Lesson 4 of 5 · 11 min

Money convexity: the adjustment in currency

Money convexity is annual convexity times the position's full value, and it turns the convexity adjustment into currency units next to money duration.

In short

  • Money duration = AnnModDur × full value of the position: the first-order change in currency.
  • Money convexity = AnnConvexity × full value of the position: the second-order effect in currency (or per 100 of par).
  • ΔPVFull≈−(MoneyDur×Δy)+12×MoneyCon×(Δy)2\Delta PV^{Full} \approx -(\text{MoneyDur} \times \Delta y) + \tfrac{1}{2} \times \text{MoneyCon} \times (\Delta y)^2.
  • The currency estimate equals the percentage estimate multiplied by the position's full value.
  • Use the full price (including accrued interest), not par and not the flat price.

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Money convexity: the adjustment in currency · Yield-Based Bond Convexity and Portfolio Properties