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How Are Bond Prices Affected by Coupon Payment Dates?

Does a bond experience the inverse of the price deterioration seen on an option, the closer it is to a coupon date?

For example, suppose you purchase a $1,000 bond with a 10% coupon, which pays $50 a year in two installments on June 15 and Dec. 15. If the bond is trading at par (100 cents on the dollar), does it experience a natural growth toward 105 as it approaches a payment date?

-- Gordon Shephard

Gordon,

Your logic is impeccable, but no, that's not how it actually works.

You correctly assume that if a bond changes hands a certain number of days after its last coupon payment, the seller should get whatever portion of the next coupon payment he is entitled to, based on how long he held the bond.



Fixed-Income Forum: Join the discussion on TSC message boards. Sellers do in fact get that payment. In bond-market lingo, it's called "accrued interest." But industry convention is to account for accrued interest separately from the price of the bond.

For example, suppose you buy a Treasury bond today at 99, or $990 per $1,000 of face value, to settle on Wednesday. This Treasury bond has a 6% coupon and makes $30 interest payments every Feb. 15 and Aug. 15.

You are buying the bond on the 122nd day of a payment period that has 184 days. The seller is therefore entitled to 121/184 of the Feb. 15, 2000, coupon payment. A quick calculation shows that amount to be $19.80.

121/184 = 0.66

0.66 * $30 = $19.80

So, the full price of your bond, as opposed to the quoted price, would be $1009.80 -- $990 plus $19.80.

It makes sense to account for accrued interest separately -- rather than having it be reflected in the quoted price -- because that way bonds with different payment dates can be compared apples to apples, rather than having to figure out what portion of each bond's price represents accrued interest.

A couple of other points. According to Robert Zipf's book How the Bond Market Works, accrued interest is calculated slightly differently for corporate and municipal bonds than for Treasuries. In those calculations, all months have 30 days, and a year is 360 days. So, if the bond in the example were a corporate, you would calculate the accrued interest as follows. (The seller would be entitled to 120/180 of the next coupon payment.)

120/180 * $30 = $20

Also note that preferred stock, a stock-bond hybrid that was discussed in a previous Fixed-Income Forum, doesn't work this way. It works the way you thought bonds worked -- the seller's accrued interest is reflected in the quoted price of the security.

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