Solutions to Ch5 and Ch6 - KsuWeb

38 Problems and Solutions
where DP is the portfolio duration, Di the duration of bond, i, andwi = Pi(y)
P(y) is
the weight of bond i in the portfolio P .
Exercise 5.7 Compute the dirty price, the duration, the modified duration, the $duration and the
BPV (basis point value) of the following bonds with $100 face value assuming
that coupon frequency and compounding frequency are (1) annual; (2) semiannual
and (3) quarterly.
Bond Maturity (years) Coupon Rate (%) YTM (%)
Bond 1 1 5 5
Bond 2 1 10 6
Bond 3 5 5 5
Bond 4 5 10 6
Bond 5 5 5 7
Bond 6 5 10 8
Bond 7 20 5 5
Bond 8 20 10 6
Bond 9 20 5 7
Bond 10 20 10 8
Solution 5.7 We use the following Excel functions “Price”, “Duration” and “MDuration” to
obtain respectively the dirty price, the duration and the modified duration of each
bond. The $duration is simply given by the following formula:
The BPV is simply
$duration =−price × modified duration
BPV = −$duration
10,000
1. When coupon frequency and compounding frequency are assumed to be annual,
we obtain the following results:
Price Duration Modified $Duration BPV
Duration
Bond 1 100 1 0.95 −95.24 0.00952
Bond 2 103.77 1 0.94 −97.90 0.00979
Bond 3 100 4.55 4.33 −432.95 0.04329
Bond 4 116.85 4.24 4 −467.07 0.04671
Bond 5 91.8 4.52 4.23 −388.06 0.03881
Bond 6 107.99 4.2 3.89 −420.32 0.04203
Bond 7 100 13.09 12.46 −1,246.22 0.12462
Bond 8 145.88 11.04 10.42 −1,519.45 0.15194
Bond 9 78.81 12.15 11.35 −894.72 0.08947
Bond 10 119.64 10.18 9.43 −1,127.94 0.11279