부산대학교 도서관

In mixed-asset portfolio allocation, the main task is to determine the optimal weights invested on cash, bond, risky assets (stocks) and real estate assets. Many researchers over the years have discussed the role of real estate assets in intertemporal portfolio allocation strategy and its optimal weights in an investment portfolio. All these studies [B.~E. Feldman, J. Portf. Manag. {\bf 29} (2003), no.~5, 112--121 \doi{10.3905/jpm.2003.319912}; H.~R. Fogler, J. Portf. Manag. {\bf 10} (1984), no.~2, 6--13, \doi{10.3905/jpm.1984.6}; C. Fugazza, M. Guidolin and G. Nicodano, J. Real Estate Financ. Econ. {\bf 34} (2007), 35--80, \doi{10.1007/s11146-007-9002-5}; M. Hoesli and B.~D. Macgregor, {\it Property investment}, Routledge, London, 2000, \doi{10.4324/9781315840482}; M.~J. Seiler, J.~R. Webb and F.~C.~N. Myer, J. Real Estate Lit. {\bf 7} (1999), 163--179, \doi{10.1023/a:1008741320860}] argued that the real estate asset can be an effective portfolio allocation asset for investors and what should be the optimal weight. In addition, the optimal portfolio allocation may depend significantly on the predictability of asset returns through their autocorrelations. However, the prediction of asset return is difficult, especially for long time periods, and varying correlation between different asset classes will modify the optimal mixed allocation due to transaction costs and lack of liquidity, as seen in real estate assets [J.~L. Pagliari Jr., Real Estate Econ. {\bf 45} (2017), no.~1, 75--132, \doi{10.1111/1540-6229.12138}]. The return predictability for long-term time horizons and of transaction costs for short- and medium-term horizons were analyzed by C. Rehring [Real Estate Econ. {\bf 40} (2012), no.~1, 65--95, \doi{10.1111/j.1540-6229.2011.00306.x}] with the use of UK commercial real estate, who concluded that the allocation of real estate assets increases strongly with the investment horizon. \par The present study analyzes a dynamic mixed-asset portfolio optimization problem with four basic financial assets: a money market account (cash), a bond with constant maturity, a real estate asset and a financial stock index. The authors extend the model introduced by C. Chiarella et al. [{\it Sustainable asset accumulation and dynamic portfolio decisions}, Dyn. Model. Econom. Econ. Finance, 18, Springer, Berlin, 2016; MR3558900] to model the multifactor term structure by avoiding any arbitrage opportunity, while emphasizing the impact of the term structure on asset returns. This intertemporal optimization problem is solved by applying the martingale approach [J.~C. Cox and C. Huang, J. Econom. Theory {\bf 49} (1989), no.~1, 33--83; MR1024460] and provides explicit solutions for the optimal portfolio values and associated portfolio weights for logarithmic, constant absolute risk aversion (CARA) and constant relative risk aversion (CRRA) utility functions. As a result, this proposed model incorporates the role of the term structure to maturities on real estate assets in a mixed-asset portfolio allocation strategy. This specific term structure comes first from the tangible aspect of real estate and second from liquidity constraints inherent to real estate assets. By considering the mean-reverting properties of asset returns, a real estate portfolio allocation closer to reality is between 10 and 20\%. \par A possible extension would examine and incorporate the effects of market incompleteness, specific constraints on portfolio weights and intertemporal consumption of the investor within the model.