## Exhibit 220 Price of a Bond Coupon Rate Equals Yield to Maturity over Time

When a bond is between coupon dates or if its first coupon differs in size from other coupons because of its irregular timing—what is known as an odd first coupon— the coupon yield of a bond trading at par is not the same as its yield to maturity.

Result 2.3 A bond between coupon dates has a flat price that is less than par when its yield to matu rity is the same as its coupon rate.

The phenomenon described in Result 2.3, known as the scallop effect, is shown in Exhibit 2.20. The scallop effect occurs because yields to maturity are geometric; that is, they reflect compound interest. The prices at which bonds are quoted—the flat prices—partly reflect compound interest and partly simple interest. The simple interest part is due to accrued interest, which is generally subtracted from the bond's traded price to obtain the bond's quoted price.

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