Question

Consider the following bond:

Loblaws Corp. Bond 6.50% due January 22, 2029 trading at a YTM of 2.534%. Assume a settlement date of May 26th, 2020.

face value = 100$

Calculate each bond's Macaulay Duration, Modified Duration and the Convexity Measure. Note, you must calculate the full market price of each bond to arrive at the duration and convexity figures (do not back out accrued interest).

Assume the actual/365 day count convention.

Answer 1

Macaulay Duration = 7.13 years

Modified Duration = 6.98

Convexity measure = 0.85

Workings:

Note:

1. Coupon payment is assumed to be annual

2. Settlement Date is on 26-May-20 and due date is on 22-Jan-29. Thus, annual coupons will be paid on 22nd Jan every year

3. 1st coupon payment will be made 22-Jan-21. The number of days between 22-Jan-21 and 26-May-20 is 241 days which is less than 1 year (365 days). This is referred to as the 'short coupon' as the coupon payment is made in a period shorter than the normal period. This is only for the first coupon payment.

4. 2nd payment will fall on 22-Jan-22, 3rd payment on 22-Jan-23 and so on till 9th and final payment fall on 22-Jan-29. On the final payment on 22-Jan-29, coupon along with principal will be paid.