CFA Level I Exam · Yield and Yield Spread Measures for Fixed-Rate Bonds

G-Spread, I-Spread, Z-Spread and OAS Explained

Updated 7 October 2026 · Fact-checked

Yield spread measures show how much extra return a bond offers over a benchmark. G-spread is the bond's yield minus a government yield. I-spread is the yield minus a swap rate. Z-spread is the constant spread added to every spot rate that reprices the bond. OAS is the Z-spread with the embedded option's value removed.

Understand Yield Spread Measures: G-Spread, I-Spread, Z-Spread and OAS

A bond's yield on its own tells you little. What matters is the extra yield you earn over a risk-free or near risk-free benchmark. That extra yield is the yield spread. It pays you for credit risk, liquidity risk and, for some bonds, option risk. Spreads are quoted in basis points, where 1 bp = 0.01%.

The two simplest measures are benchmark spreads. The G-spread is the bond's yield to maturity minus the yield on a government bond of the same maturity. The I-spread is the bond's yield to maturity minus the swap rate of the same maturity. If the exact maturity is not quoted, you interpolate between the two nearest benchmark points. Both compare one yield with one yield.

The weakness is that a bond pays cash flows at many dates, and each date has its own spot rate. The Z-spread (zero-volatility spread) fixes this. It is the single constant spread you add to every spot rate on the benchmark curve so that the present value of the bond's cash flows equals its market price. You find it by trial and error or with a solver. A higher Z-spread means a lower price, other things equal.

The Z-spread assumes cash flows are fixed. A callable or putable bond has cash flows that depend on future rates. The option-adjusted spread (OAS) removes the option's effect from the Z-spread. For a callable bond, the issuer owns the option, so the bond must pay extra yield and the Z-spread overstates the pure credit and liquidity compensation: OAS = Z-spread − option value. For a putable bond, you own the option, so the Z-spread is too low: OAS = Z-spread + option value.

For an option-free bond, the Z-spread and OAS are equal. That is the quickest way to remember how they relate. Use OAS to compare bonds with different embedded options on a like-for-like basis.

Key formulas to remember

G-spread: G-spread = YTM of bond − YTM of government bond with same maturity; Interpolate between two government yields if no exact maturity match exists. Quote in bps.
I-spread: I-spread = YTM of bond − swap rate of same maturity; Uses the swap curve as the benchmark, so it reflects the credit and liquidity of the interbank swap market, not the government.
Linear interpolation: Benchmark = Y1 + (T − T1) ÷ (T2 − T1) × (Y2 − Y1); Use it when the bond's maturity lies between two quoted benchmark maturities.
Z-spread pricing equation: Price = Σ CFt ÷ (1 + St + Z)^t; St is the benchmark spot rate for period t. Z is the same constant for every period. Solve for Z.
OAS for a callable bond: OAS = Z-spread − option value (in spread terms); OAS is lower than the Z-spread because the call option benefits the issuer.
OAS for a putable bond: OAS = Z-spread + option value (in spread terms); OAS is higher than the Z-spread because the put option benefits the investor.

How to solve Yield Spread Measures: G-Spread, I-Spread, Z-Spread and OAS questions

Use this order for any yield spread question. It keeps benchmarks, option direction and units straight.

1Identify which measure is asked: G-spread, I-spread, Z-spread or OAS. The benchmark named in the question tells you which one.
2Check whether the bond has an embedded option. If it is callable or putable, plan to use OAS rather than the Z-spread for like-for-like comparison.
3For G-spread or I-spread, find the benchmark yield at the bond's maturity. Interpolate linearly if the maturity falls between two quoted points.
4Subtract the benchmark yield from the bond's YTM. Convert the result to basis points (multiply the percentage by 100).
5For a Z-spread question, discount each cash flow at its spot rate plus Z. Compare the result with the given price to test or solve for Z.
6For OAS, apply the sign rule: callable, OAS = Z-spread − option value. Putable, OAS = Z-spread + option value.
7Sanity check: a callable bond's OAS must be below its Z-spread, a putable bond's above it, and an option-free bond's two must match.

Quickest way: Eliminate by direction and bps

When to use it: Use when you have about 90 seconds and three options. Most spread questions can be cut to one answer by direction or unit checks.

Ask first: callable or putable? That fixes whether OAS is below or above the Z-spread and removes at least one option.
For benchmark spreads, do a rough benchmark yield in your head, then subtract. Options differ by more than rounding, so the rough figure is usually enough.
Watch units. 1.00% is 100 bps. Reject options that are off by a factor of 10 or 100.
For Z-spread, test the middle option first. If the PV is too high, the true spread is higher. If the PV is too low, it is lower. That picks the answer after one calculation.
On the TI BA II Plus, compute each discount factor with 1.045 [x²] [1/x], then multiply by the cash flow. Store results with [STO] and sum with [RCL] if needed.

