Asset Pricing: Market Mispricing and Limits to Arbitrage
Paper Session
Friday, Jan. 6, 2023 2:30 PM - 4:30 PM (CST)
- Chair: Samuel Hanson, Harvard University
The Statistical Limit of Arbitrage
Abstract
In the context of a linear asset pricing model, we document a statistical limit to arbitrage due to the fact that arbitrageurs are incapable of learning a large cross-section of alphas with sufficient precision given a limited time span of data. Consequently, the optimal Sharpe ratio of arbitrage portfolios developed under rational expectation in the classical arbitrage pricing theory (APT) is overly exaggerated, even as the sample size increases and the investment opportunity set expands. We derive the optimal Sharpe ratio achievable by any feasible arbitrage strategy, and illustrate in a simple model how this Sharpe ratio varies with the strength and sparsity of alpha signals, which characterize the difficulty of arbitrageurs’ learning problem. Furthermore, we design an "all-weather" arbitrage strategy that achieves this optimal Sharpe ratio regardless of the conditions of alpha signals. We also show how arbitrageurs can adopt multiple-testing, LASSO, and Ridge methods to achieve optimality under distinct conditions of alpha signals, respectively. Our empirical analysis of more than 50 years of monthly US individual equity returns shows that all strategies we consider achieve a moderately low Sharpe ratio out of sample, in spite of a considerably higher yet infeasible one, suggesting the empirical relevance of the statistical limit of arbitrage and the empirical success of APT.The Debt-Equity Spread
Abstract
We propose the debt-equity spread (DES), the difference between the actual and equity-implied credit spreads, as a measure of the valuation gap between debt and equity at the firm and bond level. DES strongly predicts stock and bond returns in opposite directions. A strategy that takes a long position in firms with low DES (indicating that stocks are cheap relative to bonds) and a short position in those with high DES generates an average stock return of 6.31\% and bond return of --5.53\% per annum. The return predictability is consistently significant over subsamples and is stronger among smaller, less liquid, and more difficult-to-short stocks and bonds. In addition, firms with higher DES tend to have more negative revisions in long-term growth forecasts, issue equity and retire debt more aggressively, and their insiders are more likely to sell their stocks. Together, these findings support DES being a measure of relative mispricing between debt and equity.Mutual Fund Risk Shifting and Risk Anomalies
Abstract
Risk-shifting by underperforming funds increases their demand for risky stocks. We investigate its contribution to the well known risk anomalies: the apparent overvaluation of stocks with high beta, idiosyncratic volatility, and skewness. We show that these anomalies are concentrated among stocks mainly held by the laggard funds. Exploiting the Morningstar methodology change in 2002, whereby its ``star'' ratings became based on relative performance within a style category rather than across the entire fund universe, we show that the beta anomaly is significant only when beta is measured against the S\&P 500 index for the pre-2002 period and against the relevant category index for the post-2002 period. Counterfactual estimates from an asset demand system imply that removing the demand pressure from the bottom quintile of funds essentially eliminates the beta anomaly.Discussant(s)
Adriano Rampini
,
Duke University
Markus Pelger
,
Stanford University
Stefano Pegoraro
,
University of Notre Dame
Andrea Buffa
,
University of Colorado Boulder
Anna Pavlova
,
London Business School
JEL Classifications
- G1 - Asset Markets and Pricing