Bond basics
Yield to maturity
Solve for the single discount rate that equates a bond's cash flows to its price — and quote it correctly.
Learning objectives
- Solve for yield to maturity with RATE and annualise it as a bond-equivalent yield
- Distinguish the bond-equivalent yield from the effective annual yield and the current yield
- Explain the inverse, convex relationship between price and yield
- State the assumptions built into YTM
Pricing runs from yield to price. In the market you usually see the price and need the yield: it is the one number that lets you compare bonds with different coupons and maturities. Yield to maturity (YTM) is the single discount rate that makes the present value of a bond's remaining cash flows equal to its price — the bond's internal rate of return.
There is no formula to rearrange; YTM is found by trial and error, which spreadsheets do with RATE (or IRR on a list of cash flows).
Price = Σₜ₌₁ᴺ (C ÷ f) ÷ (1 + r)ᵗ + 100 ÷ (1 + r)ᴺ → solve for r, the yield per period r = RATE(N, C ÷ f, −price, 100) YTM (bond-equivalent yield) = r × f Effective annual yield = (1 + r)^f − 1
- r
- yield per coupon period (per half-year for a semi-annual bond)
- Bond-equivalent yield
- the market convention for semi-annual bonds: the per-period yield × 2 (simple annualisation)
- Effective annual yield
- the same yield with half-year compounding made explicit; always slightly higher
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