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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
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Duration

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Answer
Measure of bond price sensitivity to yield changes. Higher duration = more price volatility. Approximate % price change for 1% yield change.
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Credit Risk and Credit Analysis