Turan G. Bali1 Stephen J. Brown2
Scott Murray3 Yi Tang4
1McDonough School of Business, Georgetown University 2Stern School of Business, New York University 3College of Business Administration, University of Nebraska – Lincoln 4School of Business, Fordham University
March 30, 2015
Most Persistent Anomaly
Security Market Line is Too Flat
High β stocks generate negative abnormal returns
Low β stocks generate positive abnormal returns
Anomaly has persisted for more than 40 years
Black, Jensen, and Scholes (1972)
Blume and Friend (1973)
Fama and MacBeth (1973)
Betting Against Beta: Frazzini and Pedersen
Long low-β, short high-β portfolio generates abnormal returns
Explanation: Leverage constrained investors buy high β
Only way to increase expected return (can’t use leverage)
Pension funds, mutual funds
Alternative Explanation – Lottery Demand
We propose that lottery demand causes betting against beta phenomenon
Lottery investors want high probability of large up move
Up moves partially driven by market sensitivity
Lottery demanders likely to invest in high-β stocks
Upward (downward) price pressure on high-β (low-β) stocks
Future returns of high-β (low-β) stocks depressed (increased)
Lottery demand strong in equity markets
Bali, Cakici, and Whitelaw (2011)
Kumar (2009)
Capital Market Line
Results
Lottery Demand Explains Phenomenon
Lottery demand proxied by MAX
Average of top 5 daily returns in month
Bivariate portfolio analysis
Controlling for MAX, betting against beta disappears
No other variable explains betting against beta
Fama and MacBeth (1973) Regressions
β positively related to returns when MAX included
Orthogonal Component of β to MAX
Does not generate betting against beta phenomenon
Results
Lottery Demand is the Channel
Lottery demand falls predominantly on high-β stocks
β and MAX positively correlated in cross-section
Lottery demand generates betting against beta
Strong in high-β,MAX correlation months
Non-existent in low-β,MAX correlation months
Concentrated in low institutional holdings stocks
Lottery demand driven by retail investors – Kumar (2009)
Leverage constraints by mutual and pension funds
Aggregate lottery demand
High correlation when aggregate lottery demand high
Results
Lottery Demand Factor (FMAX)
Long High-MAX Stocks, Short Low-MAX Stocks
Proxies for returns associated with lottery investing
FMAX explains betting against beta phenomenon
Alpha of high-low β portfolio is zero when FMAX included
FMAX explains alpha of FP’s BAB factor
Alpha of BAB is zero when FMAX included in model
BAB factor cannot explain FMAX
Alpha of FMAX large and significant when BAB in model
Book-to-market ratio (BM):Fama and French (1992, 1993) Momentum (MOM):Jegadeesh and Titman (1993)
Return in months t – 11 through t – 1
Illiquidity (ILLIQ):Amihud (2002) Idiosyncratic Volatility (IVOL):Ang et al. (2006)
Variables – Risk Measures
Risk Measures
Co-skewness (COSKEW): Following Harvey and Siddique (2000) Total skewness (TSKEW): Skewness of daily returns in past year Downside beta (DRISK): Ang, Chen, Xing (2006)
Stock beta on days when market return is below average