Is stochastic volatility relevant for dynamic portfolio choice under ambiguity?

Abstract

Literature on dynamic portfolio choice has been finding that volatility risk has low impact on portfolio choice. For example, using long-run US data, Chacko and Viceira [2005. "Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets." The Review of Financial Studies 18 (4): 1369-1402] found that intertemporal hedging demand (required by investors for protection against adverse changes in volatility) is empirically small even for highly risk-averse investors. We want to assess if this continues to be true in the presence of ambiguity. Adopting robust control and perturbation theory techniques, we study the problem of a long-horizon investor with recursive preferences that faces ambiguity about the stochastic processes that generate the investment opportunity set. We find that ambiguity impacts portfolio choice, with the relevant channel being the return process. Ambiguity about the volatility process is only relevant if, through a specific correlation structure, it also induces ambiguity about the return process. Using the same long-run US data, we find that ambiguity about the return process may be empirically relevant, much more than ambiguity about the volatility process. Anyway, intertemporal hedging demand is still very low: investors are essentially focused on the short-term risk-return characteristics of the risky asset.

A Mean‐Preserving Increase in Ambiguity and Portfolio Choices

“…Our article differs from previous studies on ambiguity (e.g., Fei, ; Gollier, ; Snow, ; Alary, Gollier, and Treich Alary et al., ; Faria and Correia‐da‐Silva, ). First, the investigated effect on the problems of portfolio choices and insurance differs from that in the literature.…”

“…sign-definite comparative static result for demand for an uncertain asset (or demand for coinsurance) with respect to an increase in ambiguity. 7 Our article differs from previous studies on ambiguity (e.g., Fei, 2009;Gollier, 2011;Snow, 2011;Alary, Gollier, and Treich, 2013;Faria and Correia-da-Silva, 2016). First, the investigated effect on the problems of portfolio choices and insurance differs from that in the literature.…”

“…Regarding portfolio choices, the literature shows, theoretically and empirically, that when considering the uncertainty of expected returns and ambiguity aversion, the out‐of‐sample performance of the optimal portfolio measured by the Sharpe ratio is better than those of the mean‐variance and Bayesian portfolios (Garlappi, Uppal, and Wang, ). Several papers find that ambiguity‐averse investors’ holdings of risky assets decrease with greater ambiguity in dynamic settings (e.g., Fei, ; Faria and Correiada‐Silva, ) and with greater ambiguity aversion under certain conditions (Gollier, ). In a portfolio choice experiment, Ahn et al.…”

“…Second, for the comparative statics of ambiguity on portfolio choices, our methodology is distinct from that of previous papers. We characterize greater ambiguity by a change in the probability distribution, whereas Fei (2009) andFaria andCorreia-da-Silva (2016) characterize it by a change in parameters under the specified value function or utility function that yields the closed form of the optimal portfolio. Moreover, we consider the static portfolio choice problem under a relatively simple setting where return is determined by an uncertain distribution, whereas Fei (2009) andFaria andCorreia-da-Silva (2016) consider dynamic settings in which asset prices or asset returns and volatility follow stochastic processes.…”

Debt as a financial risk factor in SMEs in the Czech Republic

“…Aït-Sahalia and Matthys (2019) applied advanced techniques of intertemporal choice when researching consumption-portfolio allocation problem. Dealing with dynamic portfolio choice, Faria and Correia-da-Silva (2014) found out that investors are predominantly interested in the short-term risk returns of a possibly risky asset.…”