## Ahistorical Covariance

As anyone who’s studied finance even casually knows, the most celebrated principle of investing is diversification. In particular, purchasing multiple securities with low or negative *covariance* diminishes the risk an investor faces in owning a portfolio. Risk, in financial parlance, is operationalized as volatility, the variability of a security’s value. Covariance means the tendency for two securities to move simultaneously. Holding multiple securities of low covariance reduces risk, because if one security drops in value, low or negative covariance implies that it’s unlikely that all will drop in value simultaneously. The the risk — the variability in value — associated with a particular security is diluted in the portfolio by the likelihood that when one security falls, others are will rise or at least hold their value, damping any change in value of the portfolio as a whole. This is the principal of diversification.

In practice, investment managers construct portfolios by estimating the return prospects, the risk (volatility), and the covariances of various securities, and computing the portfolio that, based on these estimates, maximizes the ratio of risk to return. If managers were able to forecast expected return, variance, and covariances with 100% accuracy, rational investment would be a science, and there would be a clear “best” portfolio. To the degree that within a universe of securites, there are ample choices with low or negative covariances, investors would see great benefits to diversification. But unfortunately, future return, risk, and covariance can be forecast imperfectly at best. Portfolio managers understand this, especially with respect to return. Few professionals would rely on the naive forecasting strategy of guessing that this year’s return on some stock will simply be the same as last year’s. But variance and covariance are different. Historical values for the volatility and comovement of securities are in fact very frequently used as “best guesses” of future covariance. Investors are urged to hold portfolios that include stocks, bonds, commmodities, precious metals, currencies, and real estate, because historically these asset classes don’t typically move together.

But guessing future covariance from past covariance can be as hazardous as expecting a stock to do great this year because it did last year. Over the past while, there has been an odd spate of covariances. US stocks, real estate, precious metals, and oil have all done well. The US dollar has also done well, despite the historical negative covariance between USD and precious metal. Bonds have, until very recently, been flat. US wage perpetuities, the stream of future wages that represents most Americans’ core asset, are not directly priced. But wage growth, the value driver of this asset, has been flat, unusual in the face of rising stocks, commodities, and real estate.

In other words, covariances over the last year, viewed in terms of annual return, have been weird. There’s been a lot of simultaneous zigging where ordinarily a bit of zig and a bit of zag would have been expected. These are ahistorical covariances. Most investors haven’t minded, because nearly everything in their diverse portfolios stayed put or went up, rather than the usual won-some-lose-some scenario. It’s almost as if there’s some magnet or wind pulling normally independent spirits in the same general direction. Covariance is nice when it’s a general updraft.

But beware ahistorical covariance if the wind changes direction. The most professionally crafted portfolio won’t protect an investor from wild swings in value, if its holdings were based on historical covariance assumptions that suddenly fail to hold.

**Update History:**

- 23-Apr-2006, 12:45 a.m. EET: Changed “vaunted” to “celebrated”.