You hold a bond paying a 4% annual coupon. Market interest rates rise from 4% to 7%. What happens to the market price of your bond?
AIt rises, because your bond now yields more relative to the new rate
BIt stays the same, since the coupon payment is contractually fixed
CIt falls, because new bonds offer higher rates, making your lower-coupon bond less attractive
DIt depends on whether the issuer is a government or corporation
This is the fundamental inverse relationship: when rates rise, existing bond prices fall. Your 4% bond now competes with new bonds paying 7%. No one will pay full price for your bond when they can get a better return elsewhere. The price of your bond must fall far enough that its yield (coupon ÷ discounted price) matches the 7% market rate. This price adjustment is not optional — it is an arithmetic identity that follows from present-value discounting.
Question 2 Multiple Choice
Bond A matures in 2 years. Bond B has identical coupon and face value but matures in 20 years. Interest rates rise by 1%. Which bond loses more market value?
ABond A, because shorter bonds are more sensitive to rate changes
BThey lose the same value since both have identical coupons
CBond B, because longer duration means greater price sensitivity to rate changes
DBond A, because shorter bonds have less income to offset the price loss
Duration — a bond's weighted-average time to receive cash flows — measures interest rate sensitivity. Bond B's 20-year maturity means its cash flows are spread far into the future, so small changes in the discount rate have a large compounding effect on their present value. A rough rule: a bond with duration of 20 years loses about 20% of its price for a 1% rate rise. Bond A's cash flows are received soon, so discounting them slightly more has a small effect. Longer maturity → higher duration → greater price risk.
Question 3 True / False
Government bonds (like U.S. Treasuries) are largely risk-free investments.
TTrue
FFalse
Answer: False
False — government bonds have minimal credit (default) risk, but they still carry interest rate risk. If you hold a Treasury bond and prevailing rates rise, the market value of your bond falls. You can lose money if you sell before maturity. Bond funds holding Treasuries lost substantial value in 2022 when the Federal Reserve raised rates sharply. 'Safe' in bond context means low default risk, not freedom from price fluctuation. Duration determines how much interest rate risk a bond carries regardless of issuer.
Question 4 True / False
When market interest rates fall, existing bond prices rise.
TTrue
FFalse
Answer: True
True — this is the same inverse relationship from the other direction. If market rates fall to 1% and your bond pays 4%, your bond pays far more than newly issued alternatives. Investors will pay a premium above face value to acquire your higher-coupon bond, driving its price up. Mathematically, the bond's fixed cash flows are now discounted at a lower rate, increasing their present value. The bond-rate inverse relationship is perfectly symmetric: rates up → prices down, rates down → prices up.
Question 5 Short Answer
Explain in your own words why bond prices and interest rates move in opposite directions.
Think about your answer, then reveal below.
Model answer: A bond is a promise to pay fixed future cash flows (coupons + face value at maturity). Its price is the present value of those cash flows. When interest rates rise, future cash flows are discounted more heavily, so their present value falls — the bond's price falls. Intuitively: if new bonds offer 6% and yours pays 3%, no one pays face value for yours. Its price drops until the effective yield (annual payment ÷ discounted price) matches 6%. The fixed cash flows don't change; only the rate at which they're valued does.
The inverse relationship is not a market quirk — it is a mathematical consequence of present-value discounting. Understanding it prevents the common mistake of thinking 'safe bonds' can't lose value. They can, if rates rise and you need to sell before maturity.