BOND MATH: The Theory Behind the Formulas

An Intuitive Forward Curve

Suppose that yields to maturity on 1-year, 2-year, and 3-year zero-coupon government bonds are 1.00%, 2.00%, and 2.50%, respectively. To preserve a bit of realism, these yields are quoted on a semiannual bond basis, meaning annual percentage rates for two periods per year. The periodicity assumption is totally arbitrary on zeros, but semiannual compounding is the norm in practice. We'll call these rates the “0 × 1,” “0 × 2,” and “0 × 3.” These bonds presumably trade in the cash market, so the first number is the starting date and the second is the ending date. The difference is the time frame, or “tenor,” of the bond. So, 2.50% is the 0 × 3 yield (usually said “zero by three”)—the yield on a 3-year zero-coupon bond ...