Daily Academic Alpha: Limits of Arbitrage

Daily Academic Alpha: Limits of Arbitrage

March 10, 2015 Uncategorized
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(Last Updated On: January 18, 2017)

SHO Time for Limits-to-Arbitrage and Asset Pricing Anomalies

We examine the causal effect of limits-to-arbitrage on ten well-known asset pricing anomalies using Regulation SHO as a natural experiment. We find that asset pricing anomalies become weaker on portfolios constructed with pilot stocks during the pilot period. The effect is both statistically and economically significant, and Regulation SHO reduces the anomaly long-short portfolio returns by as much as 80 basis points per month. We also show that the effect comes only from the short legs of the anomaly portfolios. The effect remains intact after risk-adjustment with the Fama-French three-factor model.

Days to Cover and Stock Returns

The short ratio — shares shorted to shares outstanding — is an oft-used measure of arbitrageurs’ opinion about a stock’s over-valuation. We show that days-to-cover (DTC), which divides a stock’s short ratio by its average daily share turnover, is actually the theoretically correct measure because trading costs vary across stocks. Since trading costs are inversely related to share turnover, DTC is then approximately the marginal cost of the shorts. At the arbitrageurs’ optimum it equals the marginal benefit of the shorts, which is their opinion about over-valuation. Consistent with our model, DTC is a stronger predictor of poor stock returns than short ratio. It is distinct from the stock lending fee effect but has comparable forecasting power. An equal-weighted long-short strategy based on DTC generates a significant return of 1.2% per month.

Macroeconomic Expectations and the Size, Value and Momentum Factors

One of the challenges facing the prior literature when examining the link between macroeconomic risk and the size (SMB), value/growth (HML) and momentum (WML) factors is the difficulty of obtaining direct measures of macroeconomic expectations. We re-examine the link between macroeconomic risk and these factors using direct measures of investor expectations across 20 developed markets. In contrast to prior literature we find only a weak relation between HML and changes in expectations about economic activity, while SMB and WML are either unrelated to changes in macroeconomic expectations or they act as hedges against macroeconomic risk. This is inconsistent with SMB and WML being priced because they proxy for macroeconomic risks. These findings are not the result of low power tests but rather from the fact that the individual portfolios, which make up the factors, have economically and statistically similar sensitivity to the macroeconomic risks we examine. We also provide robust evidence that both local and global market returns are related to GDP growth and other measures of economic activity.


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Definitions of common statistics used in our analysis are available here (towards the bottom)

About the Author

Wesley R. Gray, Ph.D.

After serving as a Captain in the United States Marine Corps, Dr. Gray earned a PhD, and worked as a finance professor at Drexel University. Dr. Gray’s interest in bridging the research gap between academia and industry led him to found Alpha Architect, an asset management that delivers affordable active exposures for tax-sensitive investors. Dr. Gray has published four books and a number of academic articles. Wes is a regular contributor to multiple industry outlets, to include the following: Wall Street Journal, Forbes, ETF.com, and the CFA Institute. Dr. Gray earned an MBA and a PhD in finance from the University of Chicago and graduated magna cum laude with a BS from The Wharton School of the University of Pennsylvania.