Your client's "safe" bond portfolio just dropped 6.5% after a 1% rate increase. The answer is duration, and if you cannot calculate it, you are not ready for this exam.
A bond is worth the present value of all future cash flows: periodic coupon payments plus par value at maturity. When market yield equals the coupon rate, the bond trades at par. When yield exceeds the coupon, the bond trades at a discount. When yield falls below the coupon, the bond trades at a premium.
KEY: Bond prices and interest rates move in opposite directions. This is mathematical certainty from discounting, not market sentiment.
Current yield = annual coupon / market price. A $1,000 par bond with a 6% coupon ($60) trading at $950 has a current yield of 6.32%. Simple but incomplete, it ignores capital gain or loss at maturity.
Yield to maturity (YTM) is the discount rate that equates the present value of all remaining cash flows to the current price.
Common mistakes
- Using D0 instead of D1 in the DDM. Current dividend $3.00, growth 6%. D1 = $3.18. Using $3.00 gives $75.00 (trap answer). Correct: $3.18 / 0.04 = $79.50.
- Forgetting convexity is always positive for standard bonds. The yield change is squared, so the adjustment is positive regardless of rate direction. Convexity always benefits the bondholder.
- Confusing Macaulay and modified duration. The exam gives one and asks for the other. A trap answer uses Macaulay duration directly as sensitivity (7.2% decline when modified is actually 6.86%).
Bottom line
- Bond prices and interest rates always move inversely; this is mathematical, not opinion.
- Macaulay duration is the PV-weighted average time to a bond's cash flows: , with .
- Modified duration = Macaulay / (1 + y/k), where is the annual YTM and the coupon periods per year; with annual coupons this is Macaulay / (1 + YTM).
- For large rate moves add the convexity adjustment = 0.5 x convexity x (yield change) squared, always positive, so it always helps the holder.
Exam shortcut
Duration questions follow a pattern: convert Macaulay to modified (divide by 1 + yield), then multiply negative modified duration by the yield change in decimal form. If dollar impact is asked, multiply percentage by the bond/portfolio value. Practice this three-step sequence until it is automatic. Remember: "D1, Not D0. Grow Before You Go." Always multiply the current dividend by (1 + g) before plugging into the Gordon Growth Model.
The full lesson (about 2,755 words, 18 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.
Learning objectives
- D.32
Browse all free CFP lessons or jump into free CFP practice questions.