Bond issuers - Treasury

This is an introductory page in Fixed Income. If you are unfamiliar with any of the terms, you can refer to the Fixed Income Glossary.

The United States Department of Treasury issues several types of government debt instruments to finance the national debt of the United States, which are called Treasuries. There are 4 types of marketable treasuries:
* Treasury bills
* Treasury notes
* Treasury bonds
* Treasury Inflation Protection Securities

These are extremely liquid and are heavily traded on the secondary market.

A Treasury bill is a discount bond which has a maturity of less than 270 days. They pay no interest to maturity, and are sold at a discount to par value to create a positive yield. They are sold in a Dutch auction weekly, and all participants of the issue have the same purchase price.

In the secondary market, Treasury bills are quoted by the yield, based on a 360-day year. Recall that the yield is inversely proportional to the price. Because the bills are quoted by their respective yield, rather than the price, the bid will be higher than the ask, which is different from normal markets. To determine the price of a Treasury bill from the yield, we use the formula

\[ \text{Price} = \left( 1 - \frac{ \text{yield}} { 100} \times \frac{ \text{Days to maturity} } { 360 } \right) \times (\text{Face value}) \]

The ask yield is the bond equivalent yield when calculated on the basis of a 365-day year. We calculate this by assuming that the bond is purchased for the ask price / offer and annualize it over it's life. hence, the formula is

\[ r_{BEY} = \frac{ \text{Face value} - P } { \text{Face value}} \times \frac{365} { \text{Days to maturity}} = \frac{ \text{Yield} } { 100} \times \frac{ 365}{360}. \]

Treasury notes have a maturity of 2 to 10 years.
Treasury bonds have a maturity of greater than 10 years. Nowadays, they are usually issued only in 30 year maturities.

Both T-notes and T-bonds:
* Have a semi-annual coupon payment.
* Are sold in a Dutch auction.
* Are issued at face values of $1000.

In the secondary market, T-notes and T-bonds are quoted at percentage of par in thirty-seconds of a point. A quote of \( 98:06 \) (or \(98'06\) or \(98-06\)) indicates that it is trading at a discount, namely \( \left( 96 + \frac{ 6}{ 32 } \right) \% \) of \( $ 1000 = $961.875 \). Sometimes, a \(+\) is ended to the end, to indicate an additional \( \frac{1}{64} \) point. Prices are quoted

The Treasury note that matures in 18 months and pays a coupon payment of 5% semi-annually has a quote of 108:19 bid at 108:20. If you buy this note, what is the yield to maturity?

Assume that an interest payment was just made yesterday.

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Assume that the face value of the note is $1000. Then, it can be bought for a price of \( \left(108 + \frac{20}{32} \right) \% \times $1000 = 1086.25 \).

To find the yield to maturity, we need the value of \( y \) such that

\[ 1086.25 = \frac{ 50 } { ( 1 + y \%) ^ { 0.5 } }+ \frac{ 50 } { ( 1 + y \% ) ^ 2 } + \frac{ 1050} { ( 1 + y \%) ^ 3 } \]

Solving this, we obtain \( y = 4.06 \).

Treasury Inflation-Protection Securities are inflation-indexed bonds in which the principal is adjusted to the Consumer Price Index, which is a measure of inflation. When CPI rises, indicating more inflation, then the principal would increase further. The coupon rate is constant, but there are different amounts of interest generated in each period as the principal has been adjusted. This protects the holder against inflation, hence is useful for retirees or pensioners.