Negative convexity arises when a bond's price-yield relationship bends the wrong way: as yields fall the bond's price gains less than a linear duration estimate predicts, and as yields rise the price falls more. This behavior is common in securities with embedded options, notably mortgage-backed securities and callable bonds, where the issuer or borrower can change cash flows. Evidence and explanations from Darrell Duffie at Stanford Graduate School of Business link this nonlinearity to option-like features that make interest-rate sensitivity asymmetric and time-varying.
Causes and mechanics
The root cause is the presence of an embedded option that alters cash flows when rates move. For a mortgage-backed security, falling rates spur refinancing, shortening expected cash flows and capping price appreciation. For a callable corporate bond, falling rates increase the likelihood of the issuer calling the bond, again limiting upside. These option effects create negative convexity because the convex, symmetric price response of a plain-vanilla bond is offset by the option holder exercising when it is favorable to them. The magnitude depends on prepayment behavior, option moneyness, and volatility.
Consequences for portfolios
Negative convexity increases risk in several linked ways. First, it reduces the protective benefit of convexity: when rates drop, portfolio gains are muted relative to duration-only expectations, and when rates rise, losses can be larger. Second, it forces more active hedging. Dynamic hedging of negative convexity requires frequent rebalancing and often increases trading costs and funding needs, exacerbating liquidity risk during stressed markets. Third, it introduces nonlinear exposure to interest-rate volatility; portfolios with negative convexity suffer when volatility rises because option exercise probabilities change, making valuation and risk forecasts less reliable.
Portfolio managers must also consider behavioral and territorial nuances. In the United States, homeowner refinancing incentives and mortgage contract features amplify negative convexity in agency mortgage-backed securities, linking interest-rate risk to housing market dynamics and regional prepayment patterns. In emerging markets, different legal frameworks and borrower behaviors can reduce or shift negative convexity effects, changing how institutions hedge and capitalize for risk.
Recognizing and quantifying negative convexity is therefore essential for accurate risk budgeting, stress testing, and regulatory capital assessment. Ignoring it can understate potential losses and misprice the cost of hedging and liquidity provision.