Work within the stated bond model
These questions use regular fixed cash flows and the yield convention specified in the prompt. Explain the mechanism before selecting an answer: distinguish a change in the required yield from a change in the coupon, and convert basis points to decimal yield.
Review the reasoning
After answering, compare your method with the explanation for each option. If you got the direction right but the magnitude wrong, check the yield units and the squared convexity term. If the result is on the wrong side of face value, check the coupon-versus-yield comparison.
Try the questions
A fixed-rate bond’s required yield rises while its promised cash flows stay unchanged. What happens to its price?
- A.
It rises because the investor now earns a higher yield.
- B.
It falls because the discounting is heavier.
- C.
It stays unchanged because the coupon rate is fixed.
Answer and explanation
Answer: B
A higher discount rate reduces the present value of the same positive future payments.
- A
This confuses the required return with an increase in the bond’s promised cash flows.
- B
This follows from discounting fixed positive payments at a higher rate.
- C
The coupon is fixed, but the rate used to value those coupons has changed.
What is the Macaulay duration of a five-year zero-coupon bond with one payment at maturity?
- A.
Five years.
- B.
Less than five years because the payment is discounted.
- C.
Zero because the bond pays no coupons.
Answer and explanation
Answer: A
All present-value weight belongs to the payment five years away.
- A
The weighted payment time is exactly maturity when there is only one payment.
- B
Discounting changes present value, but its single payment still has weight one.
- C
The principal repayment is a cash flow and arrives five years away.
Modified duration is 5, convexity is 40 and yield rises by 100 basis points. What is the two-term approximate price change?
- A.
−5.2%.
- B.
+4.8%.
- C.
−4.8%.
Answer and explanation
Answer: C
The duration term is −5%; the convexity correction is +0.2%; the total is −4.8%.
- A
Positive convexity adds a positive correction rather than an additional loss.
- B
The positive yield change gives a negative first-order price change.
- C
Use Δy = 0.01 and include one-half of convexity times the squared yield change.