How to Shake Your Tail Risk

Lesson one: never lose money.

November 15, 2010

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squirrel on wireEvery now and again, someone comes up with a new name for an ancient practice. Take the “100-Mile Diet.” In the days of subsistence farming – which are not all that long past in North America – you ate what you grew, or bartered with your neighbours for what what you didn’t. And instead of expecting fresh fruits in winter (at least those of us who live in a northerly clime), we put in cold cellars and canned the autumn harvest to be doled out through the vitamin-D-deficient months of the year.

As so it is with tail risk. There is an industry of researchers beavering away to return us to an old investment adage: keep your powder dry. In other words, not only should your returns compensate for the risks, but you should be wary of the known risks you know about, the unknown risks that you know about and the unknown risks you don’t know about.

Cap-weighted indexes – the traditional notion of beta – don’t do that. They all operate within the traditional means/variance framework – where the stock market supplies the mean return and the portfolio variance – for the risk-averse – is supplied by the investor adjusting his or her exposure to the risk-free asset.

Which makes for a fascinating time in the investment innovation industry. While equal-weighted indexes have some history to them, it was Rob Arnott’s fundamental indexing that really broke open the field – or rather returned indexing to its economic grounding. Now there is a proliferation of definitions of beta – or should we  say tradable beta. It could be equal-weighted. It could be based on fundamental factors. But there are also “minimum variance” indexes as well as “maximum diversification” ones.

What they all focus on is minimizing (traditional beta) risk, rather than maximizing return. But it’s hard to see how that works in a two-dimensional – or rather, a two-moment – portfolio.

“Asset class return distributions are not normally distributed; yet, the typical Markowitz mean-variance optimization framework that has dominated the asset allocation process for over 50 years only relies on the first two moments of the return distribution,” note James Xiong and Thomas Idzorek, researchers at Ibbotson Associates. “Equally important, there is considerable evidence that investor preferences go beyond mean and variance. Investors are particularly concerned with significant losses, i.e., downside risk. Numerous alternatives to the mean-variance optimization (MVO) framework have emerged in the literature, but there is no clear leader amongst these alternative objective functions. … The future is hard to predict accurately, especially in greater detail.”

Still, Xiong and Idzorek make a stab at it.

“Traditional MVO leads to an efficient frontier that maximizes return per unit of variance, or equivalently, minimizes variance for a given level of return. In contrast, M-CVaR maximizes return for a given level of CVaR, or equivalently, minimizes CVaR for a given level of return. Conditional value-at-risk (CVaR) measures the expected loss in the left tail given (i.e., conditional on) that a particular threshold has been met, such as the worst 1st or 5th percentile of outcomes in the distribution of possible future outcomes.”

Worst 1st or 5th percentile outcomes? To paraphrase a former American politician, “now we’re talking real money.” Of course, we’re also talking about other things: the higher moments – or the four dimensions – of the asset management space.

“The M-CVaR process used in this article takes non-normal return characteristic into consideration, and in general, prefers assets with positive skewness, small kurtosis, and low variance. If the returns of the asset classes are normally distributed or if the method used to estimate the CVaR only considers the first two moments, both MVO and M-CVaR optimization lead to the same efficient frontier, and hence, the same asset allocations. In order to understand the implications of skewness and kurtosis on portfolio selection, it is critical to estimate CVaR in a manner that captures the important non-normal characteristics of the assets in the opportunity set and how those non-normal characteristics interact when combined into portfolios.”

Of course, this is a traditional adage restated. Lesson One: Never lose money. Lesson Two: Never forget Lesson One. The devil is in figuring out how. And so, tail risk: a seminar coming to your investment committee soon.

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