Different Durations (FRM LO 23.9)

Duration (2)

Yellow: Inputs
Orange: DV01
(n)
(C)
(P)
(C+P)
(D)
[D x (C+P)]
Green: Modified duration
Blue: Macaulay duration
Present
Semi-
Cash
Dis-
Value
Par value
$1,000.00 
Annual
Prin-
Cash
count
of Cash
n x
Years to Maturity
 10 
Period
Coupon
cipal
Flow
Factor
Flow
PVCF
Coupon, %
4.0%
1
$20.00
$20.00
0.971
$19.42
$19.42
Yield
6.00%
2
$20.00
$20.00
0.943
$18.85
$37.70
3
$20.00
$20.00
0.915
$18.30
$54.91
Semiannual equivalents:
4
$20.00
$20.00
0.888
$17.77
$71.08
Coupon, %
2.0%
5
$20.00
$20.00
0.863
$17.25
$86.26
coupon, $
$20.00
6
$20.00
$20.00
0.837
$16.75
$100.50
Periods
 20 
7
$20.00
$20.00
0.813
$16.26
$113.83
Semiannual Yield
3%
8
$20.00
$20.00
0.789
$15.79
$126.31
9
$20.00
$20.00
0.766
$15.33
$137.96
Bond Price (PV)
$851.23 
10
$20.00
$20.00
0.744
$14.88
$148.82
11
$20.00
$20.00
0.722
$14.45
$158.93
Modified Duration
12
$20.00
$20.00
0.701
$14.03
$168.33
Shock, bps
 20 
13
$20.00
$20.00
0.681
$13.62
$177.05
Shock, %
0.20%
14
$20.00
$20.00
0.661
$13.22
$185.11
Yield up
6.20%
15
$20.00
$20.00
0.642
$12.84
$192.56
Price (Shock up)
$837.85 
16
$20.00
$20.00
0.623
$12.46
$199.41
Yield down
5.80%
17
$20.00
$20.00
0.605
$12.10
$205.71
Price (Shock down)
$864.86 
18
$20.00
$20.00
0.587
$11.75
$211.46
Duration
 7.931 
19
$20.00
$20.00
0.570
$11.41
$216.71
20
$20.00
$1,000
$1,020.00
0.554
$564.75
$11,294.99
Dollar value of an '01 (DV01)
Shock up + 1 bps
Sum of [n x PVCF]
$13,907.04
Yield
5.99%
k x Price
$1,702.45 
Price
$851.90 
Macaulay Duration
 8.17 
DV01
$0.68 
Modified Duration
 7.93 
Shock down - 1 bps
Yield
6.01%
Price
$850.55 
DV01
$0.67 
DV01 another way:
(P x D)/10,000
$0.68