I am pretty confused by this topic as well, but I understand it to be that you need to use the par rate when bootstrapping because the other end of the equation is the par value and the YTM may not necesarially discount you back to par (i.e. - the bond could be selling at a premium or a discount).
“The par curve gives the yield to maturity (YTM) for (coupon-paying) bonds at each maturity: the single discount rate that you would use to discount all of the bond’s cash flows to get today’s market price.”
I would rephase it to say,
“The par curve gives the coupon at each bond maturity in order that the bond’s market value is equal to par”
reading 42 says, “The par curve represents the YTM on coupon paying government bonds, priced at par, over the range of maturities”
my point is it’s called the “par curve” so it’s important to think about everything being priced at “par”. if you start to think about “discount rates” then it becomes confusing… and easy to mix up with the other curves. (i.e. when you start talking about discounting and coupon reinvestment it’s very confusing as a definition).
Yes, I agree, that is confusing when they use the word discount rate simultaneously with yield to maturity. The discount rate should only be used if they were discounting coupon payments and the final par value back using a discount rate other than the yield to maturity. Sort of like they do here. Just my opinion.
This is an interesting concept. I’ve never heard of the par curve before. Based on the jargon and calculations in that article, I do not look forward to preparing for this on my CFA exam. Ugh!
I think another difference is YTM is an ‘aggregated’ rate - it stays the same when it is used to discount the cash flows; whist the par rate changes at each payment (due to the term structure). YTM is a result of aggregated series of spot rates.