We empirically study the economic benefits of giving investors access to index options in the standard portfolio problem, analyzing both expected-utility and nonexpected-utility investors in order to understand who optimally buys and sells options. Using data on S&P 500 index options, CRRA investors find it always optimal to short out-of-the-money puts and at-the-money straddles. The option positions are economically and statistically significant and robust to corrections for transaction costs, margin requirements, and Peso problems. Loss-averse and disappointment-averse investors also optimally hold short option positions. Only with highly distorted probability assessments can we obtain positive portfolio weights for puts (cumulative prospect theory and anticipated utility) and straddles (anticipated utility).