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Understanding the T-Bond Tables in the WSJ

Terminology:

A bond has two parts a face amount of $1000, and a coupon. Every six months the bond pays offone coupon, until the maturity date. On the maturity date the bond's owner receives the faceamount ($1000) plus the final coupon payment.

A bond's coupon rate tells you the coupon amount. The formula is (coupon rate)×1000/2. Forexample, a 6% coupon means that the owner receives $30 every six months.

Bond prices are quoted in units of 100, and net of accrued interest. The fact that a bond is quotedin units of a 100 only means that the quote is for 1/10 of the bond's value. The term unit of 100comes from the fact that 1/10 of the face value equals 100. Accrued interest is defined as follows.Let t0 represent the date of the last coupon payment, t1 the date of the next payment, and J today'sdate. Then the formula is

where, for example, t1-t0 equals the number of days between payments.

While the above accrued interest formula looks somewhat sensible it is not the exact formula usedin the corporate and municipal bond markets. For bonds in these two markets, that pay semi-annualcoupons, accrued interest is calculated under the assumption that a year has only 360 days and eachmonth 30 days! Thus, the formula becomes

Since all months are assumed to have 30 days this means that the accrued interest on August 31 andSeptember 1 will be the same. As an example, consider a bond that pays coupons on January 15 andJuly 15. On March 15 two months will have passed and so the accrued interest will equal(60/180)×coupon. Notice that even February is assumed to have 30 days! On March 31 the accruedinterest will be (75/180)×coupon and on April 1 it will still be (75/180)×coupon.

Examples:

You look in the WSJ's bond table and see the following:

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GOVT. BONDS & NOTES

Rate MaturityMo/Yr

Bid Asked Chg. Ask.Yld.

7 July 06n 105:21 105:23 11 6.15

This bond has a coupon rate of 7%, so it pays $35 every six months. It matures July 2006. The "n"means that this is a note. A note is any government bond that was issued with a maturity of 10 yearsor less. A bond is identical to a note, but was issued with a maturity of over 10 years. The bid

equals 105:21, which translates into a quote of $ . Thus, you can sell the bond for 10 times

this amount plus the accrued interest (recall quotes are per $100 of face value). Usually, whenpeople discuss what a bond costs, they will quote per $100 of face value for the accrued interest also.In other words they will quote the accrued interest as if the coupon equaled 1/10 its true value.

As a retail customer you sell at the bid, and buy at the ask. If you ever have any trouble rememberingthis, just recall that you buy high and sell low. The change of 11 means the asked was 105:12yesterday. Finally, the "Ask. Yld." is supposed to tell you the bond's yield to maturity. (The yieldto maturity equals the internal rate of return on a bond.) Alas, it does not. Personally, I do not knowthe exact formula for calculating the ask yield (it is very complicated and varies by the timeremaining until the bond matures). Unfortunately, this means that if you ever want a bond's trueyield to maturity you will have to calculate it yourself.