We analyze the mathematical foundations of three types of structured financial products: return optimization securities, yield magnet notes, and reverse exchangeable notes. These products were sold widely to retail "investors" in the mid-2000s. On the basis of their mathematical structure, we infer that these products could provide positive returns to a purchaser only if the stock market had continued on an enormous upward climb for most or all of the holding period. In particular, the purchaser ran high risk of moderate-to-large risk of high losses of principal even if the stock market had remained relatively flat for a protracted period of time. We conclude that such structured investment products are unsuitable for typical unsophisticated retail "investors". In fact, we will also show that these products generally were unsuitable for sophisticated investors.