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CFA Level I · CFA Level I Exam

Yield and Yield Spread Measures for Fixed-Rate Bonds

Yield measures express a bond's return as one annualised rate. Yield to maturity is the discount rate that equates the price to promised cash flows. Yield spreads compare a bond's yield or spot curve with a benchmark. To solve questions, identify the measure, match the compounding, then calculate or compare.

What this chapter covers

This chapter shows how to turn a bond's price and cash flows into a single annualised rate, and how to judge that rate against a benchmark. You start with current yield and yield to maturity. You then move to yield to call and yield to worst for callable bonds, yield conventions for floating-rate notes and money market instruments, spot and forward rates, and finally the spread measures: G-spread, I-spread, Z-spread and option-adjusted spread (OAS).

The common thread is discounting. Every yield is a discount rate, and every spread is a gap between two discount rates or curves. If you are solid on time value of money from Quantitative Methods, most of the chapter is a matter of applying it carefully and watching the compounding frequency.

This chapter sits inside Fixed Income and links forward to bond pricing, duration and convexity, credit analysis and bonds with embedded options. It also feeds Derivatives (forward rates and no-arbitrage pricing) and Portfolio Construction. Weak yield skills make those later chapters harder.

Fixed Income carries 11-14% of the 2027 Level I curriculum, and yield and spread questions appear across it in standalone three-option MCQs. Many questions are short calculations you can finish in the 90 seconds suggested per question, and many others are conceptual comparisons where a clear rule lets you eliminate two options fast. Since there is no penalty for wrong answers and no minimum score per topic, secure marks here are worth the effort, and the concepts also support later fixed income and derivatives chapters.

Yield and Yield Spread Measures for Fixed-Rate Bonds: topics in the order to study them

  1. 1Bond Yield Measures: Current Yield and YTMEverything else builds on yield as a discount rate, so learn the basic definitions, the annualisation and the calculator keystrokes first.
  2. 2Yield to Call, Yield to Worst and Callable BondsThese reuse the YTM calculation with a different date and price, so they come easily once YTM is secure.
  3. 3Yield Measures for Floating-Rate Notes and Money Market InstrumentsDifferent conventions apply here, such as quoted margin, discount margin and add-on or discount rates, so learn them after the fixed-rate logic is clear.
  4. 4Spot Rates, Forward Rates and the Yield CurveYou need spot rates and the curve before you can understand spreads that are measured against the whole curve.
  5. 5Yield Spread Measures: G-Spread, I-Spread, Z-Spread and OASThis is the capstone: it combines YTM, benchmarks and spot curves, and OAS also needs your understanding of embedded options.

How to prepare Yield and Yield Spread Measures for Fixed-Rate Bonds

Aim for fluent calculation first, then concepts and comparisons. Work in short sessions that suit a phone and a working day.

  1. Set up your TI BA II Plus or HP 12C early. Practise N, I/Y, PV, PMT, FV with semiannual periods until YTM keystrokes are automatic, and remember that the annual yield is the periodic rate multiplied by the number of periods per year. Doubling applies to semiannual bonds only.
  2. Write the definition of each yield in one line, including what cash flows it assumes and what it ignores. Current yield, for instance, ignores capital gain or loss and the time value of money.
  3. Practise yield to call and yield to worst by computing every possible call date and the maturity, then taking the lowest yield. Do not guess which date is worst.
  4. Draw the yield curve and sketch spot and forward rates. Practise bootstrapping a spot rate from par yields and computing a forward rate from two spot rates using (1 + z_B)^B = (1 + z_A)^A × (1 + IFR)^(B - A).
  5. Make a comparison table on paper for G-spread, I-spread, Z-spread and OAS: benchmark used, single rate or whole curve, and whether the option is included. Then drill the relationship between Z-spread, OAS and option cost.
  6. Finish with timed sets of standalone MCQs, 90 seconds each. After each miss, note whether the error was compounding, date choice or concept, and revise that pattern.

