A simple and marginally-effective strategy to reduce portfolio variance is by constructing an asset correlation matrix, selecting assets with low (preferably negative) correlations, and building a portfolio of low-correlation assets. This basic strategy involves creating a set of assets whose cross-correlations (covariances) are minimized.
One reason this basic strategy is only somewhat effective is that a correlation matrix (or covariance matrix) only provides a partial picture of the chosen investment landscape. Some fundamental limitations include non-normal distributions, skewness, and kurtosis to name a few. To most readers these are fancy words with varying degrees of meaning.
Personally, I often find the mathematics of the work I do seductive like a Siren’s song. I endeavor to strike a balance between exploring tangential mathematical constructs, and keeping most of my math applied. One mental antidote to the Siren’s song of pure mathematics is to think more conceptually than mathematically by asking questions like:
What are the goals of portfolio optimization? What elements of the investing landscape allow these goals to be achieved?
I then attempt to answer these questions with explanations that a person with a college degree but without a mathematically background beyond algebra could understand. This approach lets me define the concept first, and develop the math later. In essence I can temporarily free my mind of the slow, system 2 thinking generally required for math.
Recently, I came up with the concept of antivariance. I’m sure others have had similar ideas and a cursory web search reveals that as profession poker player’s nickname. I will layout my concept of antivariance as it relates to porfolio theory in particular and the broader concept in general.
By convention, one of the key objective of modern portfolio theory is the reduction of portfolio return variance. The mathematical concept is the idea that by combining assets with correlations of less than 1.0, the return variance is less than the weighted sums of each asset’s individual variance.
Antivariance assumes that there are underlying patterns explain why two or more assets should be somewhat less correlated (independent), but at times negatively correlated. Consider the affects of major hurricanes like Andrew or Katrina. Their effects were negative for insurance companies with large exposures, but were arguably positive for companies that manufactured and supplied building materials used in the subsequent rebuilds. I mention Andrew because there was much more and more rapid rebuilding following Andrew than Katrina. The disparate groups of stocks of (regional) insurance versus construction companies can be considered to exhibit paired antivariance to devastating weather events.
Nicholas Nassim Taleb coined the the term antifragile, because terms such as robust simply don’t convey the exact mental connections. I am beginning to use the term antivariance because it conveys concepts not well captured by terms like “negatively correlated”, “less correlated”, “semi-independent”, etc. In many respects antifragile systems should exhibit antivariance characteristics, and vice versa.
The concept of antivariance can be extended to related concepts such as anticovariance and anticorrelation.
Balhiser Financial 