CFA Level II Exam · The Term Structure and Interest Rate Dynamics

Swap Rate Curve and Spreads for CFA Level II

Updated 7 October 2026 · Fact-checked

The swap rate curve shows fixed rates on par swaps by maturity. Spreads measure a bond's extra yield over a benchmark. The I-spread is the bond yield minus the swap rate at the same maturity. The Z-spread is the constant amount added to every spot rate so discounted cash flows equal the price.

Understand Swap Rate Curve and Spreads

The swap rate curve is the set of fixed rates at which counterparties will swap fixed payments for floating payments, by maturity. Each swap rate is the fixed rate that makes the swap worth zero at the start. Because it is a par rate, it works like a par yield curve. You can bootstrap spot rates from it.

Market participants use the swap curve as a benchmark for two reasons. First, the swap market is not tied to the supply of government debt, so rates exist for many maturities. Second, a swap needs little or no upfront cash, so it is not distorted by the tax and liquidity effects that affect government bonds. A swap rate also reflects the credit risk of the floating reference rate banks, so it is usually above a government rate of the same maturity.

The swap spread is the swap fixed rate minus the government bond yield of the same maturity. It is a gauge of credit risk in the banking sector, and of general liquidity. The I-spread (interpolated spread) is the bond's yield to maturity minus the swap rate at the bond's maturity, interpolating between swap tenors if needed. It is a single-point spread.

The Z-spread (zero-volatility spread) is more precise. It is the constant spread added to each point on the benchmark spot curve so that the present value of the bond's cash flows equals its market price. It uses the whole curve, not one maturity. The two measures are close when the curve is flat. They differ more when the curve is steep, especially for amortizing bonds or bonds with early principal repayment.

Two money-market spreads reflect stress. The TED spread is the 3-month Libor minus the 3-month T-bill rate (the US Treasury bill). It widens when banks are seen as riskier. The Libor-OIS spread is Libor minus the overnight indexed swap rate. OIS has little credit risk, so the spread isolates bank credit and liquidity risk. A wider spread means more stress. Libor is being phased out, so questions test the logic of the spread, not the specific rate.

Key formulas to remember

Swap spread: Swap spread = Swap fixed rate − Government bond yield (same maturity); Reflects bank credit risk and liquidity. Can be quoted in basis points.
I-spread: I-spread = Bond yield − Interpolated swap rate at the bond's maturity; Uses one point on the curve. Interpolate linearly if the maturity falls between swap tenors.
Z-spread: Price = Σ CFt ÷ (1 + St + Z)^t; S = benchmark spot rates, Z = constant spread. Solve Z by trial and error; the exam usually gives it or asks you to compare.
TED spread: TED = 3-month Libor − 3-month T-bill rate; Wider means more perceived credit risk in the banking system.
Libor-OIS spread: Libor-OIS = Libor − Overnight indexed swap rate; Cleaner gauge of bank credit and liquidity risk. Widens in stress.

How to solve Swap Rate Curve and Spreads questions

Use this approach for any swap curve or spread question in a vignette.

1Identify the benchmark: swap curve, government curve or OIS. Note the maturity and the bond's yield or price.
2Decide which spread the question asks for. I-spread is a yield difference at one maturity; Z-spread uses the whole spot curve.
3For an I-spread, find the swap rate at the bond's maturity. If it lies between two tenors, interpolate linearly, then subtract from the bond yield.
4For a Z-spread, discount each cash flow at the spot rate plus the spread. Check which spread gives a PV equal to the price.
5For TED or Libor-OIS, subtract the safer rate from the bank rate and convert to basis points if needed.
6Interpret the direction: a wider spread means more credit or liquidity risk, and a narrower one means less.
7Check units: percent versus basis points, and the maturity match.

Quickest way: Compare-and-eliminate method

When to use it: Use when the vignette gives a few spreads and asks which is larger or what a change implies.

Write each spread as a plain subtraction before reading the options.
For a Z-spread check, discount all the bond's cash flows at the spot rate plus the spread given in an option, then compare the total PV with the market price.
Remember a higher spread lowers PV, so if the total PV is above the price, the spread must be larger.
For direction questions, link wider spreads with a flight to quality and tighter spreads with calm markets.
Eliminate options that mix up the safe rate and the bank rate.

