A Linear Approximate Robust Strategic Asset Allocation with Inflation-Deflation Hedging Demand

Abstract

This study considers a finite-time consumption-investment problem for investors with homothetic robust utility under the quadratic security market model with stochastic volatilities and inflation rates. This leads to a nonlinear nonhomogeneous partial differential equation for indirect utility. We propose a linear approximation method and derive the approximate optimal robust portfolio decomposed into myopic, intertemporal hedging, and inflation-deflation hedging demands. Furthermore, we propose a method for estimating our quadratic security market model that achieves the stability of optimal portfolio estimates. We then apply our estimation method to a two-factor quadratic security market model. Our numerical analysis shows that the market timing effects in the optimal robust allocation are significant and nonlinear, and are mainly due to inflation-deflation hedging demand in addition to myopic demand.

Strategic International Asset Allocation under a Quadratic Model with Exchange Rate and Inflation-Deflation Risks

“…Our next research project is to estimate our quadratic international security market model, but there is a problem of multicollinearity as pointed out by Kikuchi and Kusuda (2023a). In the quadratic models, the variance-covariance matrix of asset returns is stochastic, in particular, the correlations among asset returns are stochastic.…”

“…Note that such multicollinearity does not arise in constant correlation models such as affine models, but in our quadratic security market model with stochastic correlation. To deal with such multicollinearity, Kikuchi and Kusuda (2023a) have introduces a regularization term related to the inverse of the volatility matrix into the loss function to stabilize the optimal portfolio when estimating the quadratic security market model. Although Kikuchi and Kusuda (2023a) have estimated the quadratic security market model and confirm the nonlinearity and significance of market timing effects, there are three problems with their estimation.…”

“…To deal with such multicollinearity, Kikuchi and Kusuda (2023a) have introduces a regularization term related to the inverse of the volatility matrix into the loss function to stabilize the optimal portfolio when estimating the quadratic security market model. Although Kikuchi and Kusuda (2023a) have estimated the quadratic security market model and confirm the nonlinearity and significance of market timing effects, there are three problems with their estimation. First, since the regularization term depends on the volatility of the optimal portfolio, the estimation results depend on the choice of the underly-ing securities that make up the optimal portfolio.…”

Optimal Consumption-Investment and CAPMs under a Quadratic Model based on Homothetic Robust Epstein--Zin Utility

“…Such nonlinearity is attributed to the stochastic variances and covariances of asset returns, while such significance is attributed to inflation-deflation hedging demand in addition to myopic demand. Kikuchi and Kusuda (2023a) consider both these issues and study the consumption-investment problem for long-term investors with homothetic 2 robust utility under the quadratic security market model of Batbold et al (2022). Investors with homothetic robust utility, introduced by Maenhout (2004) and theoretically justified by Skiadas (2003), regard the "base probability" as the most likely probability; however, they also consider other probabilities because the true probability is unknown.…”

“…Homothetic robust utility is characterized by relative risk aversion and relative ambiguity aversion, which represents the investor's degree of distrust of the base probability. Since a nonlinear term appears in the partial differential equation (PDE) for the indirect utility function, Kikuchi and Kusuda (2023a) use a linear approximation method to derive an approximate optimal portfolio. Their numerical analysis confirms the nonlinearity and significance of market timing effects.…”