LECTURE 2 — PORTFOLIO DURATION, DURATION GAP, CONVEXITY
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Last updated 9:06 PM on 11/27/25
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12 Terms
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Portfolio Duration
D_A = Σ Xᵢ·Dᵢ
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Change in Asset Value
ΔA = (D_A·A)/(1+R) × ΔR
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Change in Liability Value
ΔL = (D_L·L)/(1+R) × ΔR
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Equity Change
ΔE = ΔA − ΔL
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Leverage Ratio
k = L / A
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Duration Gap
DG = DA − k·DL
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Duration Gap Model
ΔE = (DA − k·DL)·A·ΔR/(1+R)
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Equity Duration
DE = (DA·A − D_L·L) / E
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Convexity
CX = [1/(P(1+R/m)²)] × Σ PVₜ·t(t+1/m)
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Duration + Convexity Approx.
ΔP/P = MDΔR + ½CX(ΔR)²
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Portfolio Convexity
CX_A = Σ Xᵢ·CXᵢ
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Note 
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