Common mistakes in Swap Rate Curve and Spreads

Calling the I-spread a spread over the full curve.
Both spreads are quoted over the swap curve, so they look alike.
Fix: I-spread uses one maturity. Z-spread uses every spot rate along the curve.
Using the government yield in the I-spread instead of the swap rate.
Confusion with the swap spread, which does use government yields.
Fix: The I-spread subtracts the swap rate from the bond yield. The swap spread subtracts the government yield from the swap rate.
Reversing the TED spread, or using Libor-OIS as a government risk measure.
Students memorize names, not what each rate contains.
Fix: Libor is a bank rate with credit risk. T-bills and OIS are near risk-free. Always subtract the safe rate from the bank rate.
Applying the Z-spread to the yield instead of the spot rates.
Spread language suggests a yield difference.
Fix: The Z-spread is added to each spot rate, not to the bond's yield to maturity.
Reading a widening spread as lower risk.
Mixing up spread and yield direction.
Fix: A wider TED or Libor-OIS spread means banks are viewed as riskier or liquidity is scarcer.

Worked examples

Example 1

A 7-year bond has a yield to maturity of 4.60%. Swap rates are 3.80% for 5 years and 4.20% for 10 years. (1) Estimate the swap rate at 7 years by linear interpolation. (2) Calculate the I-spread in basis points. (3) Conceptually, which spread better captures the whole benchmark curve when the curve is steep: the I-spread or the Z-spread?

Show the solution

(1) Seven years is 2 of 5 years between the tenors, so the weight is 0.4.
Swap rate = 3.80% + 0.4 × (4.20% − 3.80%) = 3.80% + 0.16% = 3.96%.
(2) I-spread = 4.60% − 3.96% = 0.64%, which is 64 basis points.
(3) The I-spread compares the bond with a single point on the curve. The Z-spread is added to every spot rate, so it reflects the whole curve and the timing of each cash flow. On a steep curve the two can differ, and the Z-spread captures the curve better.

Answer: (1) 3.96%. (2) 64 bps. (3) Z-spread.

Example 2

A vignette reports a 3-month Libor of 1.90%, a 3-month T-bill rate of 0.40%, and a 3-month OIS rate of 1.30%. Last quarter the TED spread was 90 bps and the Libor-OIS spread was 35 bps. (1) Calculate the current TED spread and the Libor-OIS spread. (2) What does the change in each imply about bank risk?

Show the solution

(1) TED = 1.90% − 0.40% = 1.50%, which is 150 bps.
Libor-OIS = 1.90% − 1.30% = 0.60%, which is 60 bps.
(2) TED rose from 90 to 150 bps, an increase of 60 bps.
Libor-OIS rose from 35 to 60 bps, an increase of 25 bps.
Both widened, so perceived credit risk and liquidity stress in the banking system increased.

Answer: TED is 150 bps and Libor-OIS is 60 bps. Both widened, signalling higher bank credit and liquidity risk.

Exam tips

Know the definition of each spread cold. Most questions test whether you subtract the right rates.
Expect a vignette to give swap rates at only two tenors, so practise linear interpolation.
For Z-spread versus I-spread, the answer is usually that Z-spread is more precise because it uses the whole curve.
When asked about stress, a widening TED or Libor-OIS spread means more risk and often a flight to quality.
Watch units. A spread of 0.64% equals 64 bps.

Swap Rate Curve and Spreads in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Swap Rate Curve and Spreads: frequently asked questions

What is the difference between Z-spread and I-spread?

The I-spread is the bond yield minus the swap rate at one maturity. The Z-spread is the constant amount added to every spot rate on the benchmark curve so the bond's discounted cash flows equal its price. The Z-spread therefore reflects the whole curve.

Why is the swap curve used as a benchmark?

Swap rates exist for many maturities and are not affected by government bond supply. They are also less affected by tax and repo-market effects. This makes them a consistent benchmark for pricing non-government bonds.

What is the difference between the TED spread and the Libor-OIS spread?

The TED spread is 3-month Libor minus the 3-month T-bill rate. The Libor-OIS spread is Libor minus the overnight indexed swap rate. Both gauge bank credit and liquidity risk, and Libor-OIS is considered the cleaner measure.

How do I calculate the Z-spread of a bond?

Discount each cash flow at the benchmark spot rate for its date plus a constant Z. Adjust Z until the total present value equals the bond's market price. On the exam you normally test a given Z or compare it, rather than solve it from scratch.