Valuing the option to invest in an incomplete market

This paper considers the impact of entrepreneurial risk aversion and incompleteness on investment timing and the value of the option to invest. A risk averse entrepreneur faces the irreversible decision of when to pay a cost in order to receive a one-off investment payoff. The uncertainty associated with the investment payoff can be partly offset by hedging, but the remaining unhedgeable risk is idiosyncratic. Nested within our incomplete set-up is the complete model of McDonald and Siegel (Q J Econ 101:707–727, 1986) which assumes investment payoffs are perfectly spanned by traded assets. We find risk aversion and idiosyncratic risk erode option value and lower the investment threshold. Our main finding is that there is a parameter region within which the complete and incomplete models give differing investment signals. In this region, the option is never exercised (and investment never occurs) in the complete model, whereas the entrepreneur exercises the option in the incomplete setting. Strikingly, this parameter region corresponds to a negative implicit dividend yield on the payoff, and so this exercise behavior contrasts with conventional wisdom of Merton (Bell J Econ Manage 4:141–183, 1973) for complete markets. Finally, in this parameter region, increased volatility speeds-up investment and option values are not strictly convex in project value, in sharp contrast to the conclusion of standard real options models. The author thanks George Constantinides, Graham Davis, Jerome Detemple, Avinash Dixit, David Hobson, Stewart Hodges, Bart Lambrecht, Andrew Lyasoff, Robert McDonald, Pierre Mella-Barral, Jianjun Miao, Bob Nau (ES discussant), Gordon Sick, James Smith, Stathis Tompaidis, Elizabeth Whalley and Zvi Wiener for their comments. The author also thanks seminar participants at the University of Texas at Austin (2004), Kings College London, the Cornell Finance Workshop, the Oxford-Princeton Finance Workshop, the BIRS Finance Workshop (2004), the Eighth Annual Real Options conference, the Bachelier Finance Society Third World Congress (2004), Princeton University, Boston University, the Fields Institute Toronto, QMF 2004, Warwick Business School, and the Econometric Society Winter Meetings (2006). First version: July, 2004.