An investor faces a sequence of high-risk investment opportunities. The investor ranks the corresponding projects seen so far and must decide whether and how much to invest into the currently observed opportunity. Returns are realized at the end of the investment horizon, where only a small number of superstars projects generate positive returns. We derive the value functions and optimal investment rules for risk-neutral or risk averse investors. Some comparative statics results are obtained. Under weak assumptions, the expected in nite horizon utility exceeds that of initial wealth. A simulation study is performed for risk-neutral and risk-averse investors