Hunting for superstars

The “superstar economy” is characterized by payoff functions that depend in a discontinuous way on the quality level of the corresponding products and services. Firm A might generate much higher returns than firm B, although A’s product is only marginally superior to B’s product. We look at an investor who considers to invest into start-ups that want to become active in one particular technological segment. Consequently only the very best few projects generate high returns. The investor is faced with a sequence of investment opportunities, observes the objective relative rankings of 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. We derive the value functions and optimal investment rules for risk-neutral and risk averse investors. Under weak assumptions, the expected infinite horizon utility exceeds that of initial wealth. We show that for a risk-neutral investor “invest all or nothing”, depending on the project’s ranking and time of occurrence, is an optimal strategy. For a risk-averse investor the optimal rule is non-linear and path dependent. A simulation study is performed for risk-neutral and log-utility investors.