Alpha as ambiguity: robust mean-variance portfolio analysis

We derive the analogue of the classic Arrow-Pratt approximation of the certainty equivalent under model uncertainty as described by the smooth model of decision making under ambiguity. We study its scope by deriving a tractable mean-variance model adjusted for ambiguity and solving the corresponding portfolio allocation problem. In the problem with a risk-free asset, a risky asset, and an ambiguous asset, we …find that portfolio rebalancing in response to higher ambiguity aversion only depends on the ambiguous asset’s alpha, setting the performance of the risky asset as benchmark. In particular, a positive alpha corresponds to a long position in the ambiguous asset, a negative alpha corresponds to a short position in the ambiguous asset, and greater ambiguity aversion reduces optimal exposure to ambiguity. The analytical tractability of the enhanced Arrow-Pratt approximation renders our model especially well suited for calibration exercises aimed at exploring the consequences of model uncertainty on equilibrium asset prices.