Common mistakes in Yield Spread Measures: G-Spread, I-Spread, Z-Spread and OAS

Subtracting a spot rate from the YTM and calling it the G-spread.
Students mix up the spot curve with the benchmark yield.
Fix: G-spread and I-spread use yields to maturity of the benchmark. Z-spread is the only one of the four tied to spot rates.
Adding the option value to the Z-spread for a callable bond.
The sign rule is memorised without thinking about who owns the option.
Fix: The issuer owns the call, so investors demand extra yield in the Z-spread. Remove it: OAS = Z-spread − option value. For a putable bond the investor owns the option, so add it.
Forgetting to interpolate the benchmark yield.
Students use the nearest quoted maturity because it is faster.
Fix: If the bond's maturity falls between two benchmark points, use linear interpolation. Check how far the maturity lies between the two points.
Quoting the spread in percent when the options are in bps, or the reverse.
The YTMs are given as percentages, and the answer is expected in basis points.
Fix: Multiply the percentage difference by 100. A gap of 1.32% is 132 bps.
Believing the Z-spread is a different constant for each cash flow.
The Z-spread is added to each spot rate, so students assume it varies by date.
Fix: The spread Z is one constant. The spot rates differ by period, but you add the same Z to all of them.
Saying the Z-spread and OAS differ for an option-free bond.
Students memorise that they differ and forget the reason.
Fix: The only gap between them is the option value. With no option, the value is zero and the two are equal.

Worked examples

Example 1

A corporate bond with 4.5 years to maturity has a YTM of 5.62%. Government yields are 4.10% at 4 years and 4.50% at 5 years. Swap rates are 4.50% at 4 years and 4.74% at 5 years. What is the I-spread? (A) 0.88% (B) 1.00% (C) 1.32%

Show the solution

The bond matures in 4.5 years, which is halfway between 4 and 5 years. The swap rate must be interpolated.
Interpolated swap rate = 4.50% + 0.5 × (4.74% − 4.50%) = 4.50% + 0.12% = 4.62%.
I-spread = 5.62% − 4.62% = 1.00%, or 100 bps.
Check the traps. Interpolated government yield = 4.10% + 0.5 × 0.40% = 4.30%, so the G-spread is 5.62% − 4.30% = 1.32%. That is option C, which uses the wrong benchmark.
Option A comes from using the 5-year swap rate: 5.62% − 4.74% = 0.88%. That ignores interpolation.

Answer: B. The I-spread is 1.00% (100 bps).

Example 2

A 2-year annual-pay bond has a 5% coupon and a price of 100.96 per 100 par. The benchmark spot rates are 3.0% for year 1 and 3.5% for year 2. What is the Z-spread? (A) 0.60% (B) 1.00% (C) 1.40%

Show the solution

The Z-spread is the constant Z that makes PV = price, using PV = 5 ÷ (1 + 0.030 + Z) + 105 ÷ (1 + 0.035 + Z)².
Test the middle option, Z = 1.00%. The year 1 rate becomes 4.0% and the year 2 rate becomes 4.5%.
Year 1 PV = 5 ÷ 1.04 = 4.8077.
Year 2 PV = 105 ÷ 1.045². Here 1.045² = 1.092025, so PV = 96.1516.
Total PV = 4.8077 + 96.1516 = 100.9593, which rounds to 100.96. This matches the given price.
Cross-check the direction: a lower spread such as 0.60% would discount less and give a price above 100.96, and 1.40% would give a lower price. So only 1.00% fits.

Answer: B. The Z-spread is 1.00% (100 bps).

Exam tips

Read the benchmark in the question. Government means G-spread, swap means I-spread, spot curve means Z-spread, and an option-adjusted result means OAS.
If a bond is callable, expect the question to test that OAS is lower than the Z-spread. For a putable bond it is higher. Do not calculate when this logic alone picks the answer.
For interpolation questions, compute the weight first (for example, 0.5 or 0.25) and then apply it to the yield difference. Wrong options are often built from the endpoint yields.
Check units before you pick. Options are listed from smallest to largest, and the distractors often differ by a factor of 10 or by using the wrong benchmark.
You do not need to solve a Z-spread from scratch in most questions. Test the middle option and use direction (higher spread, lower price) to decide.

Practice questions from Yield and Yield Spread Measures for Fixed-Rate Bonds

Yield Spread Measures: G-Spread, I-Spread, Z-Spread and OAS in other exams

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

Yield Spread Measures: G-Spread, I-Spread, Z-Spread and OAS: frequently asked questions

What is the difference between Z-spread and OAS?

The Z-spread is the constant spread over the benchmark spot curve that reprices a bond's fixed cash flows. OAS is the Z-spread after removing the value of any embedded option. For an option-free bond they are equal.

Why is the OAS lower than the Z-spread for a callable bond?

The issuer holds the call option, so the bond must offer extra yield to compensate investors. The Z-spread includes that extra yield. Subtracting the option value leaves the compensation for credit and liquidity risk only.

How do I calculate the G-spread and I-spread?

Subtract the benchmark yield from the bond's YTM. For the G-spread, the benchmark is a government bond of the same maturity. For the I-spread, it is the swap rate of that maturity. Interpolate if the maturity is not quoted, and express the answer in basis points.

Why use the Z-spread instead of the G-spread?

The G-spread compares one yield with one yield. The Z-spread uses the whole spot curve, so it accounts for the shape of the term structure and the timing of each cash flow. This makes it a more accurate measure of the spread over the benchmark curve.