Time-varying risk components in the single-factor market model: an exact most powerful invariant test

There is mounting evidence that stock prices have a time-varying predictable component. This paper tests for time-varying systematic risk, market compensation for systematic risk, and risk premiums in the single-factor market model to determine (1) whether the predictable stock-price component is due to time-varying risk premiums in an efficient market or an inefficient market with constant risk premiums, and (2) whether the time-varying risk premiums are due to time-varying systematic risk or time-varying market compensation for systematic risk. This paper applies an exact small-sample, pointwise most powerful invariant test to ten size and 12 industry portfolios. It finds consistent evidence of time variation in all three risk components over the full 35-year sample, but largely sporadic evidence of time variation over the five seven-year subsamples. Of the portfolios that show evidence of time-varying risk premiums, they are most likely the result of time-varying market compensation for systematic risk and not time-varying systematic risk.