Macaulay duration (MacDur)

CFA Level I Fixed Income
#1

I have a question about the weight calculation. For the weights I got

w1 = .0556

w2 = .0514

w3 = .8415

Am I wrong? If so, how do you get the weights from the answer key?

An investor buys a 6% annual payment bond with three years to maturity. The bond has a yield-to-maturity of 8% and is currently priced at 94.845806 per 100 of par. The bond’s Macaulay duration is closest to:

  1. 2.62.
  2. 2.78.
  3. 2.83.

C is correct. The bond’s Macaulay duration is closest to 2.83. Macaulay duration (MacDur) is a weighted average of the times to the receipt of cash flow. The weights are the shares of the full price corresponding to each coupon and principal payment.

Period** Cash Flow Present Value Weight **Period × Weight 1 6 5.555556 0.058575 0.058575 2 6 5.144033 0.054236 0.108472 3 106 84.146218 0.887190 2.661570 94.845806 1.000000 2.828617

#2

I hope this helps.

Period

Cash flow (CF)

Present value (PV) [CFj/(1+i)N]

Weight (PVj/PVTotal)

Period × weight

1

6

6 / (1.08)1 = 5.5556

5.5556/94.845806 = 0.0586

1 x 0.0586 = 0.0586

2

6

6 / (1.08)2 = 5.1440

5.1440/94.845806 = 0.0542

2 x 0.0542 = 0.1085

3

106

106 / (1.08)3 = 84.1462

84.1462/94.845806 = 0.8872

3 x 0.8872 = 2.6616

Total

104.0470

94.845806/94.845806 = 1.000

2.8286

#3

Sorry formatting is messed up, not sure how to paste tables in here.