A Patent Race in a Real Options Setting: Investment Strategy, Valuation, CAPM Beta and Return Volatility

Abstract

This paper studies financial properties of venture-capital backed start-ups through a continuous-time real-options patent-race model. Numerical analysis shows that patent races, relative to a joint monopoly, cause over-investment, value-dissipation, a higher CAPM beta, a higher return volatility and more negative return correlation when firms intensively compete. A firm's CAPM beta is a complicated non-linear function of its position relative to its competitor. The magnitude of annualized return volatilities of start-ups can be in excess of 100%. This high level of return volatility is mainly attributed to technological risks and is consistent with empirical findings by Cochrane [2004].

Keywords: Patent race, real options, venture capital, start-ups, numerical analysis, competition

JEL Classification: G00, L1, O3