What it means
Ordinary bonds pay regular interest, which makes their overall yield a blend of rates over several years. A spot rate strips that away and shows the pure rate for a single payment received at a single future date.
If you plot these rates for one year, two years, five years, ten years and so on, you get the spot rate yield curve. It usually slopes upward, because investors normally want a higher return for tying up money for longer, but it can be flat or downward sloping in unusual conditions.
A flat or falling curve is rarer and is often read as a sign that investors expect interest rates to fall. The curve is a working tool in valuation.
To value a bond or a project, each future cash payment is discounted at the spot rate for its own date, so a payment in two years uses the two-year spot rate and a payment in five years uses the five-year rate. Real zero-coupon bonds do not exist for every maturity, so analysts build the curve from the prices of ordinary government bonds using a method called bootstrapping.
This works from the shortest maturity outwards, using each bond's price to solve for the next spot rate. The curve also reveals what the market expects.
Combining two spot rates gives a forward rate, which is the rate implied for a future period, and this is how analysts read expectations about future interest rates from today's prices. A common nuance is that the spot rate yield curve differs from the better-known yield curve in the news, which usually plots yields to maturity on coupon-paying bonds.
The two are close in many markets but not identical, particularly when the curve is steeply sloped.
In practice
Real-world examples.
Example
A pension fund discounts its future benefit payments using the spot curve, applying the 10-year rate to payments due in 10 years and the 20-year rate to those in 20 years. This gives a more accurate present value than one flat rate. Using one flat rate can overvalue or undervalue the payments, depending on the shape of the curve.
Example
A bank trading desk compares today's spot curve with last week's. A steeper curve tells the desk that the market now expects interest rates to rise.
Example
A corporate treasurer values a four-year fixed-rate loan received by the company. She discounts each scheduled payment at the matching spot rate to see whether the loan is worth more or less than its face value.
Formula
Calculation
Implied forward rate: (1 + two-year spot rate)^2 = (1 + one-year spot rate) x (1 + forward rate for year two)
Suppose the one-year spot rate is 4% and the two-year spot rate is 5%. Then (1.05)^2 = 1.1025, and 1.1025 / 1.04 = 1.0601, so the forward rate for year two is about 6.01%. Using the two-year spot rate, a $1,000 payment due in two years has a present value of 1,000 / 1.1025 = $907.03.Case study
Seen in the real world.
Cobalt Utilities is an illustrative, fictional company planning a $20,000,000 investment that will return $5,000,000 at the end of each of the next four years. Its analyst first discounted all four payments at a single 5% rate.
She then repeated the calculation using spot rates of 3.5%, 4.0%, 4.5% and 5.0% for years one to four. Using the spot curve gave a present value of roughly $17.9 million, versus about $17.7 million at a flat 5%, because the earlier payments were discounted at lower rates.
Neither figure justified the $20,000,000 cost on its own, but the illustrative lesson is that the method matters. The analyst recommended using the spot curve in future valuations because it matched each cash flow to the correct market rate for its date. The finance team updated its valuation template so that the spot curve is refreshed whenever new government bond prices are loaded.
Watch out
Common mistakes.
- Using one flat discount rate for cash flows that arrive at very different dates.
- Confusing the spot rate curve with the par yield curve quoted in the news, which is based on coupon-paying bonds.
- Reading a downward-sloping curve as a certain sign of recession, when it is only one of several signals.
Questions
People also ask.
Why is it called a spot rate?
The word spot means the rate applies to money lent or borrowed from today, not from some future date, as a forward rate does.
How is the curve built if zero-coupon bonds are scarce?
Analysts use a bootstrapping method to extract the spot rates from the prices of ordinary government bonds with coupons.
What does a steep curve tell a business?
It generally means longer-term borrowing is more expensive than short-term borrowing, which affects decisions about loan length and fixed versus floating rates.
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