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Bloomberg Securities Handbook

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12), which acts as a ceiling. 12). 12). 28354 years. Properties of Macaulay Duration Duration varies with maturity, coupon, and yield. Broadly, it increases with maturity. A bond’s duration is generally shorter than its maturity. This is because the cash flows received in the early years of the bond’s life have the greatest present values and therefore are given the greatest weight. That shortens the average time in which cash flows are received. A zero-coupon bond’s cash flows are all received at redemption, so there is no present-value weighting.

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.

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.

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