You bought a 10-year Treasury bond paying 3% annually when it was issued. Market interest rates then rise to 5%. What happens to the market price of your bond if you try to sell it today?
AIt rises — your bond is backed by the government and pays reliable income, making it more desirable
BIt stays the same — your bond's coupon rate is fixed by contract and cannot change
CIt falls — new bonds now pay 5%, so buyers will only purchase your 3% bond at a discount large enough to make its effective yield competitive
DIt rises — higher interest rates signal a stronger economy, which increases bond demand
This is the core bond insight: price and yield move inversely. Your bond's 3% coupon is fixed, but new bonds pay 5%. A rational buyer will only purchase your bond at a price low enough that the fixed $30/year payment (on $1,000 face value) represents a 5% yield on what they actually pay — roughly $600. The bond itself hasn't changed; the discount compensates the buyer for receiving a below-market coupon. The opposite is also true: if rates fall to 1%, your 3% bond becomes a premium asset, and its price rises above face value.
Question 2 Multiple Choice
An investor needs their money back in 18 months. They are choosing between a 2-year Treasury bond and a 20-year Treasury bond. If interest rates unexpectedly rise by 2%, which position creates more risk for this investor?
AThe 2-year bond — short-term interest rates are more volatile than long-term rates
BThe 20-year bond — its much longer duration means its price will fall far more per percentage point of rate increase, creating a large potential loss if sold before maturity
CBoth are equally risky because both are backed by the U.S. government and guaranteed to repay face value
DNeither creates risk because Treasury bonds cannot lose value
Duration is the key. The 20-year bond's cash flows extend far into the future; discounting all those future payments at a higher rate dramatically reduces their present value — the bond price could fall 20–25% or more. The 2-year bond matures in 24 months, so there are few future cash flows to reprice, and the price drops only modestly. The investor who needs cash in 18 months and holds the 20-year bond must sell at a large loss if rates rise. Government guarantee matters for repayment at maturity — but if you sell before maturity, market price is what you receive.
Question 3 True / False
When market interest rates rise, bond prices rise because investors are receiving more income from their fixed coupon payments.
TTrue
FFalse
Answer: False
This reverses the relationship. When market rates rise, existing bond prices FALL. The coupon payment is fixed — it does not increase when rates rise. What changes is that new bonds entering the market offer higher coupon rates, making existing lower-coupon bonds less attractive. Their prices must fall until their yield (coupon divided by current price) matches the prevailing market rate. The investor's income from holding the bond to maturity is indeed fixed, but the bond's resale value drops immediately when rates rise.
Question 4 True / False
A bond purchased below its face value (at a discount) will return exactly the face value at maturity, regardless of the purchase price.
TTrue
FFalse
Answer: True
Yes — the bond contract specifies that the issuer will repay the face value (typically $1,000) at maturity, regardless of what the bondholder paid in the secondary market. If you buy a bond at $850 and hold it to maturity, you receive $1,000 — a $150 gain above what you paid, in addition to the coupon payments received along the way. This capital gain is part of the total return and is why discount bonds can offer attractive yields even with low coupon rates. The yield to maturity (YTM) calculation incorporates both the coupon payments and this price-to-face-value change.
Question 5 Short Answer
Why do long-term bonds fall in price more than short-term bonds when interest rates rise by the same amount?
Think about your answer, then reveal below.
Model answer: A long-term bond locks in its fixed coupon rate for many more years into the future. When interest rates rise, all those future cash flows — coupons and eventual principal repayment — must be discounted at the new, higher rate, which reduces their present value substantially. A short-term bond has few future cash flows to reprice: it matures soon, returning principal quickly, after which the investor can reinvest at the new higher rates. The longer the duration, the more sensitive the price to rate changes.
This is why duration is used as the measure of price sensitivity: it reflects the weighted average time until you receive your cash flows. A 30-year bond has a high duration because most of the value comes from distant future payments; a 6-month T-bill has near-zero duration because the entire value is received almost immediately. A 1% rise in rates causes roughly a 1% price drop for a bond with 1-year duration, but a ~15–20% price drop for a bond with 15–20-year duration. Matching bond duration to your investment time horizon is the core practical insight of bond investing.