CFA L1 / FI / M10. Rate Risk
Module 10 · Fixed Income

Interest Rate Risk and Return

EN: Sources of bond returns and the price-reinvestment trade-off.
VN: Nguồn sinh lời trái phiếu và cân bằng giá–tái đầu tư.

1. Three Sources of Bond Return Core

  • 1. Coupon Periodic interest payments.
  • 2. Reinvestment Interest earned on reinvested coupons (depends on future rates).
  • 3. Capital G/L Gain or loss on sale before maturity (or amortization to par if held to maturity).

2. Annualized Holding Period Return Core

\[ HPR_{annual} = \left(\frac{\text{Total ending value}}{\text{Initial price}}\right)^{1/N} - 1 \]
Practice problem

5-year zero bond bought at $747, sold at maturity for $1,000. Compute annualized HPR.

Show solution
\((1000/747)^{1/5} - 1\)
= (1.339)^0.2 − 1
≈ 6.00%

3. Price Risk vs Reinvestment Risk Core

Trade-off when rates change

  • Rates ↑ Price ↓ (price risk), reinvestment income ↑ (reinvestment benefit).
  • Rates ↓ Price ↑ (capital gain), reinvestment income ↓ (reinvestment risk).
  • Macaulay duration Investment horizon at which price risk and reinvestment risk approximately offset → "immunization" point.

Practice problem Practice

Practice problem

An investor has a 5-year horizon and buys a bond with Macaulay duration of 7 years. If rates rise immediately, what dominates?

Show solution
Investor horizon < bond duration → price risk dominates.
Capital loss > reinvestment gain over the holding period.
If horizon = duration, the two roughly offset (immunization).
Price risk dominates — investor likely realizes a net loss.