3.2 Applying Duration to Interest Rate Scenarios
Key Takeaways
- Apply % price change ≈ −modified duration × Δyield with careful sign handling: rising yields cut prices; falling yields raise prices.
- For the same yield shock, the higher-duration instrument or fund sleeve experiences the larger percentage price move.
- Money market UITFs (short WAPL) should show milder rate-driven NAVPU swings than intermediate or long bond UITFs—still without guaranteeing principal.
- Common exam traps include treating duration as maturity alone, forgetting the minus sign, and mis-converting basis points into decimal yield change.
- Use duration language in sales to compare rate risk across UITF types, always pairing it with full risk disclosures (not deposits, not PDIC-insured).
From Definition to Decision: Using Duration in Rate Scenarios
Section 3.1 defined Macaulay and modified duration. This section forces the tools to work under exam-style interest-rate scenarios—exactly the setting where UCP candidates lose easy points by missing a sign, confusing duration with maturity, or overstating money market safety.
You will practice four applications repeatedly:
- Estimating percentage and PHP price changes for a single bond.
- Ranking two or more bonds (or fund sleeves) by rate sensitivity.
- Mapping duration thinking onto UITF product comparisons (money market vs fixed income).
- Spotting traps in wording that look technical but test basic logic.
Scenario Framework: Parallel Yield Shifts
Most introductory exam items assume a parallel yield shift: the bond's yield to maturity rises or falls by a stated number of basis points, and you apply the first-order duration estimate. Real markets can twist (short rates move differently from long rates), but UCP-level problems almost always stay with a single Δyield applied to modified duration.
Checklist before every calculation:
- Identify modified duration (not Macaulay, unless the item gives MacDur and the periodic yield so you can convert).
- Convert the shock: 100 bps = 0.01, 25 bps = 0.0025, 1% = 0.01.
- Write %ΔP ≈ −ModDur × Δy and keep the minus sign.
- Multiply the % change by the starting PHP price if the question asks for a new price level.
- State the economic story in one sentence ("rates up, bond prices down") to catch sign errors.
Worked Scenario A: Single Peso Bond, Rates Rise
Facts: A listed peso corporate bond used as an illustration for a fixed-income UITF holding is priced at PHP 102.00. Modified duration is 6.5. Market yields on comparable bonds rise by 40 basis points after a hawkish BSP policy communication.
Step 1 — convert the shock: 40 bps = 0.004.
Step 2 — percentage change: %ΔP ≈ −6.5 × 0.004 = −2.6%.
Step 3 — new approximate price: 102.00 × (1 − 0.026) = PHP 99.35 (approximately).
Sales translation (accurate, not promotional): The bond's estimated mark-to-market value declines about 2.6% for a 40 bp parallel yield increase. In a UITF that marks holdings to market daily, similar moves contribute to NAVPU movement. This is interest-rate risk, not a "loss of deposit."
Worked Scenario B: Same Bond, Rates Fall
Use the same bond at PHP 102.00, ModDur 6.5, but yields fall 40 bps (Δy = −0.004).
%ΔP ≈ −6.5 × (−0.004) = +2.6%
New approximate price ≈ 102.00 × 1.026 = PHP 104.65
Exam trap: Candidates sometimes keep the negative sign after already treating the yield change as negative, double-counting and flipping the answer. Multiply once: minus sign in the formula times the signed Δy.
Worked Scenario C: Ranking Two Bonds by Sensitivity
A trust officer compares two peso government securities for explaining fund risk:
| Bond | Price (PHP) | Modified duration | Coupon style |
|---|---|---|---|
| Bond S (short) | 99.80 | 1.8 | Coupon bond, near final cash flows |
| Bond L (long) | 97.25 | 7.2 | Coupon bond, longer cash-flow span |
Assume an identical +100 bp yield increase (Δy = +0.01) for both.
| Bond | Approx. % price change | Approx. new price |
|---|---|---|
| Bond S | −1.8 × 0.01 = −1.8% | 99.80 × 0.982 ≈ PHP 98.00 |
| Bond L | −7.2 × 0.01 = −7.2% | 97.25 × 0.928 ≈ PHP 90.25 |
Conclusion: For the same rate shock, Bond L's percentage price decline is four times larger in duration terms (7.2 vs 1.8). Longer duration → greater price volatility. If a multiple-choice item asks which holding contributes more interest-rate price risk to a fixed-income UITF, pick the higher modified duration—not necessarily the bond with the slightly lower current price.
Scenario D: Money Market UITF vs Bond UITF
Recall BSP-oriented product constraints taught for Philippine UITFs:
- Money market UITF: deposits and fixed-income instruments with remaining maturity ≤ 3 years; weighted average portfolio life ≤ 1 year.
