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We investigate mean-variance optimization when a portfolio of stocks or projects is subject to both (stock or project) return uncertainty and exogenous shocks, for instance due to announcements affecting the outlook of a stock such as product recall or design flaw, or a competitor launching a major product first. Considering exogenous shocks is a major contribution of the present paper. We develop a tractable reformulation of the problem where we minimize the variance of the portfolio return subject to the expected portfolio return at least reaching a threshold value, and show that under our model assumptions this reformulation is a second-order cone problem (SOCP). Our robust optimal allocation in the setting with exogenous shocks outperforms various benchmarks, including those where the nominal variance of the portfolio return is minimized, establishing the need to consider robust optimization approaches for portfolio optimization problems with shocks when studying robust mean-variance optimization problems.
Joint work with Hedieh Ashrafi.