Set out what yield to maturity implicitly assumes
The idea
Yield to maturity is the single rate that equates a bond's price with the present value of its cash flows, and an investor realises it only if three conditions hold: the bond is held to maturity, the issuer makes every payment in full and on time, and every coupon is reinvested at the yield to maturity itself. The third is the one most often forgotten, and it is the least likely to be true. A bond bought at 6% whose coupons are reinvested at 2% delivers materially less than 6%, which is why yield to maturity is a promised rather than an expected return.
A practice question
Which assumption underlies yield to maturity?
- That coupons are reinvested at the yield to maturity — correct
- That the bond will be sold before maturityWhy not: The opposite — the measure assumes it is held to maturity, and selling early introduces price risk the yield does not describe.
- That interest rates will fallWhy not: It assumes a specific reinvestment rate rather than a direction. That rate is the yield itself, which may be above or below where rates go.
The measure is an internal rate of return, and every internal rate of return implies reinvestment at itself. That is the assumption doing the most work.
A harder one
An investor buys a bond yielding 6% but can only reinvest coupons at 2%. What is the realised return?
- Exactly 6%, since the yield is contractualWhy not: The coupons and principal are contractual; the yield is not. It is a calculation that assumes a reinvestment rate the market did not provide.
- Below 6%, because reinvestment income falls short of what the measure assumed — correct
- Above 6%, because lower rates raise the bond's priceWhy not: A higher price benefits a seller. A holder to maturity receives par regardless and feels only the reinvestment shortfall.
Part of the promised return comes from interest on interest. When that is earned at a lower rate, the total falls short.
The hardest tier
Rates rise sharply just after purchase. What are the two offsetting effects for a holder to maturity?
- The coupon rate rises while the principal fallsWhy not: Neither moves. A fixed-rate coupon and par redemption are contractual and unaffected by market rates.
- Credit risk rises while liquidity improvesWhy not: Nothing in a change of market rates speaks to the issuer's credit, and liquidity typically worsens rather than improves in a sharp move.
- A price fall against better reinvestment — correct
The price falls at once, while every remaining coupon is reinvested at the higher rate. The two work against each other over the life, which is why a horizon can be chosen at which they very nearly cancel.
In the app: 9 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
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