Fixed-rate bonds maturity

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

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... 

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. 

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. 

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). 

Companies in need of more capital can also raise it by selling bonds. A bond is a certificate, with a face value usually much larger than that of a share, which has a fixed lifetime, usually 10 years at least, at the end of which time the bond matures and the company pays back its face value (by then, of course, much decreased in real value). However, the company also guarantees to pay interest at a fixed percentage of the bond s face value for this lifetime, usually twice a year, and this rate is usually quite an attractive one. 

The terms spread or credit spread refer to the yield differential, usually expressed in basis points, between a corporate bond and an equivalent maturity government security or point on the government curve. It can also be expressed as a spread over the swap curve. In the former case, we refer to the fixed-rate spread. In the latter, we use the term spread over EURIBOR, or over the swap curve. 

The gilts market is primarily a plain vanilla market, and the majority of gilt issues are conventional fixed interest bonds. Conventional gilts have a fixed coupon and maturity date. By volume they made up 82% of the market in June 2002. Coupon is paid on a semi-annual basis. The coupon rate is set in line with market interest rates at the time of issue, so the range of coupons in existence reflects the fluctuations in market interest rates. Unlike many government and corporate bond markets, gilts can be traded in the smallest unit of currency and sometimes nominal amounts change hands in amounts quoted down to one penny ( 0.01) nominal size. 

Interest indexation. Interest-indexed bonds have been issued in Australia, although not since 1987. They pay a coupon fixed rate at a real—inflation-adjusted—interest rate. They also pay a principal adjustment (equal to the percentage change in the CPI from the issue date times the principal amount) every period. The inflation adjustment is thus fully paid out as it occurs, and no adjustment to the principal repayment at maturity is needed. 

Tips swap. The Tips swap is based on the structure of U.S. Tips securities. It pays a periodic fixed rate on an accreting notional amount, together with an additional one-off payment on maturity. This payout profile is identical to many government IL bonds. They are similar to synthetic IL bonds described previously. 

When an option-free bond is issued, the coupon rate and the term to maturity are fixed. Consequently, as yields change in the market, bond prices will move in the opposite direction, as we will see in the next two scenarios. Generally, a bond s coupon rate at the time of issuance is set at approximately the required yield demanded by the market for comparable bonds. By comparison, we mean bonds that have the same maturity and the same risk exposure. The price of an option-free coupon bond at issuance will then be approximately equal to its par value. In the example presented above, when the required yield is equal to the coupon rate, the bond s price is its par value ( 100). 

The price is less than par value and the bond is said to be trading at a discount. This will occur when the fixed coupon rate a bond offers (6%) is less than the required yield demanded by the market (the 7% discount rate). A discount bond has an inferior coupon rate relative to new comparable bonds being issued at par so its price must drop so as to bid up to the required yield of 7%. If the discount bond is held to maturity, the investor will experience a capital gain that just offsets the lower the current coupon rate so that it appears equally attractive to new comparable bonds issued at par. ... 

Hence, bonds in contrast to stocks nsnally have a fixed maturity, their duration decreases with the course of time. Bonds with a shorter dnration are less sensitive to changes in the capital markets reflected by interest rate changes. Applying historical bond data in the Markowitz optimization framework thns can lead to biased results. As the indices ntilized here have an npper and lower matnrity bonnd for the bonds inclnded, the indexes dnrations and maturities are almost constant. Thus, the bias in historical index returns caused by aging secnrities should be small and can be neglected. 

A zero-coupon bond is the simplest fixed-income security. It makes no coupon payments during its lifetime. Instead, it is a discount instrument, issued at a price that is below the face, or principal, amount. The rate earned on a zero-coupon bond is also referred to as the spot interest rate. The notation P t, T) denotes the price at time r of a discount bond that matures at time T, where T >t - The bond s term to maturity, T - t, is... 

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. 

To understand why the rate of return is fixed even though bond prices tend to fluctuate, consider for a moment the mechanics of a typical corporate bond. Let s say an investor has bonds from a large auto manufacturer. The Jace amount of the bonds, or the dollar value of each "loan," is 1,000. The coupon rate is the amount of interest the bond will pay the investor each year, and is stated in terms of a percentage of the face amount. Therefore a 1,000 bond paying 100 per year in interest has a 10 percent coupon rate ( 100/ 1,000). The maturity date is the date in the future when the investor will get her original 1,000 back. Said another way, this is the date the company will pay the face amount of the bond to the owner. 

However—and this is the key point about fixed income—even though the value of a bond may fluctuate with changes in interest rates, if the investor buys at the face amount, and never sells until maturity, the income from the investment will be known and fixed for the life of the investment—that is, the coupon yield plus return of principal. 

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