Compare yields and spreads on the same basis

Learning goals

• Explain compounding using mechanisms and limitations.
• Explain yield interpretation using mechanisms and limitations.
• Explain spread benchmarks using mechanisms and limitations.

Draft · approximately 35 minutes, excluding further revision.

Compounding

A nominal annual yield compounded m times converts to effective annual yield as (1+y/m)^m−1; quote the convention when comparing instruments.

Current yield is annual coupon divided by current price and excludes price convergence and coupon reinvestment; it is not total holding return.

Yield interpretation

YTM is the discount rate matching promised cash flows and price; realizing it as a compound return requires holding and reinvestment assumptions and actual payment.

A government spread compares the bond yield to a specified government benchmark; maturity and convention mismatches can distort interpretation.

Spread benchmarks

A constant spot-curve spread discounts each payment against its matching spot rate plus spread; it differs from subtracting a single benchmark yield.

An option-adjusted spread attempts to remove embedded-option effects through a model; comparisons depend on interest-rate volatility and model assumptions.

Yield-to-call and a two-date spot spread

Consider a one-year-to-call bond with price102, call redemption101 and one coupon5 payable at call. Yield-to-call=(101+5)/102−1=3.9216% for annual settlement. A quoted YTM may be higher, but investors do not control an issuer call. Yield-to-worst compares the relevant contractual scenarios rather than assuming final maturity will occur.

For a two-year bond paying5 then105, annual spot rates4% and5%, a constant spot spread1% gives price=5/1.05+105/1.06²=98.2115. This uses a separate base spot rate at each date. A scalar YTM spread to a single benchmark usually differs. If an option changes cash flows, a model-based OAS is a separate concept.

Formula and assumptions

EAR=(1+nominal yield/m)^m−1; current yield=annual coupon/price

Original applied case: Compare yields and spreads on the same basis

1. A nominal yield is 6% compounded semiannually.
2. Effective annual=(1+0.06/2)²−1=6.09%.
3. Comparing this directly with a 6% effective annual quote would confuse conventions.

Errors to catch

• Do not assume: Nominal and effective yields always coincide.
• Do not assume: Current yield includes every capital gain.
• Do not assume: YTM guarantees the realized compound return.

Original knowledge check

Answer every question before checking. Review explanations after submitting; retry starts a new attempt.

Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.

• Reference · www.cfainstitute.org
• Reference · www.investor.gov