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Skew and Risk

May 13, 2012

The environment for trading contains numerous sources of potential risk, from sovereign defaults to bank failure to war in the Middle East. The ability to follow broad and protracted trends across global markets and commodities has never been more difficult. This explains the recent popularity of volatility index trading and also asset allocation methods that employ volatility management. The subject of managing tail risk by looking at “skew” is rarely discussed but remains an important complement to volatility.

I often find that the conventional definitions for skew are confusing, while the calculations cited are often based on normal distributions which are not ideal for this type of measurement. Skew is simply the degree to which the average of the distribution is tilted from its midpoint (or median). When measuring skew it is best to look at returns versus prices.

Skew= Average- Median

If the daily skew is positive, then the average of  daily returns is greater than the median of daily returns. This implies that there are probably positive outliers in the data–the “good” tail (95th percentile for example)  is often larger than the “bad” tail (the 5th percentile) . In the case that the skew is negative, the opposite is true: there are probably negative outliers in the data, and the “bad” tail is larger than the “good” tail.  Essentially, skew is a measure of the possibility of favorable or unfavorable surprises. This concept is different than just looking at a simple moving average of prices or the average of daily returns, because the skew can have a different sign than the measure of central tendency. The average can be positive, while the skew can be negative and vice versa. That is why the skew can carry vital information for traders– it can be an early warning, and sometimes even a better indicator of future returns than just a simple average.

At the very least, tail risk can be mitigated by observing skew directly and in today’s environment that is especially critical. The combination of volatility-sizing with skew can be a powerful method for risk management. In a subsequent post, I will demonstrate some practical applications of these concepts.


4 Comments leave one →
  1. Anon. permalink
    May 13, 2012 2:59 pm

    There are distributions that are skewed for which the mode > median > mean “rule” does not hold though. See

    So the Average – Median measure may severely mis-state the actual tail risks for distributions that aren’t “conventional”.

  2. John permalink
    May 23, 2012 5:55 pm

    any progress on the Minimum Correlation Portfolio whitepaper?


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