Relationship between YTM vs. Duration

CFA Level III Fixed Income
#1

All,

Can someone refresh my memory and simply explain the relationship between YTM and Duration?

Why is Duration higher at lower YTMs? I realize that higher coupons mean a lower duration, but what is usually the relationship between the lower coupons and YTM?

Thanks!

#2

The Macaulay duration is the weighted average term to maturity of the cash flows from a bond. The weight of each cash flow is determined by dividing the present value of the cash flow by the price.

and this PV is calculated at the YTM of the bond, typically.

Lower YTM - higher PV …

#3

Ok, thanks. Now, how about the relationship between coupon and YTM?

Does a higher YTM imply higher coupon?

#4

I do not recall if such a causal relationship exists.

#5

Ya it’s not a great question. A better question is relation between interest rates and duration

#6

All things equal, yes.

But it’s the high coupon rate that causes the high YTM, not the other way round.

#7

Thanks as always s2000magician.

#8

You’re welcome, as always.

#9

Sorry to revive an old thread. But in this graph from reading 22, it seems to imply that YTM increases with Duration?

Link: https://imgur.com/a/Ssqs1

What am I missing here? Thanks.