Treasury Securities - Weatherhead

2

Treasury Securities

In this chapter we will learn about ? Treasury Bills, ? Treasury Notes and Bonds, ? Strips, ? Treasury Inflation Protected Securities, ? and a few other products including Eurodollar deposits. The primary focus is on the price conventions in these markets. We also

will investigate arbitrage restrictions that exist between strips and coupon bonds.

Debt issued by the Treasury with maturities of one year or less are issued as discounted securities called Treasury bills (T-Bills). Securities with maturities greater than a year are coupon securities. Coupon securities with maturities less (greater) than 10 years are called Treasury notes (bonds).

2.1 TREASURY BILLS

A Treasury bill is a zero coupon bond with a maturity of less than one year. Treasury bills are issued in increments of $5, 000 above a minimum amount

15

16 CHAPTER 2: TREASURY SECURITIES

of $10, 000. Over $200 billion are issued per year. T-bills are unusual in that their prices are not directly quoted. The Wall Street Journal, for example, ranks T-bills by maturity. The maturity date is followed by "prices" expressed in bank discount yield form, dy, where:

F - B 360

dy =

F

? m

where m - number of days to maturity F - Face value of the Bill B - Price of the Bill.

Given the discount yield, the invoice price is given by:

B = F ? [1 - m ? dy ] 360

For example, if the bank discount yield is 6.78%, and the maturity is 160 days, then the price per $100 of face value is:

160 ? 0.0678

B = 100 ? [1 -

] = 96.98667

360

The discount yield divides the dollar gain by the face value and so is not a good indicator of return. In addition, the discount is based on a 360 day year. The difference between the bid and asked discount yield is the profit margin of the dealer. The bid ask spread is usually very small, perhaps two basis points.

In order to make yields of T-Bills comparable to yields of other types

of coupon bonds, namely T-Notes and T-Bonds, market participants often

compute the Bond Equivalent Yield (BEY) of the investment. The BEY not

only correct the shortcommings of the bank discount yield but also attempts to

set up a yield measure which is comparable to yield measures of coupon bonds

with semi annual payments based on a 365 day year. The bond equivalent

yield is given by:

(100 - B) 365

BEY =

?

B

m

The reported BEY is based on the ask discount quotes.

Actually, the market convention for computing a BEY for a T-Bill with m > 182 days is more complex. Market convention attempts to establish a bond equivalent yield for this T-Bill so that comparisons can be made with other bonds that pay coupons semi-annually. To establish this value we pretend interest of y is paid after 6 months and that it is possible to reinvest this interest for the remaining time to maturity. Hence, begining with B dollars, after six months we would have B(1 + y/2). Over the remaining n = (m - 365/2) days this value is assumed to grow to B(1+y/2)(1+n?y/365). Setting

CHAPTER 2: TREASURY BILLS 17

this value to the face value and solving for y leads to the BEY. Hence:1

y

y

B(1 + )[1 + n ? ] = F

2

365

Table 2.1 displays typical T-Bill prices quotations as reported in the financial press.

Table 2.1 Selected T-Bill Price Quotations on January 4th 1999

Maturity Date Days to Mat. Bid Ask Ask Yield

Jan 14 99

9

Jan 21 99

16

Jan 28 99

23

3.92 3.84 3.90 4.53 4.45 4.52 4.38 4.30 4.37

April 1 99

86

April 8 99

93

July 1 99

177

Dec 9 99

338

Jan 6 00

366

4.44 4.43 4.54 4.42 4.40 4.51 4.38 4.37 4.54 4.39 4.38 4.58 4.33 4.32 4.53

Consider the April 1 99 T-Bills, with 86 days to maturity. The asked

discount yield is 4.43. This implies the cost per $100 face value is 100 ? [1 -

86?0.043 360

]

=

$98.94172.

The

bond

equivalent

yield

is

4.54%,

and

is

indicated

in the last column.

Example

Consider a 13-week $10, 000 face value T-bill with an asked discount yield of 8.88%.

? The cost of this bond is B = F [1 - (m/360)dy] = 10, 000[1 - (91/360)0.0888] = $9, 775.53

? The bond equivalent yield is

F - B 365 10, 000 - 9, 775.53 365

?=

? = 9.21%.

