Scott Murray Presentation

Betting against Beta or Demand for Lottery

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

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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

Data Sources

CRSP

  • Daily and monthly stock data

Compustat

  • Balance sheet data

Kenneth French’s Data Library

  • Daily and monthly factor returns

Global Insight

  • LIBOR and U.S. Treasury bill yields

Pastor and Stambaugh (2003) Liquidity Factor

  • Lubos Pastor’s website

Institutional Holdings Data

  • Thomson-Reuters Institutional Holdings (13F) database

Variables – Beta, Lottery Demand, Returns

Beta, Lottery Demand, and Returns

Beta (β)

  • One-factor market model regression
  • 12-month’s of daily return data
  • Require minimum of 200 daily return observations

Lottery demand (MAX)

  • Average of 5 highest daily returns in past month

Monthly stock excess returns

  • Adjusted for delisting following Shumway (1997)

Variables – Firm Characteristics

Firm Characteristics

Market Capitalization (MKTCAP)

  • Size is log of MktCap (in millions)

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

Tail beta (TRISK): Kelly, Jiang (2013), Ruenzi, Weigert (2013)

  • Stock beta on days in bottom 10% of market returns

We require minimum of 200 daily return observations in past year for each of the risk variables

Variables – Funding Liquidity Measures

Funding Liquidity Measures

TED spread sensitivity (βTED

  • TED spread is three-month LIBOR rate – 3-month T-bill rate

Sensitivity to TED spread volatility (βVOLTED, 1979-2012)

  • VOLTED is standard deviation of daily TED spreads in month

T-bill rate sensitivity (βTBILL)

  • TBILL is 3-month T-bill rate

Financial sector leverage sensitivity (βFLEV )

  • FLEV is financial sector total assets / market value of equity

Calculated using 5 years of monthly data (minimum 24 months)

Sample

Monthly Sample, Aug. 1963 – Dec. 2012

  • 593 months
  • U.S. based common stocks
  • Traded on NYSE/AMEX/Nasdaq
  • Price at end of previous month ≥ $5

Univariate Portfolios Sorted on β

Excess Returns and 4-Factor Alphas

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High-Low β portfolio generates negative alpha

  • -0.51% per month
  • Similar to FP (0.55% per month)
  • Both high and low β portfolios generate significant alpha

Univariate Portfolio Firm Characteristics

Average Firm Characteristics

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  • MAX, MKTCAP, MOM, IVOL positively related to β


  • BM, ILLIQ negatively related to β


Univariate Portfolio Risk Measures

Average Risk Measures

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  • COSKEW, DRISK, TRISK positively related to β


  • TSKEW negatively related to β


Univariate Portfolio Funding Liquidity Measures

Average Funding Liquidity Measures

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  • βTED and βVOLTED positively related to β


  • βTBILL and βFLEV negatively related to β


Univariate Portfolios Sorted on MAX

Excess Returns and 4-Factor Alphas

  • Portfolios Sorted on MAX

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High-Low MAX generates negative returns and alpha

  • Average return is -1.15% per month
  • FFC4 alpha -1.40% per month
  • Both high and low MAX portfolios generate significant alpha

Bivariate Portfolios Procedure

Bivariate Dependent Sort Portfolio Analysis

Sort first on control variable

  • Firm characteristic, risk measure, or funding liquidity measure Then sort on β
  • Generates dispersion in β, holds first sort variable constant

Table reports excess return for β decile portfolios

  • Average across all deciles of control variable
  • Results show conditional relation between β and future returns

Bivariate Portfolios – Control for Firm Characteristics

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  • Controlling for MAX explains the betting against beta effect
  • Other firm charactersistics fail to explain phenomenon

Bivariate Portfolios – Control for Risk

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  • Risk fails to explain betting against beta phenomenon

Bivariate Portfolios – Control for Funding Liquidity

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  • Funding liquidity sensitivity fails to explain betting against beta phenomenon

Fama-MacBeth (1973) Regressions

Regressions with and without MAX

  • Specification indicated at bottom
  • Full results on next slide

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  • MAX included ! β positively related to future stock returns

Full Fama-MacBeth (1973) Regression Results

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Bivariate Independent Sort Portfolios

Sort Independently on β and MAX

  • High-Low β portfolio gives returns driven by β
    • Conditional on MAX
  • High-Low MAX portfolio gives returns driven by MAX
    • Conditional on β
  • Results on next slide

