Academic Attack #1: Theory Does Not Measure Up to Practice

Academic Attack #1: Theory Does Not Measure Up to Practice

Recall that the CAPM could be reduced to a very simple formula : Rate of Return = Risk-free Rate + Beta (Return from Market – Risk-free Rate).

Thus, a security with a zero beta should give a return exactly equalto the risk-free rate. Unfortunately, the actual results don't come out that way.

This damning accusation is the finding from an exhaustive study of all the stocks on the New York Stock Exchange over a thirty-five year period. The securities were grouped into ten portfolios of equal size, according to their beta measures for the year. Thus, Portfolio I consisted of the 10 percent of the NYSE securities with the highest betas.Portfolio II contained the 10 percent with the second-highest betas, etc. The chart shows the relation between the average monthly return and the beta for each of the ten different portfolios (shown by the block dots on the chart) over the entire period. The market portfolio is denoted by O, and the solid line is a line of best fit (a regression line) drawn through the dots. The dashed line connects the average risk-free rate of return with the rate of return on the market portfolio. This is the theoretical relationship of the CAPM that was described earlier.

If the CAPM were absolutely correct, the theoretical and the actual relationship would be one and the same. But practive, as can quickly be seen, is not represented by the same line as theory. Note particularly the difference between the rate of return on an actual zero-beta common stock or portfolio of stocks and the risk-free rate. From the chart, it is clear that the measured zero-beta rate of return exceeds the risk-free rate. Since the zero-beta portfolio and a portfolio of riskless assets such as Treasury bills have the same systematic risk (beta), this result implies that something besides a beta measure of risk is being valued in the market. It appears that some unsystematic (or at least some non-beta) risk makes the return higher for the zero-beta portfolio.

Furthermore, the actual risk-return relationship (examined by Black, Jensen, and Scholes) appears to be flatter than that predicted by the CAPM; low-risk stocks earn higher returns, and high-risk stocks earn lower returns, than the theory predicts. (This is a phenomenon much like that found at the race track, where long shots seem to go off at much lower odds than their true probability of winning would indicate, whereas favorites go off at higher odds than is consistent with their winning percentages). Shrewd old Adam Smith recognized this way back in 1776 when he wrote, “The ordinary rate of profit always rises more or less with the risk. It does not, however, seem to rise... so as to compensate it completely.”

Theory and Practice. Photo by Elena

Systematic Risk (Beta) vs. Average Monthly Return for Ten Different-Risk Portfolios, and the Market Portfolio, for 1931 – 1965.

Average monthly return (%) Actual relationship – Theoretical realationship – Risk-free rate of return – market portfolio. Systematic Risk (Beta). Source: Black, Jensen, and Scholes, The Capital Asset Pricing Model: Some Empirical Tests, in Studies in the Theory of Capital Markets, ed. Jensen, 1972.

(Fisher Black attempted to explain these discrepancies between theory and evidence by pointing out that with uncertain inflation, the future real value of any dollar return is also uncertain. Hence, what we have been calling the risk-free rate is actually a risky real rate of return. Indeed, when inflation is taken into account a truly riskless asset does not exist. It is therefore not surprising that the procedure of drawing a line from some supposedly risk-free return through the market portfolio (as in the theoretical relationship depicted in the chart above) does not represent the actual relationship between returns and beta.

Black argues that the true relationship between risk and return can be described by the following equation:

Rate of return = Zero-beta return + Beta (Return from Market – Zero-beta return).

He finds that the data better support this version of the CAPM.  It is, however, still subject to many of the other problems).