Saturday, December 27, 2014

Basic Investment Math - note #2

In this note I provide an introduction to some of the basics of portfolio management. The word diversification within a portfolio is used to describe the strategy of owning more than one asset. The touted benefit of diversification is reduced risk. While diversification is beneficial, too much diversification may be no different than owning the market which may not be as effective as owing a representative index that would provide similar risk and returns at a lower cost. Owning a variety of stocks with similar risk and return characteristics (e.g. in the same or related industry) may provide little diversification benefit. Also, diversification does not insulate investors from mundane or severe market volatility which occurred during the 2008 financial crises for example. Beyond a certain point, a portfolio with x number of positions does not benefit from x+1, x+2 positions as the benefits of incremental diversification diminishes.

So instead of being singularly focused on diversification I have been simultaneously focused on portfolio covariance, correlation and standard deviation. In statistical terms covariance measures the degree of movement between two variables relative to their mean over time. In portfolio construction we are typically talking about rates of returns in investments and how they move together (or not) over time. Positive covariance describes returns for two assets that move in the same direction relative to their mean returns. Negative covariance indicates rates of returns for two assets move in opposite directions relative to their means. In portfolio terminology the term correlation means correlation coefficient which is a standardized measure of covariance that indicates the strength of the covariance of the assets in question. In the context of portfolio management standard deviation is a term that encompasses the previous terms. More specifically, the standard deviation of a portfolio encompasses the variances in returns for individual assets and the covariance between assets in the portfolio. In practical terms I have applied the concepts described here to determine at the margin, what type of assets to add to a portfolio. Ideally I strive to add assets with low or negative covariances and correlations. I also attempt to simultaneously manage two or more strategies with low or negative correlations within my portfolio at the same time (e.g. value investing over multi-year holding periods and arbitrage). (1)

Depending upon my circumstances at any given time I may not formally calculate the statistical measures described above day-to-day but follow an approach in line with these statistical measures based on my knowledge of specific assets (namely stocks). In stocks and bonds for example I typically hold positions in different companies, industries and countries that have minimum or negative correlations. I also attempt to think carefully about contagion risk and not so obvious economic linkages between specific investments. Finally I invest in securities where I believe long term value is not reflected in the current day price. Patience is the primary attribute here that may allow me to at times, look past shorter term correlation and standard deviation relationships to some degree, in order to focus on long term relationships in my effort to pursue long-term returns.

'(1) Note: there are many sources of information regarding covariances, correlation and standard deviation. For the discussion here my primary source of  information was "Investment Analysis and Portfolio Management," sixth edition by Frank Reilly and Keith C. Brown., pages 104 - 105 and 265 - 267.

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