Portfolio Management For Assets With Multiscale Risk Structure

Any financial market is a coupled system where economic, market and human factors interact between themselves. It is also a multiscale system with various asstes having their own risk sructure in multiple time scales depending on investors' holding periods. In this paper, we will study a portfolio of mixed asset classes consisting of stock, bond and real estate. Real estate has a very different risk structure from stock and bond due to its illiquidity nature. The risk for real estate is holding period dependent while the risk for stock and bond can be assumed to be holding period independent. Therefore the risk for such mixed portfolio has multiple scales in time. Here we introduce a mean reversion model for the return of real estate asset. We intend to explore the effect of various parameters, including the strength of mean-reversion, risk-aversion coefficient and investment horizon etc. on investors' optimal asset allocation with real estate. We assume the investment opportunity of real estate varies with investment horizons while the return and variance of stock market and Tbond follow a constant pattern. We believe this is the first attempt to use a mean-reversion model in real estate market and the result we got from this research provides more reliable and practical suggestion for investors with different features and pursuits.