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1 Traded Securities This chapter provides the institutional background on the financial securities studied in this book. The presentation of the institutional material in this chapter is brief.

指導老師：戴天時 老師學生：謝昌宏 周立軒

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A Treasury Securities

United States Treasury securities (bonds, notes, and bills) are debt obligationsissued by the U.S. government, and their payment (coupons plus principal) isguaranteed by the taxing authority of the United States.

They are considered to be default free.

Treasury securities are issued in two basic types:(i) coupon-bearing instruments paying interest every six months with aprincipal amount (or face value) paid at maturity, called coupon bonds, and(ii) discount securities bearing no coupons and paying only a principalamount at maturity, called zero-coupon bonds.

By historic convention, the Treasury issues all securities with maturities ofone year or less as zero-coupon bonds, and all securities with maturitiesgreater than a year as coupon bearing bonds.

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The zero-coupon Treasury securities are calledbills.

The coupon bearing Treasury securities are callednotes or bonds depending upon whether thematurity at issuance is from 2 to 10 years orgreater than 10 years, respectively.

Treasury bonds issued prior to February 1985 arecallable by the Treasury Department anytimewithin the last five years of the bond's life. Thiscall provision reduces the value of the bond to itsowner.

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Figure 1.1 corresponds to Treasury prices in the secondary market. The Treasury auction mechanism is, in fact, an important component in the determination of secondary market Treasury security prices.

5Figure 1.1

6Figure 1.1 (continued)

Today’s date is 1998/9/9.

There is 344 + 21 days between 1998/9/9 and 1999/9/9, so we can know that it adopted Actual/Actual.

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Callable Treasury bonds are indicated by a five-year span in thematurity date.

Treasury securities called STRIPS (separate trading of registeredinterest and principal of securities). STRIPS are issued by theFederal Reserve. They are synthetically created zero-coupon bonds.Under U.S. Treasury STRIPS, the second column is the type ofpayment: coupon interest (ci), note principal (np), or bond principal(bp).

New Treasury securities are issued in an auction market on a regularbasis. The auction uses competitive bids, although noncompetitivebids are accepted and tendered at the average yield of thecompetitive bids. The auction market is called the primary market.

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Those Treasury security issues of a particular timeto maturity (3 months, 6 months, 1 year, 2 years, 3years, 5 years, 7 years, 10 years and 30 years) thatare the most recently auctioned are called on-the-run.

Those Treasury security issues with similarmaturities, but that were offered in previousauctions, are called off-the-run.

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B Treasury Security Markets The majority of Treasury securities are traded in the over-the-counter market (the New York Stock Exchange lists some issues, but the trading volume is small.) An over-the-counter market is a “screen based” or “phone based” market between investment banks, commercial banks, and government bond dealers. The bid price is that price the government dealer is willing to purchase the issue for, and the ask price is that price they are willing to sell the issue for. The difference between the bid and ask price is called the bid-ask spread.

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The ask yield corresponds to the internal rate of return or equivalently, the holding period return on the bond. It is computed according to:

2 / 2( )1(1 [ ]/ 2)

(2 )(1 [ ]/ 2)

T couponask pricett ask yield

face valueTask yield

where

T = the number of years to maturity from the settlement date, and

periodcoupontheindaysofnumbersettlementfromdatecouponlastthecedaysofnumber sin

The bid and asked quotes are without accrued interest.

Dirty price

Dirty price – Accrued interest = Clean price

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Askprice

Time

Coupon payment date maturity

Par value

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The price the buyer actually pays (or receives) when transacting in the bonds or notes is the quoted price plus accrued interest, which is calculated as follows:

periodcoupontheindaysofnumbersettlementfromdatecouponlastthecedaysofnumbercoupon

erestaccrued

sin2

int

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T r e a s u r y b i l l s ’ b i d / a s k q u o t e s a r e g i v e n i n p e r c e n t sa n d n o t d o l l a r p r i c e s . T h e q u o t e s a r e p r o v i d e d o na b a n k e r ' s - d i s c o u n t b a s i s . T h e b a n k e r ' s - d i s c o u n ty i e l d ( a s k o r b i d ) i s c a l c u l a t e d a s f o l l o w s :

B a n k e r ’ s d i s c o u n t y i e l d =

ma turityuntilsettlementfro md a yso fnumb erva luefa ce

p riceva luefa ce 3 6 0 .

T h e a s k y i e l d i s c a l c u l a t e d a s f o l l o w s :

A s k y i e l d =

ma turityuntilsettlementfro md a yso fnumb erp ricea sk

p ricea skva luefa ce 3 6 5 .

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Another class of traded Treasury securities areInflation-Indexed Bonds. These bonds pay fixeddollar coupon payments semi-annually.

The final principal payment is adjusted to makethe dollar coupon payment as a percent of theprincipal equal to the “real” or “inflationadjusted” rate of return on these bonds.

The principal adjustment is based on a consumerprice index. The real return is given in the firstcolumn.

Appendix - Inflation Index Bonds

• Inflation-indexed bonds are bonds where the principal is indexed to inflation. They are thus designed to cut out the inflation risk of an investment.

• Inflation-indexed bonds pay a periodic coupon that is equal to the product of the inflation index and the nominal coupon rate. The relationship between coupon payments, breakeven inflation and real interest rates is given by the Fisher equation.

Appendix - Inflation Index Bonds

• For example, if the annual coupon of the bond was 5% and the underlying principal of the bond was 100 units, the annual payment would be 5 units. If the inflation index increased by 10%, the principal of the bond would increase to 110 units. The coupon rate would remain at 5%, resulting in an interest payment of 110 x 5% = 5.5 units.

– by wikipedia