George Rebane
Here’s a little something from my financial engineering toy box that one or two RR readers may find interesting. The discussion is a tiny bit technical, but the pictures should be accessible to all. Most investors know that a stock’s beta (Greek β) is a number that indicates how well the security tracks its market, say, the SP500. And rho (Greek ρ) measures the correlation between, say, the price series of two stock’s – the way they both zig and zag together, or how much one zigs while the other zags. I’ll try to keep this short.
From august sources like Modern Portfolio Theory (MPT) by nobelists Markowitz and Sharpe, we learn that if a stock’s β equals one, then it more or less goes up and down in similar percent changes with the market. If β > 1, then the stock’s swings have a greater percentage than the market’s; and if β < 1, then the stock’s swings behave in a more reserved manner than do the market’s. Riskier stocks have the bigger swings, and more conservative stocks have the smaller swings. The referenced formula (here) for beta reflects this with its inclusion of the standard deviation of the price swings.
As stated above, ρ measures in how tight of a formation two stocks will fly. The range of ρ is between +1 and -1, with the positive values indicating tighter formations, and ρ = 1 denoting a perfectly tight formation matching each other’s zigs and zags. A small or zero ρ means that the stocks pretty much act independently of each other. In designing your investment portfolio from a selected shortlist of stocks, MPT teaches that you should try to avoid stocks that pair with high ρ values. Doing probabilistic math recommends that you pick stocks that pair with the lowest ρ values possible to give you a low volatility (i.e. low risk) portfolio.
Now after you understand all that, we’re going to throw a monkey wrench into the whole thing, a little bit of information you will not hear from your well-paid wealth advisor who manages your portfolio. (Drum roll please.) Betas and rhos, calculated from past performance, are pretty much worthless measures of securities performance for portfolio design. Why? Well, that answer depends on what is known as the investor’s ‘investment horizon’. That’s the period into the future over which the investment plan is supposed to hold with numbers such as expected portfolio appreciation, its most likely upper and lower limits, and so forth.



