Fixed-income desks talk in yields. A trader bids "at a yield of 4.89%" rather than quoting the full price; a portfolio manager compares bonds by their yield spread over Treasuries. Yet yield-to-maturity (YTM) is a compressed and imperfect summary of the discount-factor framework built in Lessons 1 and 2. Understanding what YTM does capture — and what it does not — determines when it is safe to use it as a shorthand and when it will mislead.
This note develops the price-yield formula, derives its qualitative implications (premium vs discount bonds, coupon-rate sensitivity), and then exposes three limitations: YTM is not a realised return unless coupons reinvest at exactly the YTM rate; YTM is not a relative-value measure because two bonds with the same maturity but different coupon rates can carry different yields even when priced fairly — this is the coupon effect; and YTM is approximately a holding-period return only when it remains unchanged.
Learning objectives. By the end of this note you should be able to:
- define YTM and solve the price-yield equation for either variable;
- state the closed-form price-yield formula and read off its qualitative implications (par, premium, discount);
- explain why YTM is not a reliable return measure and construct a counterexample with reinvestment risk;
- describe the coupon effect: why two bonds of equal maturity can have different YTMs even when priced fairly against the same spot curve;
- state the one valid YTM-as-return interpretation (instantaneous unchanged yield).
In this lesson
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- Yield-to-maturity defined
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- Closed-form price-yield formula
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- YTM is not a return measure
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- The coupon effect
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- YTM as a valid return measure: the one clean case
Before you start
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