Shanken (1985) derives a test for the zero-beta capital asset pricing model (CAPM) which, as he points out, is equivalent to a test of the mean/variance efficiency of the market portfolio. This note illustrates the geometry of Shanken's test in the mean/variance space.

Short-horizon return predictability from order flows is an inverse indicator of market efficiency. We find that such predictability is diminished when bid-ask spreads are narrower, and has declined over time with the minimum tick size. Variance ratio tests suggest that prices were closer to random walk benchmarks in the more liquid decimal regime than in other ones. These findings indicate that liquidity stimulates arbitrage activity, which, in turn, enhances market efficiency. Further, as the tick size decreased, open-close/close-open return variance ratios increased, while return autocorrelations decreased. This suggests an increased incorporation of private information into prices during more liquid regimes.