Level I · Fixed Income

Learning Module 7
Yield and Yield Spread Measures for Fixed-Rate Bonds

Key Outcomes Summary & Practice Problems

Learning Outcomes

What you must be able to do

Curriculum Year: 2026

LOS 1

Calculate annual yield on a bond for varying compounding periods in a year — periodicity conversions, effective annual rates, and the relationship between compounding frequency and stated yield.

LOS 2

Compare, calculate, and interpret yield and yield spread measures for fixed‑rate bonds — current yield, YTM, street convention, true yield, government equivalent yield, simple yield, yield‑to‑call, yield‑to‑worst, G‑spread, I‑spread, Z‑spread, and OAS.

1 · Periodicity and Annualized Yields

Periodicity (m): The number of compounding periods per year. Matches coupon frequency (e.g., semiannual = 2, quarterly = 4).
Effective annual rate (EAR): The actual annual return considering compounding. Periodicity = 1.
Periodicity conversion: (1 + APRm/m)m = (1 + APRn/n)n
Key rule: Compounding more frequently at a lower annual rate corresponds to compounding less frequently at a higher annual rate.
For zero‑coupon bonds, periodicity is arbitrary (no coupon payments to match).

PERIODICITY CONVERSION

(1 + APR_m/m)^m = (1 + APR_n/n)ⁿ
Example: 3.582% semiannual = 3.566% quarterly = 3.556% monthly

2 · Yield Measures and Conventions

Other Yield Measures

Current yield (CY): Annual coupon ÷ Flat price. Crude measure — ignores coupon reinvestment, time value, and capital gains/losses.
Street convention yield: YTM assuming payments are made on scheduled dates (ignores weekends/holidays). Most commonly used in practice.
True yield: YTM using actual payment dates (accounting for weekends/holidays). Always ≤ street convention yield due to delayed payments.
Government equivalent yield: Restates a 30/360 yield to actual/actual basis: YieldACT/ACT = (365/360) × Yield30/360
Simple yield: Sum of coupon payments + straight‑line amortized share of gain/loss, divided by flat price. Used mostly for Japanese government bonds (JGBs).

Convention	Description
Actual/Actual	Actual days in period/year. Used for government bonds.
30/360	Assumes 30‑day months, 360‑day year. Used for corporate bonds.
Street Convention	Does not account for weekends/holidays; assumes payments on scheduled dates.
True Yield	Accounts for weekends/holidays; uses actual payment dates. ≤ Street convention.
Government Equivalent Yield	Restates 30/360 yield to actual/actual basis for spread comparison.
Simple Yield	Coupon + straight‑line amortization ÷ flat price. Used for JGBs.

3 · Bonds with Embedded Options

Yield‑to‑call (YTC): IRR assuming the bond is called on a specific call date at the call price.
Yield‑to‑worst (YTW): The lowest of all yields‑to‑call and the yield‑to‑maturity. Provides the most conservative return estimate.
Option‑adjusted yield: The required market discount rate after adjusting the price for the value of the embedded option.
The value of the call option = Price of option‑free bond − Price of callable bond.

YIELD‑TO‑CALL

PV = Σ PMT/(1+r)ⁿ + Call Price/(1+r)ᴺ
where N = number of periods to the call date

4 · Yield Spread Measures

G‑Spread

Yield spread in basis points over an actual or interpolated government bond yield.

G‑spread = Bond YTM − Government benchmark YTM (same maturity)

I‑Spread

Yield spread over the standard swap rate in the same currency and tenor. Common for euro‑denominated corporate bonds.

I‑spread = Bond YTM − Swap rate (same tenor)

Z‑Spread (Zero‑Volatility Spread)

Constant spread added to each benchmark spot rate that makes the present value of cash flows equal the bond's price.

PV = Σ PMT/(1 + z_n + Z)ⁿ

OAS (Option‑Adjusted Spread)

Z‑spread adjusted for the value of an embedded call option. Option value (in bps) is subtracted from Z‑spread.

OAS = Z‑spread − Option value (bps)

Benchmark Rates and Spreads

Benchmark rate captures macroeconomic (top‑down) factors: expected inflation, economic growth, monetary/fiscal policy.
Yield spread captures microeconomic (bottom‑up) factors: credit risk, liquidity risk, tax status.
On‑the‑run government bonds: most recently issued; most liquid; trade at slightly lower yields than off‑the‑run.
Off‑the‑run government bonds: seasoned issues; less liquid; trade at slightly higher yields.

YIELD DECOMPOSITION

Bond YTM = Government benchmark yield + Credit spread + Liquidity spread + Tax adjustment
Credit spread ≈ POD × LGD (Expected loss)

5 · Quick Reference — Spread Summary

Spread	Benchmark	Use
G‑spread	Government bond yield	US, UK, Japan; most common
I‑spread	Interest rate swap rate	Euro‑denominated bonds
Z‑spread	Government spot curve	More precise, accounts for term structure
OAS	Government spot curve	Callable bonds; adjusts for option value