In finance, par yield (or par value yield) is the yield on a

$\backslash frac\; +\; \backslash frac\; +\; \backslash cdots\; +\; \backslash frac\; =\; 100.$ This can be more succinctly expressed with the prices of zero coupon bonds: $c=\backslash frac$ Here $R(0,n)$ denotes the yield (on annual interest rate basis) of an $n$-year

G. Questa: Fixed income analysis for the global financial market Chapter 7 Section 4

fixed income security
Fixed income refers to any type of investment under which the borrower or issuer is obliged to make payments of a fixed amount on a fixed schedule. For example, the borrower may have to pay interest at a fixed rate once a year and repay the pri ...

assuming that its market price is equal to par value (also known as face value
The face value, sometimes called nominal value, is the value of a coin, bond, stamp or paper money as printed on the coin, stamp or bill itself by the issuing authority.
The face value of coins, stamps, or bill is usually its legal value. H ...

or nominal value). Par yield is used to derive the U.S. Treasury’s daily official “Treasury Par Yield Curve
In finance, the yield curve is a graph which depicts how the yields on debt instruments - such as bonds - vary as a function of their years remaining to maturity. Typically, the graph's horizontal or x-axis is a time line of months or ye ...

Rates”, which are used by investors to price debt securities traded in public markets, and by lenders to set interest rates on many other types of debt, including bank loans and mortgages.
Compared to yield to maturity

Par yields are used to address a problem known as the "coupon effect." As finance scholars Martellini, Priaulet and Priaulet and others have pointed out, two bonds with the exact same maturity date but differentcoupon
In marketing, a coupon is a ticket or document that can be redeemed for a financial discount or rebate when purchasing a product.
Customarily, coupons are issued by manufacturers of consumer packaged goods
or by retailers, to be used in r ...

rates will not necessarily have the same yield to maturity. This disparity is due to differing coupon cash flow streams over the life of the two bonds, even when the maturity date and coupon payment dates are exactly the same. Finance scholar Frank J. Fabozzi
Frank J. Fabozzi is an American economist, educator, writer, and investor, currently Professor of Practice at The Johns Hopkins University Carey Business School and a Member of Edhec Risk Institute. He was previously a Professor of Finance at ED ...

has stated that because of the coupon effect, a yield-to-maturity yield curve should not be used to value bonds. Par yield analysis is useful because it avoids the coupon effect, since a bond trading at par has a coupon yield equal to its yield to maturity, according to Martinelli et al.
Calculation of par yield

Par yield is based on the assumption that the security in question has a price equal to par value. When the price is assumed to be par value ($100 in the equation below) and the coupon stream and maturity date are already known, the equation below can be solved for par yield.$\backslash frac\; +\; \backslash frac\; +\; \backslash cdots\; +\; \backslash frac\; =\; 100.$ This can be more succinctly expressed with the prices of zero coupon bonds: $c=\backslash frac$ Here $R(0,n)$ denotes the yield (on annual interest rate basis) of an $n$-year

zero-coupon bond
A zero coupon bond (also discount bond or deep discount bond) is a bond in which the face value is repaid at the time of maturity. Unlike regular bonds, it does not make periodic interest payments or have so-called coupons, hence the term zer ...

(ZCB), and $P\_n$ denotes the price of an $n$-year ZCB.
U.S. Treasury par yield curve rates

In the United States, the Department of the Treasury publishes official “Treasury Par Yield Curve Rates” on a daily basis. According to Fabozzi, the Treasury yield curve is used by investors to price debt securities traded in public markets, and by lenders to set interest rates on many other types of debt, including bank loans and mortgages.Other uses

Par yield is also used to design fixed income securities and interest swaps.See also

Nominal yield The coupon rate (nominal rate, or nominal yield) of a fixed income security is the interest rate that the issuer agrees to pay to the security holder each year, expressed as a percentage of the security's principal amount or par value. The coupon ...

References

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