# Spot Rate Treasury Curve

## 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.

## BREAKING DOWN 'Spot Rate Treasury Curve'

Because many bonds typically have multiple cash flows (coupon payments) at different points in the bonds' lives, 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 price.

For example, suppose that a corporate two-year 10% coupon bond 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, \$5, \$5, \$105. The present value for each respective cash flow will be \$4.81, \$4.62, \$4.44 and \$89.50. Therefore, the sum of all the cash flows will be \$103.36.

However, \$103.36 is not necessarily the price at which the corporate 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.