The introduction of asymmetric beta to the CAPM framework can allow an investor to construct a portfolio with expectations well above the security market line.

Incorporating asymmetric beta provides evidence of a mispricing in certain payoff profiles, namely tail hedged equities, that can be analyzed by using variants of the CAPM type of framework. CAPM based asset allocations are misspecified and ill-equipped to handle asymmetric returns.

The capital asset pricing model is a fundamental building block with which investors make allocation decisions over time. Investment decisions are made based on risk-return constructs, and in this framework, CAPM, for the most part, has stood the test of time. Due to its simplicity, it is widely used when an equity investor wants to roughly estimate the expected returns of one's portfolio.

We want to appraise the value of tail hedging within a CAPM framework, and thereby show the efficacy of tail hedging and the misspecificity of the model itself.

By using Harry Markowitz's efficient frontier, one can roughly compare different asset classes based on their consensus expected returns and observed risk (mostly computed using standard deviation of asset returns). However, this measure of risk is fairly naive since it has been well documented that most, if not all, asset classes have non-normal fat-tailed and often asymmetric return distributions. Asymmetric properties are not well accounted for in a mean-variance framework as it underestimates tail risk in negatively skewed portfolios. Stress tests should thus be used, as they are critical risk estimation tools that transparently demonstrate vulnerabilities to large deviations that can impact long-term expected returns. (We recognize successful empirical research stating that multifactor models can explain and predict investment returns, but they have similar limitations.)

Due to the principal-agent problem in the asset management industry, most money managers rationally have a propensity to use a negatively skewed payoff distribution. This kind of behavior, in aggregate, is also evidenced in the historical data, which shows significant losses for professional investors during the largest market downturns. Most investors and asset allocators, in addition to these negatively skewed positions, further view the returns of hedging strategies in a vacuum, rather than as a holistic part of their broader portfolio. Thus, they are likely to consider portfolio hedging programs to be a drag on their performance numbers and further undervalue them. We believe these factors, among others, contribute to a market segmentation that creates an undervaluation in tail-risk hedges.

Assuming there are such opportunities in hedging tail risk, let's evaluate how one can depict an asset class' risk-return profile and see if using a fair proxy tail-risk hedging program could help investors better maneuver these not-so-uncommon market crashes. We use Mr. Markowitz's efficient frontier type of framework to plot a “risk measure” on the x-axis (which is the average semi-variance for three-year rolling monthly returns) and the corresponding asset's annualized returns on the y-axis.