- Bond / fixed-income UITF: can hold longer-dated instruments (subject to the fund's plan rules and investment policy), so portfolio duration can be materially higher.
Illustrative (not official published fund figures):
| Fund | Illustrative portfolio modified duration | +50 bp parallel rise | Approx. fixed-income value impact |
|---|---|---|---|
| Money market UITF | 0.6 | −0.6 × 0.005 = −0.30% | Mild mark-to-market pressure |
| Intermediate bond UITF | 4.5 | −4.5 × 0.005 = −2.25% | Several times larger impact |
Correct client framing for CUSP / marketing personnel:
- Money market UITFs are designed for short portfolio life and therefore lower interest-rate sensitivity than longer bond funds.
- Lower sensitivity is not a capital guarantee. NAVPU can still move with credit events, liquidity, mark-to-market of short instruments, fees, and residual rate moves.
- UITF units are not bank deposits and are not PDIC-insured; the Risk Disclosure Statement (RDS) and Product Highlights materials must still be used.
This comparison is exactly how duration bridges Module 1 investment theory and Module 2 UITF products on the UCP blueprint.
Scenario E: Portfolio Sleeve Math (Exam-Style)
A simplified peso multi-asset UITF has 40% of NAV in a bond sleeve with modified duration 5.0 and 60% in equities (ignore equity rate beta for this item). If only the bond sleeve experiences a +80 bp yield rise and equity prices are unchanged for the question:
Bond sleeve %Δ ≈ −5.0 × 0.008 = −4.0%
Fund-level impact from bonds only ≈ 0.40 × (−4.0%) = −1.6% of total NAV (approximate).
You will not always get multi-sleeve math on the UCP, but the logic reinforces that duration applies to the rate-sensitive portion of the portfolio, weighted by allocation.
Exam Traps Checklist
| Trap | Wrong instinct | Correct approach |
|---|---|---|
| Sign of price change | "Duration is positive so price rises when yields rise" | Always use minus ModDur × Δy; rates up → prices down for option-free fixed bonds |
| Basis points | Use 50 instead of 0.005 | 50 bps = 0.50% = 0.005 in the formula |
| Duration = maturity | Pick longest maturity automatically | Compare modified duration (or cash-flow structure); high coupons shorten duration |
| Money market = risk-free | "WAPL ≤ 1 year means no loss possible" | Short duration reduces rate sensitivity; it does not eliminate market, credit, or liquidity risk |
| Confusing MacDur and ModDur | Plug Macaulay years straight into % price formula without conversion | % price formula uses modified duration; MacDur is the weighted-time concept |
| Forgetting PHP scaling | Report only % when asked for price | New price ≈ old price × (1 + %Δ) |
Client Conversation Patterns That Stay Accurate
When explaining rate risk to a prospective UITF participant:
- Start with the inverse rule: if market yields rise, existing fixed-rate bond prices tend to fall.
- Introduce duration as the speedometer of that sensitivity—not a promise of return.
- Contrast fund types: money market funds keep short weighted lives under BSP rules; bond funds can take more duration risk for higher yield potential.
- Close with mandatory truths: units are trust participations, marked to market, not PDIC-insured, and subject to the fund's plan rules and the client's CSA risk profile.
Integrating With Adjacent Topics
Duration sits between earlier interest-rate and bond-pricing chapters and later portfolio risk measures:
- Interest rate risk (Chapter 2 themes): qualitative inverse relationship.
- Duration (this chapter): quantitative sensitivity.
- Standard deviation / beta (later risk chapters): broader volatility and market sensitivity tools beyond pure yield shifts.
If an item mentions "which risk measure estimates the percentage price change for a small change in yield," the answer is modified duration, not beta and not standard deviation alone.
Practice Discipline Before You Sit the UCP
Under timed conditions, write the formula every time, convert basis points deliberately, and narrate the sign in words. Most duration errors on multiple-choice exams are process errors, not conceptual mysteries. With the PHP scenarios above, you should be able to estimate direction and approximate magnitude, rank funds by rate sensitivity, and defend money market versus bond comparisons without overselling safety.
A peso bond priced at PHP 100.00 has modified duration of 5.5. If yields fall by 20 basis points, the duration-based approximate new price is closest to:
Bond A has modified duration 2.0 and Bond B has modified duration 8.0. For an identical +75 basis-point parallel yield increase, which statement is correct?
A marketing officer tells a client that a BSP-compliant money market UITF cannot experience any NAVPU decline when interest rates rise because its weighted average portfolio life is at most one year. The best evaluation of that statement is:
Which error would most likely produce the wrong sign on an estimated bond price change when yields rise?