the term structure of interest rates

Up to now we have pretended there is one interest rate for everything, but reality is richer. Lending money for one year and lending it for thirty years usually command different rates. The relationship between the length of an investment and the interest rate it earns is the term structure of interest rates, and when you plot rate against term you get the familiar yield curve.

Usually the curve slopes upward: longer commitments pay higher rates, partly to compensate lenders for tying up money longer and bearing more uncertainty. But the curve can be flat, or even invert (short rates above long rates), which historically has often preceded recessions. The shape is explained by competing theories — expectations of future rates, a liquidity or term premium for going long, and supply-and-demand in particular maturity segments — none of which is the whole story on its own. The point is that a single flat rate is a simplification; the real world has a different rate for each horizon.

For actuaries the term structure is not academic. Discounting a stream of future liabilities using a single flat rate can misstate their value when the curve is steep; modern valuation standards increasingly require discounting each cash flow at the rate appropriate to its own term. Pension and insurance liabilities, which stretch across many maturities, are especially sensitive to the curve's shape, and asset-liability management lives and dies by it. Treating the yield curve as a flat line is convenient but can quietly introduce material error.