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Yield to Maturity (YTM)

The annualized return if you hold the bond to maturity, assuming all coupons are reinvested at the same rate.

Yield to maturity (YTM) is the bond's internal rate of return — the single discount rate that makes the present value of all future cash flows (coupons and principal) equal the bond's dirty price. Think of it as the bond's 'all-in' yield, but with an important catch: YTM assumes you can reinvest every coupon payment at the same YTM rate, which rarely happens in practice. Because YTM appears inside the discounting formula, there's no closed-form solution — it's solved numerically using methods like Newton-Raphson or bisection, similar to IRR calculations in Excel. Despite its limitations, YTM is the industry standard for comparing bonds because it captures both income and capital gains/losses in a single number.

Formula
Pdirty=∑t=1nCFt(1+ym)tP_{\text{dirty}} = \sum_{t=1}^{n} \frac{CF_t}{\left(1 + \frac{y}{m}\right)^{t}}
Where
PdirtyP_{\text{dirty}}=Dirty (full) price
CFtCF_t=Cash flow at period t
yy=Yield to maturity
mm=Coupon periods per year
nn=Total number of periods
Assumptions
  • Initial bracket: -5% to +50% yield
  • Bracket expands (doubles upper bound) up to 8 times if needed
  • Maximum 80 iterations for convergence
  • Tolerance: 10^-10 price error
vs. Industry Tools
Excel YIELD() — Uses Newton-Raphson; may differ at edge cases
Bloomberg YLD — Generally matches for standard bonds
Related Terms

Dirty Price

The total settlement price paid for a bond, including accrued interest.

Modified Duration

Measures the percentage price change for a 1% yield change.

Convexity

Measures the curvature of the price-yield relationship — how duration itself changes.

DV01

Dollar change in value for a 1 basis point (0.01%) yield move.

Current Yield

Annual coupon income divided by the bond's clean price.

Running Yield

Annual coupon income divided by the bond's dirty price (clean price plus accrued interest).