3.1 Duration and Modified Duration

Why Duration Matters for UITF Marketing Personnel

In Module 1 of the TOAP UITF Certification Program (UCP) Qualifying Exam, you already learn that bond prices and market interest rates move in opposite directions. That inverse relationship is necessary but not sufficient for client conversations. A participant who buys units of a peso fixed-income UITF will ask a practical follow-up: How much can the NAVPU move if Bangko Sentral ng Pilipinas (BSP) policy rates, Treasury yields, or corporate bond yields shift?

Duration answers that question. It is the standard fixed-income tool for measuring interest-rate sensitivity—how much a bond's price (or a fund's bond portfolio value) is expected to change when yields change. For UITF sales and marketing personnel, duration is not an abstract formula to memorize in isolation. It supports suitability discussions, risk disclosures, and honest comparisons among money market, bond, multi-asset, and equity funds.

This section builds two linked ideas:

1. Macaulay duration — a time-weighted measure of when cash flows arrive.
2. Modified duration — the percentage price-sensitivity measure used in rate-shock estimates.

Macaulay Duration: Weighted Average Time to Cash Flows

Macaulay duration (often abbreviated MacDur or simply "duration" in older texts) is the present-value-weighted average time until a bond's contractual cash flows are received. Each coupon and the final principal repayment is discounted to today, expressed as a fraction of the bond's full price, and then multiplied by the time (in years) when that cash flow occurs. Summing those products gives Macaulay duration in years.

Intuition without the full formula first

Think of a bond as a series of future PHP payments. A large final principal payment far in the future pulls the weighted average toward the maturity date. Regular coupon payments earlier in the life of the bond pull the average closer to today. Therefore:

• A zero-coupon bond has Macaulay duration equal to its maturity—all of the cash arrives at one date.
• A high-coupon bond has Macaulay duration shorter than maturity—more of the total present value is paid as interim coupons.
• Holding other factors constant, higher yield shortens Macaulay duration slightly because distant cash flows are discounted more heavily and receive less weight.

Simple numerical illustration (PHP cash flows)

Suppose a 3-year annual-pay peso bond with face value PHP 1,000, coupon rate 6%, and yield 6% (priced at par). Cash flows are PHP 60, PHP 60, and PHP 1,060 at years 1, 2, and 3. Because the bond is at par at a 6% yield, each cash flow's present value is easy to interpret as a weight of price:

Macaulay duration is about 2.83 years, which is less than the 3-year maturity because the interim coupons pull some weight forward. You do not need to reproduce multi-decimal precision on the UCP exam; you must know the direction, the unit (years), and the meaning (weighted average receipt time of cash flows).

Modified Duration: From Time Measure to Rate Sensitivity

Modified duration converts Macaulay duration into a price-sensitivity statistic:

Modified duration = Macaulay duration / (1 + periodic yield)

If yields are quoted annually and coupons are annual, the denominator is simply (1 + YTM). With semi-annual coupons and a semi-annual yield, use the matching period convention. The UCP-level takeaway is conceptual: modified duration is not just "time until money comes back"; it is the first-order estimate of how much percentage price changes when yield changes.

The core approximation formula

For small yield changes on an option-free fixed-rate bond:

Approximate % price change ≈ − (modified duration) × (Δyield)

Critical exam points embedded in this one line:

• The minus sign encodes the inverse relationship: if yields rise, estimated price change is negative; if yields fall, estimated price change is positive.
• Δyield must be in decimal form consistent with the duration units (for example, a 100 basis-point rise is 0.01, not 100).
• The result is an approximation. For large rate moves, convexity and other effects matter, but first-order duration is the standard exam and sales starting point.

Worked PHP price example

A Philippine government peso bond (or a corporate peso bond held in a fixed-income UITF) is priced at PHP 98.50 per 100 face and has modified duration of 5.0. BSP-related market rates push the bond's yield up by 80 basis points (0.80%, or 0.008).

Approximate % price change ≈ −5.0 × 0.008 = −4.0%

Approximate new price ≈ 98.50 × (1 − 0.04) = PHP 94.56

If instead yields fall by 80 basis points:

Approximate % price change ≈ −5.0 × (−0.008) = +4.0%

Approximate new price ≈ 98.50 × 1.04 = PHP 102.44

Same duration, opposite yield move, opposite price move—always check the sign of Δyield before you answer.

Duration vs Maturity: A Classic Exam Trap

Candidates often treat duration and maturity as synonyms. They are related but not identical:

• Maturity is the final contractual date when principal is due.
• Duration is a weighted average timing of all discounted cash flows and (in modified form) a sensitivity measure.

Two bonds can share the same maturity and have different durations if coupons or yields differ. A 10-year zero has Macaulay duration of 10 years; a 10-year high-coupon bond has Macaulay duration well below 10. On the exam, if a question asks which bond's price is more sensitive to a parallel yield shift, answer from duration (and coupon structure), not from maturity alone.

Linking Duration to BSP Money Market UITFs

BSP rules for money market UITFs (as reflected in Circular 1152 and related MORB UITF standards taught in the product modules) constrain how long the portfolio can "wait" for cash:

• Eligible deposits and fixed-income instruments generally have remaining maturity of not more than 3 years.
• The fund's weighted average portfolio life is limited to not more than 1 year.

Those constraints keep money market portfolios in the short end of the curve. Short remaining lives and frequent rolling of short instruments produce low portfolio duration relative to intermediate or long bond funds. Low duration means smaller percentage price (NAVPU) reactions to a given yield shock—though money market funds are not risk-free, are not deposits, and are not PDIC-insured.

By contrast, a peso bond UITF that holds intermediate or long government and corporate issues can show materially higher duration and therefore greater NAVPU volatility when rates reprice. Multi-asset and equity funds add other risks (equity beta, currency if applicable, credit), but pure interest-rate sensitivity of the fixed-income sleeve still scales with duration.

What You Must Recall Under Exam Pressure

1. Define Macaulay duration as a PV-weighted average time to cash flows.
2. Define modified duration as the percentage price change per unit yield change (with the negative sign in the formula).
3. Apply %ΔP ≈ −ModDur × Δy with correct basis-point conversion.
4. State that longer duration → larger price swings for the same Δy.
5. Connect BSP money market constraints to lower rate sensitivity versus bond funds—without promising capital protection.

Master these five points and the quizzes that follow, then move to Section 3.2 for scenario applications, client-facing language, and more PHP rate-shock practice.