The one-year par rate equals the one-year zero coupon rate because, with the assumption of annual coupons, the bond is a pure discount instrument.
I’m confused by this statement - how can a bond be a pure discount instrument if it is trading at par?
That’s not what they’re saying, though it’s understandable that it’s confusing.
Suppose that the 1-year par rate is 3%. A $1,000 par coupon-paying bond with a 3% annual coupon would trade at $1,000: par. A $1,000 par zero-coupon bond would trade at $970.87. It will earn $29.13 in interest at maturity; not coincidentally, $29.13 is 3% of $970.87.
They’re trading at the same _ yield _, not at the same price.
Many thanks for the reply.
What you have said makes absolute sense and I did wonder to myself if that’s what they were getting at but I couldn’t and still can’t get my head around the wording when trying to think about it intuitively. It’s worded almost exactly the same way in the curriculum as well. I can’t understand the linkage between the annual coupon assumption and the bond (is this the zero coupon or coupon paying bond they are referring to?) effectively acting as a pure discount instrument?
The par curve gives the YTM of bonds at each maturity; whether the bond pays a coupon or not (and, if it does, what the coupon rate is) does not matter. If the 3-year par rate is 4%, then a 4%-coupon bond will trade at a yield of 4% (which means that it will trade at par), a 5%-coupon bond will trade at a yield of 4% (so it will trade above par), and 3%-coupon, 2%-coupon, 1%-coupon, and 0%-coupon bonds will each trade at a yield of 4% (so they will trade below par).
I wrote an article on yield curves that may be useful here: http://financialexamhelp123.com/par-curve-spot-curve-and-forward-curve/
I’ve actually read your article already amongst others. Your website is extremely helpful.
I understand the relationshop between coupon rates and yields in terms of pricing at par/premium/disount however I’m still confused.You mention that it doesn’t matter if the bond pays a coupon or not but doesn’t the par curve show the YTM for coupon paying bonds only?
The statement in bold on my first post just doesn’t make sense to me. Maybe I’m overthinking it or maybe I just don’t get it. I should probably move on from it either way.
All that bold sentence is saying is that you can consider a 1-period zero-coupon bond to be a 1-period coupon paying bond, because each has only one payment: at the end of the period. In the example I gave above, if the 1-year YTM is 3%, you can think of a 1-year, $1,000 par, zero-coupon bond as a 1-year, $970.87 par, 3% coupon bond. They’re identical in that:
- You would pay $970.87 for each today
- One year from now you will receive $1,000 for each
- There will be no other cash flows for either
Got it now, thanks.
You’re quite welcome.
This clears up the rather foggy understanding i have of YTM
Thanks!!!