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CFA Level I Exam · Credit Risk

Credit Spreads and Their Effect on Bond Price

Updated 7 October 2026 · Fact-checked

A credit spread is the extra yield a risky bond pays over a benchmark bond of similar maturity. When the spread changes, price moves opposite to it. Estimate the percentage price change as ≈ −(modified duration × Δspread) + ½ × convexity × (Δspread)². Duration alone gives the first-order estimate.

Understand Credit Spreads and Spread Measures

A credit spread is the extra yield investors demand for taking credit risk. You get it by subtracting the yield of a benchmark bond from the yield of a risky bond with similar maturity. The benchmark is usually a government bond. The spread pays you for default risk, loss severity, and often for lower liquidity.

A yield spread is the general term for any yield difference between two bonds. The G-spread is the bond's yield minus the interpolated government bond yield at the same maturity. The I-spread is the bond's yield minus the swap rate at the same maturity. The Z-spread is the constant amount added to each spot rate on the benchmark spot curve, usually the government curve, so that the discounted cash flows equal the bond's price. Z-spread uses the whole curve, so it is more precise than a single-point spread when the curve is steep.

Bond price and yield move in opposite directions. If the benchmark yield is unchanged and the spread widens, the bond's yield rises and its price falls. If the spread narrows, the price rises. Spread changes come from rating downgrades (credit migration), weaker economic conditions, and falling liquidity.

To measure the effect, use spread duration, which is the price sensitivity to a change in spread. For an option-free fixed-rate bond, spread duration is approximately equal to modified duration. When the bond has embedded options, use effective duration or an OAS-based duration instead. For a first estimate, ignore convexity. Add the convexity term when the spread change is large and the question gives you convexity.

Credit migration matters because a bond rated lower than before trades at a higher spread. A downgrade makes the bond's spread widen, and the price drops. An upgrade does the opposite. The price impact is the same duration calculation applied to the new spread.

Key formulas to remember

Credit spread
Credit spread = Yield on risky bond − Yield on benchmark bond of similar maturity
Quoted in basis points. 1 bp = 0.01%.
Price change using duration only
%ΔPrice ≈ −ModDur × ΔSpread
Use ΔSpread as a decimal (50 bps = 0.0050). Assumes benchmark yield is unchanged.
Price change with convexity
%ΔPrice ≈ −ModDur × ΔSpread + ½ × Convexity × (ΔSpread)²
The convexity term is always positive, so it reduces the loss when spreads widen and adds to the gain when they narrow.
Return impact of a spread change
Return ≈ Yield income (carry) − ModDur × ΔSpread + ½ × Convexity × (ΔSpread)²
For a one-year horizon, carry is roughly the yield. Add benchmark-yield effects if given.
G-spread
G-spread = Bond YTM − Interpolated government YTM at same maturity
Uses a single point on the government curve.
Z-spread
Price = Σ CFt ÷ (1 + zt + Z)^t
zt are the spot rates on the benchmark spot curve, usually the government curve. Z is the same constant added to every spot rate.

How to solve Credit Spreads and Spread Measures questions

Use this method for any question on spreads and their price effect.

  1. 1Identify what is given: the old and new spread, or the old and new yields of the risky bond and the benchmark.
  2. 2Compute ΔSpread = new spread − old spread. A positive value is widening. Convert basis points to decimals.
  3. 3Check whether the benchmark yield also changed. If it did, the price effect has a benchmark part and a spread part.
  4. 4Pick the duration: modified duration, or effective duration if the bond has embedded options.
  5. 5Apply %ΔPrice ≈ −Duration × ΔSpread. Add ½ × Convexity × (ΔSpread)² if convexity is given.
  6. 6Convert the percentage to a currency change if asked: multiply by the starting price.
  7. 7Check the sign. Widening must give a price fall. Narrowing must give a price rise.
  8. 8If the question asks for total return, add the carry (yield income) over the holding period.

Quickest way: Duration shortcut for spread changes

When to use it: Use it when the question gives modified duration and a spread change in basis points, with no convexity.

  1. Take the spread change in bps and multiply by duration.
  2. Divide by 100 to get a percentage. Example: 4.5 × 80 bps = 360, which is 3.60%.
  3. Put a minus sign if the spread widened, plus if it narrowed.
  4. If convexity is given, add ½ × convexity × (Δspread)² with the spread in decimals.
  5. Pick the option with the right sign and size. The two wrong options usually have the wrong sign or a missing ÷100.

