Optimal Time to Sell in Real Estate
Published online: 7 June 2008
Springer Science + Business Media, LLC 2008
Abstract This paper examines the properties of optimal times to sell a diversified
real estate portfolio. The portfolio value is supposed to be the sum of the discounted
free cash flows and the discounted terminal value (the discounted selling price).
According to Baroni et al. (Journal of Property Investment and Finance 25(6):603–
625, 2007b), we assume that the terminal value corresponds to the real estate index.
The optimization problem corresponds to the maximization of a quasi-linear utility
function. We consider three cases. The first one assumes that the investor knows the
probability distribution of the real estate index. However, at the initial time, he has to
choose one deterministic optimal time to sell. The second one considers an investor
who is perfectly informed about the market dynamics. Whatever the random event
that generates the path, he knows the entire path from the beginning. Then, given the
realization of the random variable, the path is deterministic for this investor.
Therefore, at the initial time, he can determine the optimal time to sell for each path
of the index. Finally, the last case is devoted to the analysis of the intertemporal
optimization, based on the American option approach. We compute the optimal
solution for each of these three cases and compare their properties. The comparison
is also made with the buy-and-hold strategy.
Keywords Real estate portfolio
Optimal holding period
JEL Classification C61
J Real Estate Finan Econ (2009) 38:59–87
F. Barthélémy (*)
THEMA, Université de Cergy-Pontoise, 33, Boulevard du Port, 95011 Cergy-Pontoise, France