The Curious Incident of the Investment in the Market: Real Options and a Fair Gamble
Jonathan D. Evans
University of Bath
University of Warwick; University of Oxford - Oxford Man Institute
David G. Hobson
University of Bath - School of Mathematical Sciences
AFA 2006 Boston Meetings Paper
Is there any point to which you would wish to draw my attention? To the curious incident of the investment in the market. The agent did nothing in the market. That was the curious incident. (with apologies to Sir Arthur Conan-Doyle.)
In this paper we study an optimal timing problem for the sale of a non-traded real asset. We solve this problem for a risk-averse manager under two scenarios: firstly when the manager has access to no other investment opportunities, and secondly when he may also invest in a continuously traded financial asset. We construct the model such that the financial asset has zero risk premium and thus represents a fair gamble, and such that it is uncorrelated with the real asset, so that it is not useful for hedging. In the absence of the real asset, the manager would not include the financial asset in his optimal portfolio.
Although the problem is designed such that naive intuition would imply that the optimal strategy is the same irrespective of whether the manager is allowed to invest in the financial asset or not, curiously we find that for certain parameter values this is not the case. Access to the fair gamble improves the manager's expected utility in some situations, and reduces the probability that the real asset is ever sold. Our work has implications for modeling of portfolio choice problems since seemingly extraneous assets can impact on optimal behavior.
Number of Pages in PDF File: 43
Keywords: Real assets, Perpetual options, Optimal stopping, Incomplete markets, Portfolio choice, Real options, Portfolio constraints
JEL Classification: G11, G12, G31
Date posted: March 24, 2005