Common mistakes in Credit Spreads and Spread Measures

  • Getting the sign wrong: showing a price rise when the spread widens.

    Students focus on the word 'widening' as something bigger and forget it means higher yield.

    Fix: Wider spread means higher yield means lower price. Write the minus sign first.

  • Using basis points as whole numbers, for example 4.5 × 80 = 360%.

    The units are not converted.

    Fix: Convert bps to decimals (80 bps = 0.0080) or divide the product by 100 to get a percentage.

  • Forgetting that the convexity term uses the spread change squared and ½.

    Students remember convexity but not the exact form.

    Fix: Write ½ × Convexity × (Δ)² every time. Squaring a decimal makes it very small, so check that your answer is small.

  • Mixing up G-spread, I-spread and Z-spread.

    All three are called yield spreads and look alike.

    Fix: G uses government yields at one maturity. I uses swap rates at one maturity. Z is a constant added to the whole spot curve.

  • Applying spread change to the price but ignoring a change in the benchmark yield.

    Questions often change only the spread, so students assume benchmark never moves.

    Fix: Read the stem. If the benchmark yield changes too, apply duration to the total yield change, or to each part.

  • Ignoring carry when asked for the return over a period.

    Students stop after the price change.

    Fix: Return = income earned + price effect. Add the yield over the horizon when the question asks for return.

Worked examples

Example 1

A corporate bond has a modified duration of 6.0. Its credit spread widens from 150 bps to 210 bps. The benchmark yield is unchanged. Estimate the percentage price change using duration only. Options: (A) −3.60%, (B) −0.36%, (C) +3.60%.

Show the solution
  1. ΔSpread = 210 − 150 = +60 bps = +0.0060.
  2. %ΔPrice ≈ −6.0 × 0.0060 = −0.036.
  3. Convert to percent: −3.60%.
  4. Check the sign: widening gives a price fall, so C is out. B comes from dividing by 100 twice, that is, treating 60 bps as 0.00060. That makes the result 10 times too small.

Answer: (A) −3.60%

Example 2

A €1,000 face value bond trades at €1,000. Modified duration is 5.0 and convexity is 40. The credit spread narrows by 100 bps with no change in the benchmark yield. Estimate the new price. Options: (A) €1,020.00, (B) €1,050.00, (C) €1,052.00.

Show the solution
  1. ΔSpread = −100 bps = −0.0100.
  2. Duration effect = −5.0 × (−0.0100) = +0.0500 = +5.00%.
  3. Convexity effect = ½ × 40 × (0.0100)² = 20 × 0.0001 = 0.0020 = +0.20%.
  4. Total %ΔPrice ≈ 5.00% + 0.20% = 5.20%.
  5. New price = €1,000 × 1.0520 = €1,052.00. Option B is the duration-only value, so it leaves out the convexity gain.

Answer: (C) €1,052.00

Exam tips

  • Exam items give spread changes in basis points. Convert them before multiplying.
  • Check the sign first. It removes at least one option in many items.
  • Know which spread is which: G-spread uses government yields, I-spread uses swap rates, Z-spread uses the whole spot curve.
  • If a bond has embedded options, the question will give effective duration. Use it as the duration.
  • Read whether the question asks for price change, new price, or total return. Each needs a different last step.

Practice questions from Credit Risk

Credit Spreads and Spread Measures in other exams

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

Credit Spreads and Spread Measures: frequently asked questions

How do you calculate the price impact of a credit spread change?

Multiply modified duration by the change in spread (in decimals) and put a minus sign in front. This gives the approximate percentage price change. For larger moves, add ½ × convexity × (Δspread)².

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

G-spread is the bond yield minus a government yield at the same maturity. I-spread is the bond yield minus the swap rate at the same maturity. Z-spread is a constant added to each government spot rate so the discounted cash flows equal the price.

Why does a wider credit spread lower a bond's price?

A wider spread raises the bond's required yield. Cash flows are discounted at a higher rate, so their present value, which is the price, falls.

What is credit migration?

Credit migration is the change in a bond's credit rating over time. A downgrade usually widens the spread and lowers the price. An upgrade usually narrows the spread and raises the price.