How Level I tests bond return sources, duration measures, convexity, and curve-based interest-rate risk.
Level I interest-rate-risk questions are usually not about reciting a definition. They are about knowing what a duration number is really summarizing and when that summary becomes too weak.
Candidates often memorize duration formulas but still miss the question because they cannot answer simpler conceptual prompts:
The stronger reader treats duration as an interpretation tool first and a formula second.
For a fixed-rate bond over a holding period, total return can reflect:
That is why realized holding period return can differ from yield to maturity. Yield to maturity assumes a specific reinvestment and holding pattern; realized return depends on what actually happens.
| Measure | What it tells you | Common Level I trap |
|---|---|---|
| Macaulay duration | Weighted-average time to receive the bond’s cash flows | Treating it as a direct percentage price sensitivity measure |
| Modified duration | Approximate percentage price change for a small change in yield | Forgetting the approximation works best for small parallel yield changes |
| Money duration | Dollar price sensitivity derived from modified duration and price | Mixing dollar change and percentage change |
| PVBP | Price value of a basis point, usually the price change for a 1 bp move | Forgetting it is a very small-yield-change measure |
| Effective duration | Sensitivity when cash flows can change because of embedded options | Using modified duration mechanically for callable or putable bonds |
| Key rate duration | Sensitivity to shifts at a specific maturity point on the curve | Treating all yield-curve moves as parallel |
The exam often becomes easier the moment you identify which duration concept the question actually wants.
For a small change in yield:
$$ \frac{\Delta P}{P} \approx -D_{mod} \Delta y $$
Adding convexity improves the approximation:
$$ \frac{\Delta P}{P} \approx -D_{mod} \Delta y + \frac{1}{2} \times \text{Convexity} \times (\Delta y)^2 $$
The reason convexity matters is simple: bond prices do not move in a perfectly straight line as yields change.
| Property | Typical effect on rate sensitivity | Why |
|---|---|---|
| Longer maturity | More sensitive | Cash flows arrive later, so discount-rate changes matter more |
| Lower coupon | More sensitive | More value is concentrated in the final payment |
| Lower yield level | More sensitive | Present values react more when discount rates start from a lower base |
| Embedded call option | Often lower upside and different effective sensitivity | Cash flows may shorten when rates fall |
These relationships are the quick filters Level I uses before or alongside calculations.
Level I introduces the idea that not all yield changes are parallel shifts. That is why:
You do not need Level II depth here. You do need to know why one summary measure can fail.
Two bonds have the same maturity and credit quality, but one is a zero-coupon bond and the other pays a high coupon. A weak answer says their interest-rate sensitivity should be similar because maturity matches. A stronger answer recognizes that the zero-coupon bond’s cash flows arrive later on average, so its duration is higher.
That is exactly how Level I separates surface reading from actual fixed-income understanding.
An analyst uses modified duration to compare the rate sensitivity of a non-callable bond and a callable bond. What is the strongest critique?
Best answer: Modified duration may be less appropriate for the callable bond because the expected cash flows can change when yields change, so an effective measure is usually better.
Why: Level I often tests whether you understand when the input cash flows are stable and when they are not.