Abstract
Optimization based solely on the REIT returns in a historical time window is severely restricted by that set of realized historical returns, leaving the portfolio vulnerable to downturns unseen in the historical data. Dynamic portfolio optimization, which determines portfolio composition using a massive ensemble of return predictions that are statistically consistent with historical returns but include extreme events safeguard against this vulnerability. Dynamic optimization, based upon ARMA-GARCH models with heavy-tailed innovations and non-Gaussian copulas, is developed in this Chapter for mean variance and conditional value-at-risk measures as well as for the Black–Litterman model. Dynamically optimized portfolios comprised of domestic REITs are computed and their performance compared to corresponding portfolios optimized under the classical historical return approach. Fairly dramatic performance improvement is seen under dynamic optimization.
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Notes
- 1.
To be sure, there are variations of the GARCH model (Bollersley, 1986) designed to include additional behaviors. Some examples are the I(ntegrated)GARCH (Engle & Bollersley, 1986); F(ractionally)I(ntegrated)GARCH (Baillie et al., 1996); E(xponential)GARCH (Nelson, 1991); GARCH-M(ean) (Engle et al., 1986); T(hreshold)GARCH (Zakoian, 1994); and G(losten)J(agannathan)R(unkle)GARCH (Glosten et al., 1993) models.
- 2.
In practice, Σ and μ are estimated from sample data. Thus, fitting the distribution tv(x; μ, Σ) to a sample of multivariate data reduces to finding a best-fit value for ν.
- 3.
Popular rank correlation tests include Spearman’s ρ, Kendall’s τ, Goodman and Kruskal’s γ, and Somers’ D.
- 4.
This is another reason why rank correlation tests are not useful for this data set. The ranking of this subsample of 8 of the 14 items is perfectly correlated from one optimization scheme to the next.
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Lindquist, W.B., Rachev, S.T., Hu, Y., Shirvani, A. (2022). Dynamic Portfolio Optimization: Beyond MPT. In: Advanced REIT Portfolio Optimization. Dynamic Modeling and Econometrics in Economics and Finance, vol 30. Springer, Cham. https://doi.org/10.1007/978-3-031-15286-3_7
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