We present a standard model of financial innovation, in which intermediaries engineer securities with cash flows that investors seek, but modify two assumptions. First, investors (and possibly intermediaries) neglect certain unlikely risks. Second, investors demand securities with safe cash flows. Financial intermediaries cater to these preferences and beliefs by engineering securities perceived to be safe but exposed to neglected risks. Because the risks are neglected, security issuance is excessive. As investors eventually recognize these risks, they fly back to safety of traditional securities and markets become fragile, even without leverage, precisely because the volume of new claims is excessive. Financial innovation can make both investors and intermediaries worse off. The model mimics several facts from recent historical experiences, and points to new avenues for financial reform.