Academic journal article Journal of Risk and Insurance

A Mean-Preserving Increase in Ambiguity and Portfolio Choices

Academic journal article Journal of Risk and Insurance

A Mean-Preserving Increase in Ambiguity and Portfolio Choices

Article excerpt

INTRODUCTION

Since Ellsberg (1961) uncovered the phenomenon from the experiment that people are generally averse to the uncertainty of probabilities, ambiguity and ambiguity aversion have received much attention in the literature. In particular, the literature shows the importance of ambiguity and ambiguity aversion in financial markets. (1) Regarding asset pricing, some papers demonstrate that ambiguity-averse investors react asymmetrically to good and bad news in stock markets (Epstein and Schneider, 2008) and prefer trading stocks according to aggregate information rather than separable information (Caskey, 2009). Other papers find evidence from survey data that ambiguity aversion can help to explain several anomalies in stock markets, such as the higher risk premiums of small firms (Olsen and Troughton, 2000) and the equity premium puzzle (Rieger and Wang, 2012).

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, 2007). Several papers find that ambiguity-averse investors' holdings of risky assets decrease with greater ambiguity in dynamic settings (e.g., Fei, 2009; Faria and Correiada-Silva, 2016) and with greater ambiguity aversion under certain conditions (Gollier, 2011). In a portfolio choice experiment, Ahn et al. (2014) find that about 25 percent of subjects exhibit ambiguity aversion. (2) Further, increasing numbers of papers point out the significant impact of ambiguity and/or ambiguity aversion on equilibrium in the insurance markets (e.g., Koufopoulos and Kozhan, 2014), (3) insurance decisions such as demand for self-insurance and self-protection (e.g., Snow, 2011; Alary, Gollier, and Treich, 2013), (4) and the pricing of insurance premiums (e.g., Cabantous, 2007; Cabantous et al., 2011; Huang, Huang, and Tzeng, 2013). (5)

Although the above-mentioned papers provide insight into the influence of ambiguity and ambiguity aversion on portfolio choices and insurance decisions, none has explored the impact of an increase in ambiguity in terms of a change in the probability distribution on demand for a risky asset (or demand for coinsurance) when the return distribution is uncertain. As in Gollier (2011), throughout this article we refer to a risky asset with an uncertain return distribution as an uncertain asset. (6) Following this line of literature, the aim of this article is to find the conditions under which there is a 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. We study the effect of an increase in ambiguity on demand for an uncertain asset (or demand for coinsurance). However, Gollier (2011) studies the effect of an increase in ambiguity aversion on demand for an uncertain asset, Snow (2011) examines the effects of introducing ambiguity (8) and greater ambiguity aversion on demand for self-insurance, and Alary, Gollier, and Treich (2013) explore the effect of ambiguity aversion on demand for self-insurance. 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) and Faria and Correia-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. …

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