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Financial Instruments, Markets and Conventions / Fixed Income: Bonds, Yields, and Interest Rate Risk

Yield to Maturity, Spot Rates, and the Term Structure

The price of a bond is straightforward: it is the present value of its cash flows. But what rate should be used to discount those cash flows? The yield to maturity (YTM) answers this with a single number — the internal rate of return that equates the present value of all cash flows to the current market price. It is the most widely quoted yield measure on Wall Street and the first number a salesperson gives you when you ask "what's the yield on this bond?"

The problem is that the YTM is, in a precise sense, wrong. It implicitly assumes that every coupon is reinvested at that same YTM — an assumption violated as soon as interest rates move. For a 30-year bond, more than half the promised total return may come from reinvesting coupons, and that reinvestment income is earned at whatever rates the market offers in the future, not at today's YTM. This reinvestment risk means the YTM overstates the actual return for high-coupon or long-maturity bonds.
The correct answer is the spot rate curve (zero curve): a schedule of discount rates, one for each maturity, extracted by bootstrapping from the prices of observed coupon bonds. The zero curve is the market's true term structure — and it is the input that makes the discount-factor framework correct.
Learning objectives. By the end of this note you should be able to:
  • define the yield to maturity and compute it for a semiannual coupon bond;
  • state the three limitations of YTM: reinvestment risk, horizon dependence, and the comparison problem;
  • describe the three potential sources of a bond's return and quantify their contribution;
  • construct the theoretical spot rate curve from par coupon yields using bootstrapping;
  • derive the forward rate between two maturities from the zero curve;
  • state the three term-structure theories (pure expectations, liquidity, preferred habitat / market segmentation) and explain what each implies for the slope of the yield curve.

In this lesson

  1. Conventional yield measures
  2. The three sources of bond return
  3. Why the yield curve is not enough: spot rates
  4. Bootstrapping the theoretical spot rate curve
  5. Term structure theories
  6. The par yield and its relation to zero rates

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