Inflation-Indexed Bonds and Real vs. Nominal Rates

Real vs. Nominal Rates

The nominal interest rate i is the rate quoted in the market. The real interest rate r adjusts for inflation: (1 + r) = (1 + i) / (1 + pi), where pi is the inflation rate. For small rates, r is approximately equal to i - pi. Real rates measure the increase in purchasing power, while nominal rates measure the increase in dollar amount.

On Exam FM, you may need to convert between real and nominal cash flows. A nominal cash flow of C at time t has a real value of C / (1 + pi)^t. To find the present value in real terms, discount real cash flows at the real rate, or equivalently, discount nominal cash flows at the nominal rate.

Inflation-Indexed Bonds

Inflation-indexed bonds (like TIPS in the U.S.) adjust their principal and coupon payments for inflation. If the face value is F and cumulative inflation from issue to time t is I_t, the adjusted principal is F * I_t and the coupon is r * F * I_t, where r is the real coupon rate. The real return on these bonds is approximately the real coupon rate, regardless of actual inflation.

The price of an inflation-indexed bond in real terms is computed using real interest rates: P_real = r * F * a-angle-n(real rate) + F * v^n(real rate).

Exam FM Applications

Exam FM problems may ask you to compare the returns on nominal bonds and inflation-indexed bonds under various inflation scenarios. They may also test the Fisher equation and the calculation of real rates from nominal rates and inflation. A key insight: inflation-indexed bonds eliminate inflation risk but not real interest rate risk. Their duration and convexity should be computed using real rates.