This article models the riskiness of structured securitization deals. The deals are put together by “banks,” which can exercise strategic options over the risk put into the deals. The banks face a trade‐off between the benefits of risk‐taking now and future franchise benefits if the deal pays off. The key insight is a convex relationship between the value of the bank's equity position and the risk in the deal. Although there is a continuum of possible risk, banks choose either the highest or lowest levels of risk open to them. Changes in strategy are discontinuous and unpredictable; a history of low risk‐taking may be a prelude to increased risk‐taking later. Competition, to the extent of reducing franchise value, can lead to more risk‐taking, as can more information in the market. The model provides insights into the risk‐taking that led up to the Great Recession and to institutions that are “Too Big to Fail.”