What is Convexity?
Convexity measures the second-order sensitivity of a loan's price to interest rate changes; it captures how duration itself changes as rates move. Positive convexity means the asset gains more in a rally than it loses in a selloff (desirable). Negative convexity, common in prepayable loans, means the opposite: when rates drop, borrowers prepay and you lose the high-coupon cashflows. Whole loans typically exhibit negative convexity because of the embedded prepayment option. Understanding convexity is essential for hedging and ALM.
Formula
Convexity = (P(-) + P(+) - 2 x P(0)) / (P(0) x delta_y^2) Price Change ≈ -Duration x delta_y + 0.5 x Convexity x delta_y^2
How LoanBook Uses Convexity
LoanBook calculates convexity as part of the scenario analysis framework, using the 7-point rate shock grid (-300 to +300bp). Convexity is reported in portfolio analytics and used in EVE (Economic Value of Equity) calculations for ALM risk assessment.
Frequently Asked Questions
Why do whole loans have negative convexity?
Because of the prepayment option. When rates drop sharply, borrowers refinance, returning principal at par; you lose the above-market coupon and must reinvest at lower rates. The price upside is capped by prepayments, but the downside (rates rising) has no such cap.
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