### What Is the Spot Rate Treasury Curve?

The spot rate treasury curve is a yield curve constructed using Treasury spot rates rather than yields. The spot rate Treasury curve can be used as a benchmark for pricing bonds. This type of rate curve can be built from on-the-run treasuries, off-the-run treasuries, or a combination of both. Alternatively, the Treasury curve can be calculated by using Treasury coupon strips.

### The Spot Rate Treasury Curve Explained

To reflect market expectations of changing interest rates, bonds may be priced based on Treasury spot rates rather than Treasury yields. When spot rates are derived and plotted on a graph, the resulting curve is the spot rate Treasury curve.

Spot rates are prices quoted for immediate bond settlements, so pricing based on spot rates takes into account anticipated changes to market conditions. Theoretically, the spot rate or yield for a particular term for maturity is the same as the yield on a zero-coupon bond with the same maturity.

The spot rate Treasury curve provides the yield to maturity (YTM) for zero-coupon bonds that is used to discount a single cash flow at maturity. Thus, to determine the price of a coupon-paying bond, the YTM is used to discount the first coupon payment at the spot rate for its maturity, and the second coupon payment at the spot rate for its maturity, and so on.

Because many bonds typically have multiple cash flows (coupon payments) at different points during the duration of the bond, it is not theoretically correct to use just one interest rate to discount all of the cash flow. Therefore, in order to make a sound bond valuation, it is good practice to match up and discount each coupon payment with the corresponding Treasury spot rate for pricing the present value of each cash flow.

### Example of the Spot Rate Treasury Curve

For example, suppose that a two-year 10% coupon bond with par value of $100 is being priced using Treasury spot rates. The Treasury spot rates for the subsequent four periods (each year is composed of two periods) are 8%, 8.05%, 8.1% and 8.12%, and the four corresponding cash flows are$5 (calculated as 10% / 2 x $100),$5, $5,$105 (coupon payment plus principal value at maturity). When the spot rates are plotted against the maturities, we get the spot rate or the zero curve.

Using the bootstrap method, the number of periods will be designated as 0.5, 1, 1.5, and 2, where 0.5 is the first 6-month period, 1 is the cumulative second 6-month period, and so on.

The present value for each respective cash flow will be:

﻿\begin{aligned} &=\5/1.08^{0.5}+\5/1.0805^1+\5/1.081^{1.5}+\105/\1.0812^2\\ &=\4.81+\4.63+\4.45+\89.82\\ &=\103.71\\ \end{aligned}﻿

Theoretically, the bond should be offered at a price of \$103.71 in the markets. However, this is not necessarily the price at which the bond will ultimately be sold. Because the spot rates used to price bonds reflect rates that are from default-free Treasuries, the corporate bond's price will need to be further discounted to account for its increased risk compared to Treasury bonds.

It is important to note that the spot rate Treasury curve is not an accurate indicator of average market yields because most bonds are not zero-coupon.