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Bond Par Price, Notional Amount, and Outstanding Principal

Article Quant Q&A · Author: Gus Montano
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Summary

The document explains why a bond’s quoted price, notional amount, and par value should not be treated as interchangeable. A quoted price of 100 is generally expressed per 100 units of principal; institutional trade conventions can make a standard quote correspond to a much larger total notional. Thus a price of 100 does not necessarily mean the whole position is worth 100 dollars. The distinction matters when translating a quoted bond price into cash paid or received.

Notional and par value can also diverge as a security changes. The examples describe an inflation-linked bond whose indexed principal rises above its original notional and a mortgage-backed security whose outstanding principal falls below its original amount. At issuance, the values may coincide, while indexation or amortization changes the principal represented by a price of 100. These conventions help clarify bond valuation inputs, but the document does not provide enough information to solve the question’s coupon-rate calculation; actual settlement can also involve accrued interest.

Key ideas

  • A bond price quoted at 100 is a price per unit of principal, not necessarily the total cash value of the position.
  • Trade-size conventions can make one quoted unit represent a large notional amount.
  • Notional usually refers to the original or reference principal, while par value can reflect an adjusted amount.
  • Inflation indexation can raise the principal associated with a bond price of 100.
  • Mortgage amortization can reduce the principal associated with a price of 100.

Tags

Fixed incomeDerivatives pricing
Full text
# The Difference between Notional and Par Value of a Bond


# The Difference between Notional and Par Value of a Bond












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,

## Answer by JoshK (score 3, accepted)

https://quant.stackexchange.com/a/25572

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.

## Answer by user20429 (score 4)

https://quant.stackexchange.com/a/25570

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.