A 10-year zero-coupon bond with face value $1,000 is priced at $614 when the yield is 5%. Market rates for 10-year instruments then rise to 7%. What happens to the bond's price?
AThe price rises above $614 because higher rates signal a stronger economy
BThe price stays at $614 because zero-coupon bonds have no coupon rate to change
CThe price falls below $614 because higher discount rates reduce the present value of the future payment
DThe price falls to $0 because the bond becomes worthless when market rates exceed its yield
P = FV/(1+y)^n. As y increases, the denominator grows, so P falls. At y = 7%, P = 1000/(1.07)^10 ≈ $508 — well below $614. Price and yield always move in opposite directions: the fixed future payment is worth less when discounted at a higher rate. Zero-coupon bonds are especially sensitive to rate changes (they have high duration) because all cash flow is concentrated at maturity with no intermediate coupons to partially offset the repricing.
Question 2 Multiple Choice
A zero-coupon bond with face value $1,000 matures in 3 years and currently trades at $864. What is its yield to maturity?
AApproximately 15.7%, calculated as (1000 − 864) / 864
BApproximately 5%, calculated as (1000/864)^(1/3) − 1
CApproximately 5%, calculated as (1000 − 864) / 1000
DCannot be determined without knowing the bond's coupon rate
Solving P = FV/(1+y)^n for y: y = (FV/P)^(1/n) − 1 = (1000/864)^(1/3) − 1 ≈ 0.050 = 5%. Option A computes a simple (uncompounded) return over three years, ignoring the time value of compounding. Option D is wrong because zero-coupon bonds have no coupon — the yield is entirely derived from the discount at which the bond trades. Yield to maturity is the implied compound annual return that equates today's price to the discounted face value.
Question 3 True / False
A zero-coupon bond with a positive yield always trades below its face value prior to maturity.
TTrue
FFalse
Answer: True
P = FV/(1+y)^n. If y > 0 and n > 0, then (1+y)^n > 1, so P < FV. The only exception is a negative yield (y < 0), which occurs in some markets when investors pay a premium for safety. At maturity (n = 0), (1+y)^0 = 1, so P = FV — the bond redeems at exactly face value. The investor's entire return is the difference between the purchase price and par, accruing as the bond approaches maturity.
Question 4 True / False
The yield to maturity on a zero-coupon bond is set by the issuer at issuance and does not change over the bond's lifetime.
TTrue
FFalse
Answer: False
Yield to maturity is derived from the bond's market price, not set by the issuer. The issuer determines the face value and maturity date; the market determines the trading price, and yield is whatever rate makes the discounted face value equal to that price. As market interest rates change, the bond's price adjusts to remain competitive, and the implied yield changes accordingly. Yields are prices in disguise — a more convenient way to express the relationship between today's price and the promised future payment.
Question 5 Short Answer
Why are zero-coupon bonds especially useful as building blocks for constructing the spot rate curve, compared to coupon bonds?
Think about your answer, then reveal below.
Model answer: Each zero-coupon bond has exactly one cash flow at a single maturity date. Its yield is therefore an unambiguous discount rate for that specific maturity — a 'pure' interest rate for that horizon. Coupon bonds have multiple cash flows at different dates, so their yield to maturity is a blend of rates across multiple maturities rather than a clean rate for any single point on the curve. Zero-coupon bonds provide direct, unambiguous readings of the price of money at each horizon without coupon reinvestment complications.
The spot rate curve represents the pure cost of money at each time horizon, free from reinvestment assumptions. Coupon bonds carry reinvestment risk — intermediate coupons must be reinvested at future rates that are unknown today. A zero-coupon bond eliminates this: one investment today, one payment at maturity. That simplicity makes them the natural instrument for building the term structure, which is why even when zero-coupon bonds don't directly exist for a maturity, analysts 'strip' coupon bonds to synthetically construct them.