Duration FI

CFA Level I
#1

Which of the following statements regarding Macaulay duration is correct?

  1. For a given coupon rate, Macaulay duration can be lower for a long-term discount bond than for a short-term discount bond.
  2. For a given time to maturity and yield to maturity, Macaulay duration is lower for a zero-coupon bond than for a low-coupon bond trading at a discount.
  3. For a given time to maturity and yield to maturity, Macaulay duration is lower for a low-coupon bond trading at a discount than for a high-coupon bond trading at a premium.

Answer is A
but i didn’t understand how, Higher the maturity higher is the duration right?

#2

Think of the other thing that can change - YTM

McD - weighted average time to receipt of cash flows (Edit corrected)

Think of 20 year 10% coupon bond with YTM of 20%. Final payment has low weight as it is a long way of and heaviliy discounted. Initial coupons have a much higher weighting.(For ref McD = 6.2)

Now think of 18 10% coupon year bond with YTM 0f 1%. Final payment has a much higher weight due to low discount rate. More balance in weighting of cash flows (For ref McD = 12.1)

#3

So for discount bond the theory HIGHER MATURITY- HIGHER DURATION does not hold?

#4

Generally it does but you can come up with scenarios where it does not.

#5

okay, but this gets confusing

#6

With all due respect, this isn’t correct.

Macaulay duration is the weighted average time to receipt of cash flows; it’s not a weighted average of the PVs of the cash flows. The PVs of the cash flows are the weights.

#7

Thank - laziness on my part. I have editted the comment.