Life insurance companies, the largest institutional holders of corporate bonds, tilt their portfolios towards higher-yield bonds when interest rates decline. This tilt seems to be primarily driven by an increase in duration rather than credit risk and insurers do not seem to increase the credit risk of their bonds as interest rates decline. Moreover, the duration gap between their assets and liabilities deviates from zero for extended periods of time both in negative and positive directions. These patterns cannot be explained by incentives to reach for yield. We propose a new model of duration-matching under adjustment costs that conforms with these patterns and test other implications of this model.