Common mistakes in Yield and Yield Spread Measures for Fixed-Rate Bonds

  • Forgetting to adjust N and the rate for semiannual coupons.

    Fix: Multiply years by the number of periods per year, divide the annual rate by the same number, and at the end multiply the periodic yield back up.

  • Using yield to maturity for a callable bond that trades above its call price.

    Fix: Compute yield to each call date and to maturity, and report the lowest as yield to worst. A premium callable bond often has a lower yield to call.

  • Confusing the benchmark in G-spread and I-spread.

    Fix: Link G to government yields and I to swap rates. Each compares the bond's yield with a single interpolated point on the government or swap curve, unlike the Z-spread, which uses the whole benchmark spot curve.

  • Treating Z-spread and OAS as the same measure.

    Fix: Remember that Z-spread ignores embedded options, while OAS removes the option value: Z-spread = OAS + option cost. For a callable bond OAS is below the Z-spread; for a putable bond OAS is above it.

  • Mixing up forward rates with spot rates or using the wrong time periods.

    Fix: Write the formula with explicit periods and check that the total time on each side matches before solving.

  • Applying the wrong rate convention to money market instruments.

    Fix: Note whether the quoted rate is on face value or on price, and what day-count basis applies, before converting to a comparable yield.

Last-day revision: Yield and Yield Spread Measures for Fixed-Rate Bonds

  • Current yield = annual coupon ÷ price. It ignores capital gains and reinvestment.
  • YTM is the discount rate that equates price to promised cash flows; it assumes the bond is held to maturity and coupons are reinvested at the YTM.
  • The annualised YTM is the periodic rate × the number of periods per year. For a semiannual bond this means periodic rate × 2, which gives the bond-equivalent yield. Do not double for other frequencies.
  • Price below par means YTM above the coupon rate, and price above par means YTM below the coupon rate.
  • Yield to worst is the lowest of the yields to each call date and to maturity.
  • A callable bond's required yield or coupon is typically higher than that of an otherwise identical non-callable bond, to compensate the investor for call risk.
  • Floating-rate notes use a quoted margin and discount margin; the discount margin is the spread that makes the FRN price equal to its cash flows.
  • Spot rates discount single cash flows. Forward rates are implied by spot rates through no-arbitrage.
  • G-spread is the bond's yield minus the government yield at the same maturity (interpolated if needed); I-spread is the yield minus the swap fixed rate at the same maturity (interpolated if needed). Each is measured against a single point on the government or swap curve.
  • Z-spread is the constant spread added to every spot rate on the whole benchmark spot curve so that the discounted cash flows equal the price.
  • Z-spread = OAS + option cost (in spread terms). For a callable bond OAS is lower than the Z-spread; for a putable bond OAS is higher than the Z-spread.

Yield and Yield Spread Measures for Fixed-Rate Bonds practice questions

Yield and Yield Spread Measures for Fixed-Rate Bonds in other exams

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

Yield and Yield Spread Measures for Fixed-Rate Bonds: frequently asked questions

What is the difference between current yield and yield to maturity?

Current yield is the annual coupon divided by the price, so it captures only income. Yield to maturity is the discount rate that equates the price to all promised cash flows, so it includes coupons, the redemption value and the time value of money.

Why is yield to worst important for callable bonds?

The issuer may call the bond when it is favourable to them, so the investor's realistic minimum return is the lowest yield across all call dates and maturity. Yield to worst gives that conservative figure.

What is the difference between Z-spread and OAS?

The Z-spread is the constant spread added to each spot rate to match the bond's price, and it ignores embedded options. OAS adjusts the Z-spread for the option, so it shows the spread for credit and liquidity risk alone.

Do I need the calculator for this chapter?

Yes, for YTM, yield to call and some price questions. The TI BA II Plus or HP 12C is approved, and practising the keystrokes saves time under the 90-second guideline per question.