What is Modified Duration?
Modified Duration measures the sensitivity of a bond or loan's price to changes in yield. A modified duration of 4.5 means the price drops approximately 4.5% for a 100 basis point increase in yield (and rises 4.5% for a 100bp decrease). Modified duration is derived from Macaulay duration (the weighted average time to receive cashflows) adjusted for yield: Modified Duration = Macaulay Duration / (1 + yield/n), where n is compounding periods per year. For loans with prepayment risk, effective duration (calculated using scenario analysis) is more appropriate than modified duration because cashflows change when rates change.
Formula
Modified Duration = Macaulay Duration / (1 + yield/n) Effective Duration = (P_down - P_up) / (2 × P_base × Δy) Where P_down and P_up are prices at ±Δy rate shock
How LoanBook Uses Modified Duration
LoanBook calculates effective duration using ±100bp rate shocks with rate-dependent prepayment adjustment. This accounts for the fact that prepayment speeds change when rates change, which modified duration does not capture. Duration is displayed in the portfolio analytics summary and used for ALM and hedging analysis.
Frequently Asked Questions
Why use effective duration instead of modified duration?
Modified duration assumes cashflows do not change when rates change. For loans, prepayments accelerate when rates fall and slow when rates rise, changing the cashflow pattern. Effective duration captures this by recalculating price at shocked rate levels with adjusted prepayment speeds.
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