# Par rate vs yield to maturity

What is the difference between these two and how are they linked together?

The par rate is the rate that you would use to discount all the cash flows so that the price of the bond is 100 (par).

The YTM is the rate that you would use to discount all the cash flows so that the price of the bond is at discount, at par or at premium.

So the par rate can be YTM but the YTM isn’t necessarily always the par rate. Is this right?

So when you use the bootstrapping technique to calculate the spot rates, can you use YTM or do you HAVE to use the par rate?

EDIT: I’ve read this article http://financialexamhelp123.com/par-curve-spot-curve-and-forward-curve/ but I was stil confused because reading 43 EoC 1-6 gives “yield to maturity par rates” so does it mean that this is the same as “par rate”?

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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 rate is the YTM.

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“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.

The par rate does not change at each payment; spot rates might do so, but the par rate is the YTM: the same discount rate for all payments.

Simplify the complicated side; don't complify the simplicated side.

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It’s covered in the Level I curriculum.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams

http://financialexamhelp123.com/