Par vs. Spot Curve

This is driving me nuts. So you use a par curve to discount multiple cash flows in a coupon paying bond to have the bond trade at par-- but you have a spot curve for each cash flow?

par curve is the yield on a bond so that it would trade as par. (coupons reinvested)

spot curve is the interest for a single cashflow, i.e. a zero or a strip.

So in practice, if you saw 4% on the par curve and 4% on the spot curve at y10, it would break down as follows:

PAR: you would earn 4% with your coupons reinvested for 10 year (when are the coupons reinvested? at what rate?)

SPOT: you would earn 4% on a zero to y10

Thank you for your help, I really appreciate it!

I wrote an article on yield curves that may be of some help here:

PAR, it means there is a bond with a market price of 100, which pays an annual coupon of 4.

SPOT, it means the 10y zero is price at (say) 75 and the 11yr zero is priced at 75/1.04

thats how i think of it, could be wrong…

Spot curves are usually placed slightly higher than par curves, although they follow a simillar shape. This is because a spot (bullet) security pays once at the end of the term, and this is your YTM (spot rate).

A par curve uses commonly traded securities which normally pays coupons, but the difference is that you usually lend out the par value, and recieve it at the end of the term, unlike spot securities where you get your yield exclusively from a discount price at issue date. The present value of the coupons you recieve are treated as spot securities themselves, think of coupons and repayments as individual cashflows (which they practically are). You add up all the present value of the cashflows with the discount rate (spot rate) matching their duration, and the single hypothetical discount rate that equates the intrinsic value of all your cash flows, is your YTM, which also the IRR.

Since the YTM will always be less than the spot rate of the same tenor, since you recieve cash flows earlier for a coupon paying security, then the Par curve will be lower than the spot curve, for every maturity.

Hope this makes sense.

Very helpful. Thanks!