Spot Rate

A spot rate (or zero-coupon rate) is the yield on a bond that makes a single payment at maturity with no intermediate coupons. It represents the pure discount rate for a specific time horizon and is the building block of the term structure.

The par yield curve published by the Treasury shows yields on coupon-bearing bonds. The spot curve (or zero curve) is derived from the par curve through a process called bootstrapping: solving iteratively for the discount rates that correctly price each coupon bond.

Spot rates are important because they provide a cleaner measure of the term structure:

• Par yields blend information from multiple maturities (each coupon payment is discounted at a different rate)
• Spot rates isolate the pure discount rate for each specific maturity

The relationship between spot rates and forward rates is fundamental to fixed-income pricing. The forward rate between any two future dates is determined by the ratio of the two corresponding spot rates.

In practice, spot rates are used to:

• Price any fixed cash flow by discounting each payment at the appropriate spot rate
• Extract forward rates for swap and derivative pricing
• Identify relative value along the curve (comparing spot rates to par yields reveals where coupon bonds are cheap or rich)

The difference between the par yield and the spot rate at the same maturity depends on the slope and curvature of the curve. When the curve is upward-sloping, spot rates exceed par yields at longer maturities.