(12C) 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-12C 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=6719]
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
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.

Code:


Line    Keystroke    Display
000
001    STO 0    44 0
002    g INTG   43 25
003    STO 1    44 1
004    R↓      33
005    STO 3    44 3
006    1        1
007    +        40
008    STO 4    44 4
009    R↓       33
010    STO 5    44 5
011    RCL 0     45 0
012    g FRAC    43 24
013    STO 2    44 2
014    g  X=0    43 35
015    g GTO 22    43 33 22
016    1        1
017    X<>Y        34
018    -        30
019    STO 2    44 2
020    1        1
021    STO + 1    44 40 1
022    RCL 4        45 4
023    RCL 2        45 2
024    RCL 3        45 3
025    ×        20
026    -        30
027    RCL 4        45 4
028    RCL 1        45 1
029    Y^X        21
030    ×        20
031    RCL 4        45 4
032    -        30    
033    RCL 3        45 3
034    RCL 1        45 1
035    RCL 2        45 2
036    -        30
037    ×        20
038    -        30
039    RCL 5        45 5
040    ×        20
041    RCL 3        45 3
042    2        2
043    Y^X        21
044    RCL 1        45 1
045    RCL 2        45 2
046    -        30
047    ×        20
048    +        40
049    RCL 4        45 4
050    RCL 1        45 1
051    Y^X        21
052    1        1
053    -        30
054    RCL 3        45 3
055    ×        20
056    RCL 5        45 5
057    ×        20
058    RCL 3        45 3
059    2        2
060    Y^X        21
061    +        40
062    +        10
063    GTO 00    43 33 00

f CLEAR REG
1. GTO 00
2. Bond's Coupon Rate (in decimal) ENTER
3. Bond's Yield (in decimal) ENTER
4. Bond's Maturity (in periods) R/S
running
Bond's Duration (in periods)

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.
0.04 ENTER
0.06 ENTER
9.75 R/S
running
8.0315 periods (= 4.0157 years)

"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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