Standard deviation and variance have been the default measures of investment risk at least since Markowitz’s seminal contribution to portfolio selection in 1952. Intuitively, though, investors may not be symmetric around the mean in their attitude toward risk. In other words, they may be much more concerned about the possibility that realized returns are significantly lower than expected (“left tail risk”) than the alternative of returns being significantly higher than expected. We study the asset allocation decision for a life insurance company, which is an environment where left tail risk is of utmost concern to the investor. Due to the long-term nature of a life insurance company’s liabilities, the insurer must necessarily select asset portfolios with a high premium on avoiding left tail risk for regulatory and long-term profitability reasons. We use extreme value theory, downside risk measures, and copulas to model the market risk of a life insurer’s assets for the purpose of selecting an optimal portfolio in such an environment. We find that the current industry allocations to at least one of the primary drivers of life insurer market risk (equities) are close to optimal as of 2013. In addition, we study how the optimal General Account corporate bond and equity allocations, which are chosen by the company, are affected by policyholder investment decisions in the Separate Account and other allocations in the General Account over the past two decades.
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