(19BII) Bond Duration Between Coupon Payment Dates

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An extract from the article Bond Duration Between Coupon Payment Dates by Mark A. White in the Journal of Financial Education, FALL 1995, pages 49-51.

The widespread use of bond duration analysis creates a need for more accurate and efficient computational tools. This paper shows how one may program … Hewlett Packard's … HP-19B II- to determine the duration of annual and semiannual coupon bonds purchased on and between interest payment dates.

According to the author, duration is computed with "bonds purchased exactly on coupon payment dates," whereas it is "far more likely for bonds to be purchased between interest payment dates." The author references the following equation
[attachment=6717]
by J. H. Chua in his article A Generalized Formula for Calculating Bond Duration in the Financial Analysts Journal, SEP-OCT 1988, pages 65-67.
where
D = duration
C = periodic coupon
y = periodic bond yield
M = number of remaining coupon payments
f = fraction of period since the last coupon payment

formula
DUR:DUR=IF(FP(N)=0:(CP
Nx((l+YLD)^(N+1)-(1+YLD
)-YLDxN)+NxYLD^2)-(CPNx
YLDx((1+YLD)^N-1)+YLD^2
):(CPNx ((1+YLD-(1-FP(N)
)xYLD)x(l +YLD)^(IP(N)+1
)-(l+YLD)-YLDxN)+NxYLD^
2)-(CPNxYLDx((1+YLD)^(I
P(N)+1)-1)+YLD^2))

… menu … with four keys labelled [DUR] , [N], [CPN] and [YLD], corresponding to the bond's duration, maturity, coupon rate and yield, on a per period basis.

example
Consider an 8 percent, semiannual coupon bond matur- ing in exactly 4.875 years (9.75 semiannual periods) with a nominal yield to maturity of 12 percent.
9.75 [N]
0.04 [CPN]
0.06 [YLD]
[DUR] 4.874 yrs (9.75 semiannual periods)

"This note has presented methods for programming … of financial calculator to compute the duration of semiannual coupon bonds both on and between coupon payment dates. The increased accuracy and ease of calculation afforded by their use is beneficial …, allowing better integration of "real-world" data into … decision-making …"

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