Real estate investment : market volatility and optimal holding period under risk aversion

This paper deals with real estate portfolio optimization when investors are risk averse. In this framework, we ex-amine an important decision making problem, namely the determination of the optimal time to sell a diversifiedreal estate portfolio. The optimization problem corresponds to the maximization of a concave utility function de-fined on both the free cashflows and the terminal value of the portfolio. We determine several types of optimaltimes to sell and analyze their properties. We extend previous results, established for the quasi linear utility case,where investors are risk neutral. We consider four cases. In thefirst one, the investor knows the probability dis-tribution of the real estate index.In thesecondone,the investor isperfectlyinformedabout therealestate marketdynamics. In the third case, the investor uses an intertemporal optimization approach which looks like anAmerican option problem. Finally, the buy-and-hold strategy is considered. For these four cases, we analyze inparticular how the solutions depend on the market volatility and we compare them with those of the quasi linearcase. We show that the introduction of risk aversion allows to better account for the real estate market volatility.We also introduce the notion of compensating variation to better measure the impacts of both the risk aversionand the volatility