Expected Returns - Are They Unmeasurable?

by: Eric Falkenstein

Aaron Brown writes over at Willmott Forum (.pdf; you need to register):

I treasure the perfection in the Capital Asset Pricing Model, a necessary advance, even if expected return is nonmeasurable so the model cannot be tested.

Alas, I see often in my critique of the standard theory that I am only using historical returns, not expected returns, so my take is invalid. Now, it is one thing to say expected returns are difficult to measure, quite another to say they are unmeasurable. If large sample averages are not vaguely correlated with population averages, what does 'expected return' mean? It must mean one rationally expects randomness, making such a theory rather trivial. If a theory is by definition untestable, that is not merely 'imperfection', but rather, a bad theory (like asserting there are unmeasurable ghosts in my garage)?

Nobel Prize Winner William Sharpe mentioned that expected returns are much more difficult to measure than anticipated in the 1960s, and I will admit these early tests contained several errors that needed fixing. For example, there's the 'two pass' sort, an adjustment for the 'errors in variables' such that high betas tend to be overestimated and low betas underestimated. But it has been 40 years, and we have data in the US back to 1927, and broader data, and only a small, ungeneralizabe fraction of it generates an intuitive scatter plot where some metric of risk is positively correlated with average returns. At what point does one say, this theory isn't untestable, it's wrong?

Currently, in empirical finance we know that size, value and momentum are related to returns, but it's not clear why. In the nineties most thought value reflected distress risk, but when measured financial distress actually is inversely related to future returns. One thing that is clear is beta and volatility are not positively correlated with returns. To say that financial theory is successful while the main facts were discovered via simple sorts, and sophisticated tests like GMM have uncovered nothing interesting to an investor, suggests current theory is pretty and consistent to be sure. Yet I would only call a theory beautiful if it's true, because it in non-empirical, it's simply mathematical masturbation.