B

m

9, 775.53

91

1An alternative formula might require

B(1

+

y/2)1+

2n 365

= 100

but this is not the market convention here!

18 CHAPTER 2: TREASURY SECURITIES

? The effective annual rate of return compounded on a daily basis is [ 10, 000 ]365/91 - 1 = 0.0953 or 9.53% 9, 775.53

? The effective annual rate of return compounded on a continuous basis

is:

10, 000 365

log[

] ? = 0.0911 or 9.11%

9, 775.53 91

2.2 TREASURY NOTES AND BONDS

T-bills are short term instruments that pay no coupons prior to maturity. We now turn attention to coupon bonds issued by the treasury. All treasury bonds are identified by their coupon and maturity. The 101/2 of 1999 means the Treasury bond with a 10 1/2% annual coupon rate that matures in 1999. The dollar amount of interest paid per year is 101/2% of the face value. In practice the coupon are paid in two equal installments, six months apart.

Quotations for Treasury notes and Treasury bonds are usually reported together, ordered by maturity. The bid and ask prices are reported in a special form. For example a quotation of 86 - 12 means the price is 86 12/32% of face value. A plus sign following the the number of 32nds means that a 64th is added to the price. To actually purchase a bond, the investor must pay the asked price together with accrued interest since the last coupon payment. Accrued interest is computed by taking the size of the last coupon payment and multiplying by the ratio of the actual number of days since the last coupon payment, relative to the actual number of days in the coupon period.

Table 2.2 illustrates typical price quotations of selected notes and bonds.

As an example, consider the November 2008 Treasury note with coupon 4 3/4. The "n" indicates the contract is a note rather than a bond. The bid quotation price is 100 16/32 and the ask quotation price is 100 17/32. Interest payments are semiannual on the 15th of November and 15th May. The ask invoice price is the asking quotation price plus the accrued interest. Using this price the yield to maturity is computed as 4.68%.

Some T-bonds are callable, with the first-call date coming 5 years before the bond matures. Newspaper quotations typically indicate if the bond has a call feature. For callable bonds, the yield to maturity is reported if the price is below par. If the price is above par, then the yield to the call date is computed. Over the last decade, however, the auctions have not included callable Treasury securities, so the number of such contracts is diminishing.

CHAPTER 2: TREASURY NOTES AND BONDS 19

Table 2.2 Selected Note and Bond Price Quotations for Settlement on January 6th 1999

Rate Maturity (Mo/Yr) Bid Price Ask Price Ask Yield

6 3/8 5 5 7/8 5 8 7/8

Jan 99n Jan 99n Jan 99 Feb 99n Feb 99n

100:00

100:02

3.95

99:31

100:01

4.46

100:01

100:03

4.43

100:00

100:02

4.35

100:13

100:15

4.49

7 1/8 4 5/8 6 1/4 4 1/4 4 3/4 8 1/8 5 1/4

Feb 00n Dec 00n Feb 02n Nov 03n Nov 08n Aug 21 Nov 28

102:19

102:21

4.72

100:02

100:03

4.5

104:10

104:12

4.74

98:20

98:21

4.56

100:16

100:17

4.68

134:12

134:18

5.45

101:16

101:17

5.15

Viewed from a coupon date, and including the date 0 coupon, the yield-tomaturity of a Treasury bond is linked to its market price by the usual bond pricing equation:

m-1 C/2

100 + C/2

B0 =

(1 + y/2)j + (1 + y/2)m

j=0

where 100y% is the annual yield to maturity, C is the annual coupon rate and m is the number of coupon payouts remaining to maturity.

If, however, the time to the first coupon date is not exactly 6 months, then

the bond pricing equation must be modified. Specifically, the pricing equation

is given by

B0

=

1 (1 + y/2)p

m-1

C/2 (1 + y/2)j

+

100 (1 + y/2)m-1

j=0

where p = tn/tb and tn is the number of days to the next coupon payment, and tb is the number of days from the last coupon date to the next coupon date.

The price that an investor pays is the quoted price, together with the accrued interest. The accrued interest, AI say, equals the proportion of the current coupon period that has elapsed, times the coupon size. That is:

AI = [1 - p]C/2

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