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CFA® Level I · Fixed Income · free lesson
Interest Rate Risk and Return
The yield-to-maturity is only a promise; what a bond investor actually earns depends on coupons, on the rates at which those coupons are reinvested, and on the price at which the bond is sold. This module breaks a bond's return into its sources, shows how a change in interest rates helps some investors and hurts others depending on their investment horizon, and introduces Macaulay duration as the horizon at which those effects offset.
What you will learn
1. Calculate and interpret the sources of return from investing in a fixed-rate bond, including coupons, reinvestment income and capital gains or losses, and calculate a horizon yield.
- Sources of return: coupons, reinvestment income on coupons, and capital gain or loss on sale.
- Horizon yield = (total accumulated value / purchase price)^(1/H) - 1.
- Horizon yield = YTM only if there is no default and coupons are reinvested at the YTM, with the bond held to maturity or sold at a price consistent with the original yield.
- Rising rates: more reinvestment income but lower prices; falling rates: the opposite.
- Measure capital gains and losses against carrying value (amortized cost at the original YTM).
2. Describe the relationships among a bond's investment horizon, its Macaulay duration and the investor's exposure to interest rate risk, including the duration gap.
- Macaulay duration is the horizon at which price risk and reinvestment risk roughly offset.
- Duration gap = Macaulay duration - investment horizon.
- Positive gap: exposed to rising rates (price risk). Negative gap: exposed to falling rates (reinvestment risk).
- A zero gap approximately immunizes against a one-time parallel rate change.
- Institutions with mismatched asset and liability durations face the same risks on their balance sheets.
3. Define, calculate and interpret Macaulay duration, and describe how it varies with coupon rate, maturity and yield.
- Macaulay duration = weighted average time to receipt of cash flows, weights = PV share of price.
- Compute in periods, then divide by periods per year to get years.
- Zero-coupon bond: Macaulay duration = maturity.
- Higher coupon or higher yield lowers duration; longer maturity generally raises it.
- Longer Macaulay duration means more price sensitivity and is the basis for modified duration.
Module at a glance
- Bond returns come from coupons, reinvestment income and capital gains or losses on sale.
- Horizon yield = (total accumulated value / purchase price)^(1/H) - 1; it equals the YTM only under the YTM assumptions.
- Rising rates raise reinvestment income but cut prices; the investor's horizon decides which matters more.
- Measure rate-driven capital gains and losses against carrying value, not purchase price.
- Duration gap = Macaulay duration - horizon: positive gap fears rising rates, negative gap fears falling rates.
- Macaulay duration = PV-weighted average time to cash flows; zero-coupon duration = maturity.
- Higher coupons and higher yields shorten duration; longer maturities lengthen it.
This free module has 3 lessons, 13 practice questions with full explanations.