coupon payments uncertain. The main pim-pose of this debt instrument is to hedge the risk of rising interest rates. Although the financial crisis and liquidity provided by central banks have decreased the level of interest rates, they will at some point of course rise in future years. 

FIGURE 10.2 The price trend of Italy floating and fixed-rate bonds. (DcOa source Bloomberg.)... 

Chapter 8 shows several spread measures that can be used to compare fixed-rate bonds. Conventionally for floating-rate notes, traders use the discounted margin. To analyse a floating-rate note with a fixed-rate note, one method is to compare the discounted margin of a floater with the asset swap spread of fixed-rate bonds. 

Another approach is to compare the floating-rate note with a derived yield of a fixed-rate bond by using an interest rate swap curve matched with floater coupons. Figure 10.4 shows the Bloomberg YASN screen for Mediobanca float... 

The problem is, what spread is assumed to change There are three measures that are commonly used for fixed-rate bonds nominal spread, zero-volatility spread, and option-adjusted spread. Each of these spread measures were defined earlier in this book. 

A sensible question arises How do you know whether a spread duration for a fixed-rate bond is a spread based on the nominal spread, zero-volatility spread, or the OAS The simple answer is you do not know You must ask the broker/dealer or vendor of the analytical system. To add further to the confusion surrounding spread duration, consider the term OAS duration that is referred to by some market participants. What does it mean On the one hand, it could mean simply the spread duration that we just described. On the other hand, many market participants use the term OAS duration interchangeably with the term effective duration. Once again, the only way to know what OAS is measuring is to ask the broker/dealer or vendor. 

There are fixed-rate bonds with at least one year to maturity and minimum outstanding amounts (face value) of 300 million and 150 million. 

Issues are initially priced and sold at a fixed spread over the reference rate. The price of an FRN can fluctuate considerably during the life of the issue, mainly depending on trends in the issuer s credit quality. The frequent resets in the reference rate means that changes in market interest levels have a minimal impact on an FRN s price. For investors, movements in an FRN s price are reflected in changes in the discount rate. The discount rate is effectively the yield needed to discount the future cash flows on the security to its current price. It thus functions in the same way as the yield to maturity for a fixed-rate instrument. And like a fixed-rate bond, the market convention is to use a constant spread... 

In nearly all these cases, the structured product can be engineered using a combination of a straightforward fixed-rate bond and one or more interest rate derivatives. Examples follow. 

It can be seen from the net cash flow in Exhibit 19.1 that a fixed-rate payer has a cash market position that is equivalent to a long position in a floating-rate bond and a short position in a fixed-rate bond— the short position being the equivalent of borrowing by issuing a fixed-rate bond. 

There is no net outflow or inflow at the start of these trades, because the 100 million spent on the purchase of the FRN is netted with the receipt of 100 million from the sale of the Treasury. The subsequent net cash flows over the three-year period are shown in the last column. As at the start of the trade, there is no cash inflow or outflow on maturity. The net position is exactly the same as that of a fixed-rate payer in an interest rate swap. For a floating-rate payer, the cash flow would mirror exactly that of a long position in a fixed-rate bond and a short position in an FRN. Therefore, the fixed-rate payer in a swap is said to be short in the bond market—that is, a borrower of funds—and the floating-rate payer is said to be long the bond market. 

Since a floating-rate bond is valued on its principal value at the start of a swap, a swaption may be viewed as the value on a fixed-rate bond, with a strike price that is equal to the face value of the floating-rate bond. 

FIGURE 7.10 PVBPs of a 5-Year Swap and a Fixed-Rate Bond... 

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. 

FIGuRE 7.11 PVBPof a 5- Year Swap and Fixed-Rate Bond Maturity Period ... 

Equation (1.27) may be stated in terms of discount factors instead of the reference rate. The. yield to maturity spread method of evaluating FRNs is designed to allow direct comparison between FRNs and fixed-rate bonds. The yield to maturity on the FRN rmf) is calculated using (1.27) with both re + DM) and (re + DM) replaced with rmf. The yield to mamrity on a reference bond rmb) was shown earlier in this chapter. The yield to maturity spread is defined as ... 

It was suggested earlier that a swap be seen as a bundle of cash flows arising from the sale and purchase of two cash-market instruments a fixed-rate bond with a coupon equal to the swap rate and a floating-rate bond with the same maturity and paying the same rate as the floating leg of the swap. Considering a swap in this way, equation (7.23) can be rewritten as (7.24). 

An asset swap is a package that combines an interest-rate swap with a cash bond, the effect of the combined package being able to transform the interest-rate basis of the bond. Typically, a fixed-rate bond will be combined with an interest-rate swap in which the bond holder pays fixed coupon and received floating coupon. The floating coupon will be a spread over LIBOR (see Choudhry et al. 2001). This spread is the asset-swap spread and is a function of the credit risk of the bond over and above interbank credit risk. Asset swaps may be transacted at par or at the bond s market price, usually par. This means that the asset swap value is made up of the difference between the bond s market price and par, as well as the difference between the bond coupon and the swap flxed rate. 

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