4
Fixed IncomeModule 4 of 5

Interest Rate Risk and Duration

5

Concepts

5

Formulas

1

Decisions

4

Quiz Questions

Key Concepts

5 concepts covered in this module.

Duration

Measure of bond price sensitivity to yield changes. Higher duration = more price volatility. Approximate % price change for 1% yield change.

Macaulay Duration

Weighted average time to receive cash flows. In years. Duration of zero-coupon = maturity.

Modified Duration

ModDur = MacDur / (1 + y/m). ΔP/P ≈ -ModDur × Δy. Direct measure of price sensitivity.

Convexity

Curvature of price-yield relationship. Duration is linear approximation; convexity corrects for non-linearity. Positive convexity: good for investor.

Duration Properties

Higher for: longer maturity, lower coupon, lower yield. Portfolio duration = weighted average of bond durations.

Formulas

5 essential formulas for this module.

Modified Duration

ModDur = MacDur / (1 + y/m)

Where: y = YTM, m = compounding periods per year

Price Change (Duration)

ΔP/P ≈ -ModDur × Δy

Where: First-order approximation

Price Change (Duration + Convexity)

ΔP/P ≈ -ModDur × Δy + ½ × Convexity × (Δy)²

Where: More accurate with convexity adjustment

Effective Duration

EffDur = (P- - P+) / (2 × P0 × Δy)

Where: Used for bonds with embedded options

Effective Convexity

EffConv = (P- + P+ - 2P0) / (P0 × Δy²)

Where: Curvature correction

Decision Frameworks

1 decision frameworks to guide your analysis.

How to manage interest rate risk?

  • Match duration of assets and liabilities (immunization)
  • Extend duration if expecting rates to fall
  • Shorten duration if expecting rates to rise

Mind Map

Visual overview of how concepts connect in this module.

Duration & Convexity
Duration Types
Macaulay (in years)
Modified (price sensitivity)
Effective (with options)
Key rate duration
Duration Drivers
Maturity (+)
Coupon (-)
Yield (-)
Convexity
Curvature correction
Positive: all else equal, good
Negative: callable bonds
½×Conv×(Δy)²
Applications
Immunization
Portfolio construction
Rate expectations
Risk management

Study Interest Rate Risk and Duration

This module has 11 flashcards and 4 quiz questions to test your knowledge.

Open the study dashboard to access interactive flashcards, timed quizzes, and track your progress.

Open Study Dashboard

No signup required. Create an account anytime to save progress.

Previous Module

Fixed-Income Bond Valuation

Next Module

Credit Risk and Credit Analysis