Is there a gap between the profitability of a trading strategy on paper and that which is achieved in practice? We answer this question by developing a general technique to measure the real-world implementation costs of financial market anomalies. Our method extends Fama-MacBeth regressions to compare the on-paper returns to factor exposures with those achieved by mutual funds. Unlike existing approaches, ours delivers estimates of all-in implementation costs without relying on parametric microstructure models or explicitly specified factor trading strategies. After accounting for implementation costs, typical mutual funds earn low returns to value and no returns to momentum.

Many theories in finance imply monotonic patterns in expected returns and other financial variables. The liquidity preference hypothesis predicts higher expected returns for bonds with longer times to maturity; the Capital Asset Pricing Model (CAPM) implies higher expected returns for stocks with higher betas; and standard asset pricing models imply that the pricing kernel is declining in market returns. The full set of implications of monotonicity is generally not exploited in empirical work, however. This paper proposes new and simple ways to test for monotonicity in financial variables and compares the proposed tests with extant alternatives such as t-tests, Bonferroni bounds, and multivariate inequality tests through empirical applications and simulations.

We propose a new decomposition of the traditional market beta into four semibetas that depend on the signed covariation between the market and individual asset returns. We show that semibetas stemming from negative market and negative asset return covariation predict significantly higher future returns, while semibetas attributable to negative market and positive asset return covariation predict significantly lower future returns. The two semibetas associated with positive market return variation do not appear to be priced. The results are consistent with the pricing implications from a mean-semivariance framework combined with arbitrage risk driving a wedge between the risk premiums for long and short positions. We conclude that rather than betting against the traditional market beta, it is better to bet on and against the “right” semibetas.