Par Yield Curve

Updated on 2023-08-29T11:56:27.191508Z

What is Par Yield Curve?

The par yield curve refers to a graphical representation that represents the yield to maturity for different kind of bonds. Frequently, par yield curve is used to thoroughly inspect in order to determine whether investments of treasury bonds are strong or not in the present conditions of bond market.

It provides single discount rate that is used to discount the totality of cash flow of bonds in the bonds’ open market at the current price. The par yield curve is usually compared with the forward yield curve and the spot yield curve for treasuries.

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Understanding Par Yield Curve

The par yield curve represents the connection (relationship) between interest rates and bond yields with different date of maturities, starting the range from three months Treasury bills to thirty-year treasury bonds. The par yield curve’s represented geographical or plotted depicting interest rates on y-axis and increasing time durations on x-axis. Generally, researchers use line charts to present the relationship between various bond yields and interest rates in the current bond market.

The par yield curve takes place when the security’s yield to maturity is bought at par with interest rates of Treasury bonds. The graphical presentation of par yield curve shows the coupon bonds’ yield to maturity at their various maturities. It is total profit that is expected by the investors to make in order to hold the instrument till its period of maturity.

With the fluctuation of interest rate over the period, the yield to maturity would rise or decline in order to show the current rate conditions of market.

Generally, bonds with short duration have lower yields in the comparison of the bonds with longer duration, and the slope of par yield curve plotted upwards to the right. The yield curve also refers to the spot yield curve, mainly, for risk-free bonds. Though, in some instances where another kind of yield curve is also referred as the par yield curve. The par yield curve plotted the coupon-paying bonds’ yield to maturity (YTM) of various maturity dates. The yield to maturity may refer to the return expected by the bond investors to make by holding the bonds till their maturity dates. The bonds issued at par value has yield to maturity that is equal to the rate of coupon.

In other words, a par yield is the rate of coupon at which prices of bonds are nil (zero), the par yield curve shows the bonds that are buy or sell at par value. The curve is plotted the yield to maturity on a graph against the different maturity period of bonds which are priced at par value. The curve is used to estimate the coupon rate that a newly issued bond with a certain maturity will pay to sell at par value. The curve (par yield) provides a yield which is used to discount various cash flows for a coupon-paying bond, and use the data in the spot yield curve, which is also called as zero percent coupon curve, in order to discount every coupon by the suitable spot rate. The spot yield curve always lies above the par yield curve at the condition of upward sloping of par yield curve, and in the condition of downward sloping of par yield curve the spot curve lie below the par yield curve because the duration is longer on the spot yield curve.

Frequently Asked Questions (FAQs)

How does a Par Yield Curve influenced by Interest Rates?

In the condition of fall in interest rates after bond issuance, there is consequent rise in the value of the bond as the bond’s coupon rate is now more than the market’s present rate. Therefore, the interest rate will be more than the YTM (yield to maturity) in result and will be presented in the form of visualized yield curve. The Par yield occurs at the situation when the bond and interest rates are buying or sell at par that means the interest rates of bonds and interest rates are so similar to each other in the open market.

When the new bond rates are issued on the primary market the pay yield curve is used because the issuer of the bonds is not wanted to make due to interest rates that is unattractive. That is the reason, at the time a par yield curve is similar to the market interest rates, even graphically, it will look identical.