Which of the following statements is FALSE?[Fill in the blank]

Question

BlackTom AI · Accepted Answer

Zero-coupon bond pricing has a closed-form solution for yield: P0 = F / (1 + y)^n, so y can be solved directly. Start with the zero-coupon pricing formula and isolate y:

1) Relevant concepts:
- Coupon payment = coupon rate × face value.
- Yield to maturity (YTM) is the IRR that equates bond price to discounted future cash flows.
- For zero-coupon bonds there is a single cash flow at maturity; for coupon bonds there are multiple cash flows.
- Closed-form vs. numerical solution: when cash flows lead to a simple algebraic equation you can solve for y explicitly; otherwise you may need numerical methods.

2) Step-by-step reasoning and algebra (intermediate steps shown):
Price equation for a zero-coupon bond:
P0 = F / (1 + y)^n
Invert both sides:
(1 + y)^n = F / P0
Take the n-th root:
1 + y = (F / P0)^(1/n)
Solve for y:
y = (F / P0)^(1/n) − 1

This is an explicit formula for the yield of a zero-coupon bond; no iterative IRR search is required.

3) Why option D is FALSE:
Option D states there is no simple formula for YTM for zero-coupon bonds. That contradicts the derived explicit formula above. Therefore D is false.

4) Why the other options are correct:
A: True — each coupon payment equals coupon rate × face value.  
B: True in context — price and yield are invertible, so markets often reference either (though they are not numerically identical, they convey equivalent information).  
C: True — yield is a percentage return and does not depend on the face value scaling (face value cancels in yield calculation).  
E: True — the IRR of a bond investment is called the yield to maturity.

Conclusion: Option D is the false statement, which matches the provided answer.

Which of the following statements is FALSE?[Fill in the blank]单项选择题

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