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22) where Pc = the price of a coupon bond C = the bond coupon tn = the coupon payment dates, with n ≤ N , and t = 0 at the time of valuation w = the coupon frequency (annual or semiannual for plain vanilla bonds; monthly for certain floating-rate notes and asset-backed securities), expressed in number of times per year T = the maturity date Note that “100” on the right-hand side captures the fact that prices are quoted per 100 of the bond’s principal, or nominal, value. 23). 22) can be simplified by substituting Df for the part of the expression representing the discount factor.

30) Conversely if the coupon bond prices PC1, PC2 ,…. 32). 31) PCN − PN −1C − ..... 32) Finally, a regression technique known as ordinary least squares, or OLS (discussed in chapter 5), is applied to fit the term structure. 30) restricts coupon-bond prices by requiring them to be precise functions of the prices of other coupon bonds. In practice, this strict relationship is vitiated by the effects of liquidity, taxes, and other factors. 33). PC i N i = PC 1 i + P2C i + ..... 33) the regressor parameters are the coupons paid on each coupon-payment date, and the coefficients are the prices of the zerocoupon bonds Pj where j = 1, 2, … , N.

These figures demonstrate the impact that the coupon-payment and discounting frequencies have on a bond’s redemption yield calculation. Specifically, increasing the frequency of discounting lowers the calculated yield, while increasing the frequency of payments raises it. When comparing yields for bonds that trade in markets with different conventions, it is important to convert all the yields to the same calculation basis. It might seem that doubling a semiannual yield figure would produce the annualized equivalent; the real result, however, is an underestimate of the true annualized yield.

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