You hold a corporate bond with a 6% coupon rate on a $1,000 face value. Market interest rates rise to 8%. What happens to the market price of your bond?
AIt rises — investors pay a premium because the 6% coupon is now above the market rate
BIt stays the same — the coupon rate is fixed at 6% regardless of market conditions
CIt falls — investors won't pay full price when new bonds offer 8% coupons
DIt rises — higher interest rates signal a stronger economy, which improves bond values
When market rates rise to 8%, newly issued bonds pay $80 per year on $1,000 face value. Your bond pays only $60 per year. Rational investors won't pay $1,000 for your bond when they can buy a new one yielding 8%. The price of your bond must fall until the $60 coupon represents an 8% return on the lower price — the bond becomes a 'discount bond.' This inverse relationship between bond prices and interest rates is mechanical: it follows directly from the present-value formula. This is the most important thing to internalize about bonds.
Question 2 Multiple Choice
A bond with a 5% coupon rate is currently trading at $920 (below its $1,000 face value). What can you conclude about its yield to maturity (YTM)?
AYTM is less than 5% — the discount reduces the effective return
BYTM equals 5% — the coupon rate defines the return regardless of price
CYTM is greater than 5% — buying below par increases the effective return
DYTM cannot be determined without knowing the maturity date
When a bond trades below par (a discount bond), its YTM exceeds its coupon rate. The buyer pays $920 for a bond that will return $1,000 at maturity — that $80 capital gain adds to the $50 annual coupon payment, so the total return exceeds 5%. The coupon rate is a fixed contractual feature set at issuance; YTM is the actual return earned by buying at today's market price and holding to maturity. Coupon rate = YTM only when the bond trades at exactly face value. The maturity date is needed for the precise YTM calculation, but the directional relationship (YTM > coupon rate when trading at a discount) holds as stated.
Question 3 True / False
US Treasury bonds are essentially risk-free because the US government can seldom default on dollar-denominated debt.
TTrue
FFalse
Answer: False
Treasury bonds have essentially no *default* risk in nominal terms — the government can always create dollars to repay. But they carry substantial *interest rate risk*: if market rates rise, the market value of existing Treasury bonds falls, potentially significantly. A 30-year Treasury bond is highly sensitive to rate changes; a 1% rise in rates can reduce its market value by 15–20%. For investors who may need to sell before maturity, this is very real risk. The common misconception is equating 'no default risk' with 'no risk' — two distinct things.
Question 4 True / False
A bond's coupon rate and its yield to maturity are both measures of the bond's return, so they will converge to the same value over time.
TTrue
FFalse
Answer: False
The coupon rate is a fixed contractual feature set at issuance — it never changes. The yield to maturity changes every day as the bond's market price changes. They are equal only when the bond trades at exactly face value (par). If the bond trades at a discount, YTM > coupon rate; at a premium, YTM < coupon rate. They do not 'converge' over time — if anything, as a bond approaches maturity its price gravitates toward face value (pulling price toward par), which in turn brings YTM toward the coupon rate, but this is a price-convergence effect, not an inherent feature of the two rates themselves.
Question 5 Short Answer
Explain in your own words why bond prices fall when market interest rates rise. What is the underlying logic, and why is this relationship described as 'mechanical'?
Think about your answer, then reveal below.
Model answer: A bond's price is the present value of all its future cash flows (coupons plus face value). When market interest rates rise, the discount rate used to calculate present value rises, so the present value of each future payment falls. Equivalently: new bonds now offer higher coupons, so existing bonds with lower fixed coupons must sell at a discount to offer the same total return. The relationship is 'mechanical' because it follows necessarily from the present-value formula — it's not a market sentiment effect but arithmetic.
The intuition: your bond is locked into paying $50/year when the market now demands $70/year for the same risk. The only way your bond can compete is if its purchase price drops enough that the $50 coupon plus the capital gain at maturity (buying at a discount, receiving face value) equals the market return. Present value math converts this intuition into a precise price. Every percentage-point rise in rates translates into a price drop whose magnitude depends on the bond's maturity and coupon — longer maturities are more sensitive because there are more future cash flows being discounted at the higher rate.