Understanding Coefficients in Money Management

Understanding Coefficients in Money Management

Understanding Coefficients in Money Management

In the late 1960s and early 1970s, there was a general and enthusiastic endorsement of the value of beta coefficients as a measureof risk and an indicator of reasonable expectations of the returns onportfolios, given specified behavior of the market. Beta coefficientswere embedded in an intricate, comprehensive, and plausible theory and had the further advantage of an esoteric name. Some leadingbrokerage firms and others began to manufacture and distribute betason a large scale.

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Controversies quickly arose. One of the least important was overthe method of estimating betas for individual assets. The practical importance of the differences between the best and worst estimates wasnever large.

Of greater apparent importance, initially, was the instability ofbetas for individual stocks. Even betas produced by the most sophisticated methods were quite unstable. Betas based on actual data fora previous period, say, two years, typically accounted for less thanone third of the variation among betas of the same stocks in the future.

The seriousness of this fact is not great when one realizes that one is interested in betas for portfolios rather than for their component assets. The law of large numbers helps somewhat. Estimates of beta are sometimes too high and sometimes too low. These discrepanciesare partially offsetting with the result that estimates for portfolios are often quite good predictors of future betas for portfolios.

The virtue of the historical beta as a predictor of the future betais quite sensitive to the correlation between the actual portfolio andthe market index for which the beta is relevant. If the correlationwere 1.0, the historical beta would be a perfect predictor. That is,if a portfolio always moved in perfect lockstep with the market index,the beta of the portfolio would always predict the portfolio's responseto the market. A portfolio with a beta of 0.5 would move up anddown half as fast as the market, a portfolio with a beta of 0.75, three fourths as fast, and so forth.

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Skepticism about the value of betas became acute in some financialinstitutions when they calculated betas for their own portfolios anddiscovered that future reactions to the market were quite differentfrom expectations created by the historical betas. A portfolio supposedto decline only half as much as the market sometimes declined muchmore and sometimes much less. This was true whether the historicalbeta for the portfolio was estimated by calculating its own averagesensitivity to the market in the past or whether it was considered tobe a weighted average of the betas of the component assets.

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