Which yield shock and bond features does the price approximation assume? This original fictional exercise focuses on explaining a bond-price approximation and its assumptions. The task is to build a bond sensitivity and unit-convention worksheet, not copy a confident conclusion. It is not a live recommendation, client record or employer assessment.
The inputs and the question
Fixed-income preparation should distinguish a price approximation from a realized bond return. This guide uses stated modified duration and convexity for an option-free example. It does not quote an actual bond or recommend a trade.
| Supplied item | Fictional input |
|---|---|
| Modified duration | 5 |
| Convexity under the stated convention | 60 |
| Yield increase | 100 basis points, or 0.01 |
| Other changes | Ignored in this exercise |
Use the supplied inputs together. When dates, units or definitions are not given, identify the gap rather than silently filling it with a convenient assumption. An actual assignment may require more detail than this deliberately limited case.
Work through the base case
Approximate percentage price change is −5 × 0.01 + 0.5 × 60 × 0.01² = −0.047, or −4.7%. Duration alone gives −5%; the stated convexity term adds 0.3 percentage points.
Units and the yield convention must match the supplied sensitivities. The approximation omits carry, roll, spread changes and any cash distributions. Embedded options can require a different treatment.
The arithmetic or evidence check is only one part of the answer. Explain the definition that makes it valid and what remains outside the exercise. Do not convert a result from this case into a claim about a real company, market or client.
Change the assumption and follow the consequence
For a 30 basis point increase, the same approximation is −5 × 0.003 + 0.5 × 60 × 0.003² = −1.473%. Do not input 30 as if it were a decimal yield change.
Keep the unchanged inputs visible. State whether the change is an observed fact or a scenario you introduced. If the information needed to calculate a fuller result is missing, say what you would request instead of manufacturing precision.
The interpretation to avoid
Confusing basis points with percent, calling the price estimate total return or applying option-free sensitivities to every instrument overstates the result.
A useful response names the limitation without abandoning the task. Show the part you can establish, then explain the condition or document needed for the next conclusion. Being explicit about that boundary is different from refusing to reason about the case.
Build the evidence artifact
Prepare a sensitivity calculation, unit check and limitations note. Explain which additional risks and instrument features require analysis.
Answer these questions before presenting it:
- Are duration, convexity and the shock defined under matching yield conventions?
- Does the instrument contain embedded options?
- Which spread, currency, liquidity and cash-flow effects are omitted?
For your own practice, write the supplied facts, your method, the base result, the changed assumption and one unresolved question on a single page. Label professional work, public-data projects and fictional exercises accurately. Remove confidential data and do not use the example to imply a decision you did not own.
What to use next
Use the fixed income analyst preparation guide to connect the exercise to a readiness and next-resource decision. Compare the adjacent preparation task if your gap is different. The primary-source background supplies concept or role context; the facts and worked exercise above are original and fictional.
This free preparation resource does not provide a fixed-income recommendation or pricing service. Inspect scope before choosing support. A readable and reproducible explanation is the immediate objective; this case does not promise an interview, qualification, investment result or a particular search ranking.