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I have reached a confusing dilemma regarding the par and notional values of a bond.

I have been told that the par value of a coupon bond is $100. However, the notional value of the bond is 1,000,000.

Do they not represent the same thing; the face value of the bond? Is there a difference? Through my years in finance I assumed they were equivalent. Google does not provide an answer.

Furthermore, if some context helps, I have been told that

  • Par Value = 100
  • Market Value = 100
  • Maturity = 5
  • Notional Value = 1,000,000
  • YTM = 2.8% p.a.
  • Mod. Duration = 2.35% p.a.

I am required to find the coupon rate of the bond. Naturally, I would rely on the standard discounting of cash flows to create an equation, thereby allowing to solve for the coupon rate. However, the par/notional values are creating problems

Kind regards,

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    $\begingroup$ When you request the price of a bond it is quoted to you as a percentage of 100, for example 98 21/32. At other times things are calculated using a par/notional value expressed in dollars (usually 1000 per bond in textbooks or in your case 1,000,000 USD for the entire position). Just be consistent in you calculation, understanding when you have a peercentage and when a dollar amt and you will be OK $\endgroup$
    – nbbo2
    Apr 22, 2016 at 12:48
  • $\begingroup$ For example one solution might be: the optimal annual coupon is 5%, another might be the optimal coupon is 50,000 per year. THESE ARE EXACTLY THE SAME THING for your problem. $\endgroup$
    – nbbo2
    Apr 22, 2016 at 13:12
  • $\begingroup$ The terminology seems incorrect; "100" is the par PRICE and the market PRICE in your example. There may be some confusion or disagreement about what "par" means but there is no confusion about market VALUE: that is the notional value times the market price. In your case the market VALUE is 1,000,000. $\endgroup$
    – user20429
    Apr 22, 2016 at 18:50
  • $\begingroup$ @mathguy. From the example I have in front of me, Notional Value = 1,000,000, Market Price = 100, Par Value = 100. $\endgroup$
    – Gustavo Louis G. Montańo
    Apr 22, 2016 at 21:41
  • $\begingroup$ "From the example you have in front of you"? Seriously? Does it show a modified duration expressed in percent p.a.? Then you can throw the whole example away - whoever wrote it has no clue. $\endgroup$
    – user20429
    Nov 21, 2021 at 14:43

2 Answers 2

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You are being confused by the convention. Just using simple treasuries, look at it this way. The usual size that an institution quotes is for ten thousand \$100 par bonds. So, if you buy one bond for \$100 you are actually getting 10,000 little bonds and paying \$100 each. That's \$1mm total (forget about accrued interest to make it simple).

The convention could have been that the standard quote size of one is for 1,000 bonds, but it isn't. It doesn't matter that much, you can trade .0001 bond. Beyond that they can't settle in GSCC as far as I know. Although there might even be a way to do that.

So if you buy .0001 bond for \$100 you are paying \$100 and actually getting one bond.

Then the $100 is the price per. That is whatever you agree to with your counterparty. eg, I offer you one 10 year note for 101. You lift my offer and now need to give me 101x10,000=\$1,010,000.

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    $\begingroup$ Oh! So are you saying that with my example the bond portfolio consists of 10,000 - 100US bonds? This will lead a "notional value" of 1,000,000US $\endgroup$
    – Gustavo Louis G. Montańo
    Apr 22, 2016 at 21:35
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    $\begingroup$ Basically. Just remember that it all has to be able to settle. You can't settle on GSCC a half bond. $\endgroup$
    – JoshK
    Apr 25, 2016 at 0:52
  • $\begingroup$ Thank you @JoskK for you help. Very much appreciated. Have a good week. $\endgroup$
    – Gustavo Louis G. Montańo
    Apr 26, 2016 at 2:18
  • $\begingroup$ Np. Good luck. It's confusing at first but then you will get the hang of it. Just terminology. $\endgroup$
    – JoshK
    Apr 26, 2016 at 16:01
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Using the words the way I have in my old job: Par PRICE of 100, market PRICE of 100, notional value of 1,000,000 - then the par VALUE is also 1,000,000 (and the market value as well). Rephrasing your question: aren't par value and notional value the same thing?

Answer: not always. For example, for inflation-index bonds (TIPS), in the United States, you may have a notional value of \$1,000,000. If the inflation index factor is 1.1, then the "par value" of the bond (meaning, at a "bond price" of 100) is \$1,100,000, different from the "notional" value. Similarly, for a mortgage backed security, if the notional value is \$1,000,000, if the factor is 0.3 (meaning only 30% of the original principal is still outstanding), the "par value" of the security, meaning at a bond price of 100, is only \$300,000. "Notional value" is equal to "par value" when a bond or fixed income security is first issued; in most cases (except call events and such), the notional value doesn't change, while the par value can change with an "index" or "factor" like the inflation index for TIPS, or the remaining principal "factor" for MBS's.

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