The Curious Incident of the Investment in the Market

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 utility maximizing, risk averse manager under two scenarios: firstly when the manager has access to no other investment opportunities, and secondly when they may also invest in a continuously traded financial asset. We construct the model such that the financial asset is uncorrelated with the real asset, so that it cannot be used for hedging the real asset, and such that the financial asset has zero risk premium. In the absence of the real asset, the manager would not include the financial asset in her optimal portfolio. Although the problem is designed such that naive intuition would imply that the optimal strategy and value functions are the same irrespective of whether the manager is allowed to invest in the financial asset, we find that curiously, for certain parameter values this is not the case. Our work has implications for modeling of portfolio choice problems since seemingly extraneous assets can impact on optimal behavior.