Calculating duration

CFA Level I Fixed Income
#1

Question on Wiley Qbank

Calculate the percentage change in full price of 30-year, 6% semiannual pay bond current trading at 7% for an increase in yield of 50 basis points.

−6.09%

+6.065%

−6.065%

The first choice is correct. First calculate the missing values in the formula approximate the modified duration = (PV– − PV+)/(2 × Change in yield × PV0). The price of a bond at a yield of 6% + 0.5% is 821.9656. The price of a bond at a yield of 6% is 875.2763. The price of a bond at a yield of 6% − 0.5% is 934.3659.

Proceed in calculating the approximate modified: (934.3659 − 821.9656)/(2 × 875.2763 × 0.0050) = 12.8417. Next compute the approximate convexity is using the formula ((PV– − PV+) − 2 PV0)/((Change in yield)2 × PV0): (934.3659 + 821.9656 − (2 × 875.2763))/(0.00502 × 875.2763) = 264.0949.

The expected change in bond price is then (−12.8417 × 0.005) + (264.0949 × 0.0052/2) = −6.0907%

My question of the above is :

1) Do you calculate the duration at the current YTM ?

2) Do you calculate the duration on a semi annual basis as the bond is on a semi annual basis ?

If both the responses to my questions are yes then, the duration should be calculated using 3.5% YTM + 0.5%, 3.5% YTM - 0.5% (that is, would the semi annual yeld be increased by 50 bps or 25bps)??

#2

  1. Yes

  2. Pretty much ALL time value problems are solved on a “periodic” basis. In this case, cash flows occur on a semi-annual basis, so duration should be calculated on a semiannual basis.

  3. The convention is that yields are expressed on an annual basis, so the 50bps change is an ANNUAL change. However, since this is a semiannual bond (see statement #2 above), the yield change you use is the change per 6 months.

#3

thanks!