FOUNDATION 07 / Markets & risk
Bonds, yields & rate risk
Price promised cash flows and understand why coupon rate, yield and realized return differ.
By the end of this lesson
- Identify face value, coupon, maturity and yield.
- Price a plain annual-coupon bond.
- Explain price–yield sensitivity and missing risks.
IBBC Capital Finance Foundations · Original content drafted with AI assistance. IBBC Capital is responsible for editorial review and content. General education, not an official CFA Institute curriculum or credential.
A contractual sequence of cash flows
A plain fixed-rate bond promises coupons and repayment of face value at maturity. For annual coupons, coupon cash flow C = face value×coupon rate. A 1,000 face bond with a 5% coupon pays 50 a year, regardless of its current market price.
A promise is not a guarantee: credit risk can change cash flows. Real instruments may have embedded options, collateral, floating rates and special terms. Read the actual documentation before choosing a pricing model.
Discount coupons and principal
For a bond priced on a coupon date with n annual periods, P = Σ C/(1+y)^t + F/(1+y)^n. This exercise uses one yield y for every cash flow. A term-structure approach can use different spot rates for different dates.
The calculator excludes accrued interest and assumes no default, call or put feature, taxes or fees. Between coupon dates, settlement conventions and clean versus dirty prices matter; they are outside this first model.
Coupon is not yield
If yield equals coupon rate, this plain bond prices at par. If yield rises above the coupon rate, its price falls below par; if yield falls below the coupon rate, price rises above par. This relationship assumes the same promised cash flows.
Yield to maturity is an internal discount rate that matches price to promised cash flows. Realized return can differ because of default, reinvestment rates, sale timing, fees and taxes. Current yield, annual coupon divided by price, omits capital gains and losses.
Interest-rate sensitivity
Holding other bond features equal, longer maturity and lower coupon generally increase price sensitivity to yield changes. Modified duration approximates percentage price change as −duration×change in yield in decimal units. It is a local approximation, not an exact price formula.
Credit spread, liquidity, inflation and currency risk are separate sources of uncertainty. A low duration does not eliminate credit losses. Compare two bonds only after aligning currency, seniority and contractual terms.
A two-year annual-coupon bond
- Face 1,000; coupon 5%; yield 6%; annual coupon 50.
- Price = 50/1.06 + 1,050/1.06² = 981.67.
- At a 5% yield, the price is exactly 1,000. Higher required yield lowers the price.
Try before looking at the explanation
Change one input in the practice tool below. Predict the direction first, calculate second, then explain why it changed.
Work the numbers
Common mistakes to catch
- Discounting the final coupon but forgetting principal.
- Calling the coupon rate a guaranteed realized return.
- Entering a 1 percentage-point yield move as 1 instead of 0.01 in a duration formula.
Knowledge check · 6 original questions
Answer all six. At least five correct marks the lesson complete for self-study. You can retry; this is not a credential.
Keep these ideas
- A bond price is the present value of its modeled cash flows.
- Rate risk and credit risk are different.