Results

MAX explains betting against beta effect

  • High-Low β portfolios have insignificant alphas

Lottery demand effect persists after controlling for β

  • High-Low MAX portfolios have large and significant alphas

Bivariate Independent Sort Portfolio Returns

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Univariate β⊥MAX Portfolio Excess Returns

β⊥MAX is portion of β that is orthogonal to MAX

  • Run cross-sectional regression of β on MAX
  • β⊥MAX is intercept plus residual

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β⊥MAX unrelated to returns

  • High-Low alpha of 0.05% small and insignificant
  • MAX explains betting against beta phenomenon

Univariate MAX⊥β Portfolio Excess Returns

MAX⊥β is portion of MAX that is orthogonal to β

  • Run cross-sectional regression of MAX on β
  • MAX⊥β is intercept plus residual

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MAX⊥β negatively related to returns

  • High-Low alpha of -1.44% large and significant
    • Similar to unconditional result (FFC4 α = -1.40%)
  • β fails to explain lottery demand phenomenon

High and Low β, MAX Correlation Months

Univariate Portfolios for Months with High and Low Correlation Between β and MAX:ρβ;MAX

  • Median cross-sectional correlation is 0.29
  • Low correlation months: correlation < median
  • High correlation months: correlation > median
  • Correlation measured during portfolio formation month
  • Returns from month after measured correlation

High and Low β, MAX Correlation – β Portfolios

Univariate Portfolios Sorted on β

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  • Betting against beta effect driven by high correlation months
  • Phenomenon does not exist in low correlation months

High and Low β, MAX Correlation – MAX Portfolios

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  • Lottery demand effect present in both correlation regimes
  • Effect not driven by relation between MAX and β

Institutional Holdings and Betting against Beta

Bivariate Portfolios Sorted on INST then β

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  • Betting against beta only works in low INST stocks
  • Not held by mutual funds, pension funds, etc.

Institutional Holdings and Lottery Demand

Bivariate Portfolios Sorted on INST then MAX

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  • Lottery demand stronger in low INST stocks
  • Consistent with retail phenomenon

Lottery Demand Factor

Lottery Demand Factor (FMAX)

  • Sort stocks into 2 market capitalization groups
    • Breakpoint is median NYSE market capitalization
  • Independently sort stocks into 3 MAX groups
    • Breakpoints are 30th and 70th percentiles of MAX
    • Calculated using all NYSE/AMEX/Nasdaq stocks
  • FMAX factor is average return of 2 high MAX portfolios
  • minus average return of 2 low MAX portfolios

FMAX Factor Returns

  • -0.54% average monthly returns
  • 4.83% monthly return standard deviation
  • Newey and West (1987) t-statistic = -2.55

Factor Analysis of High-Low β Portfolio

Factor Sensitivities Using 4 Different Factor Models

  • PS is Pastor and Stambaugh (2003) liquidity factor
    • Only available 1968 – 2011

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Lottery demand factor explains alpha of High-Low β portfolio

β Decile Portfolio Alphas

Alphas of β Sorted Decile Portfolios

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FMAX explains alpha of high-β and low-β portfolios

BAB Factor

BAB Factor

  • Return of long-short beta portfolio
    • Long stocks with low beta
    • Short stocks with high beta
  • Breakpoint is median beta
  • Weights determined by distance from median
    • More extreme betas have higher weight
  • Positive abnormal returns using standard factor models
  • Data from Lasse Pedersen’s website
    • Covers August 1963 – March 2012

BAB Factor Sensitivities

Factor Analysis of BAB Factor Returns

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FMAX factor explains returns of BAB factor

FMAX Factor Sensitivities

Factor Analysis of FMAX Factor Returns

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FMAX factor returns not explained by BAB factor

Proxy for Risk-Factor Sensitivity?

Does MAX capture a factor sensitivity?
βFMAX

  • Sensitivity to FMAX factor
  • Calculated using five years of monthly data

Proxy for Risk-Factor Sensitivity?

Does MAX capture a factor sensitivity?
βFMAX

  • Sensitivity to FMAX factor
  • Calculated using five years of monthly data

Univariate Portfolio Analysis
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Fama-MacBeth (1973) Regressions

Regressions with and without MAX

  • Full results on next slide
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  • βFMAX has no relation with future stock returns
  • β remains positively related to future stock returns
  • MAX remains negatively related to future stock returns

Full Fama-MacBeth (1973) Regression Results

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Characteristics of high-MAX and low-MAX stocks

Lottery stocks characterizations – Kumar (2009)

  • Low prices, high idiosyncratic vol, high idiosyncratic skew

Contemporaneous Characteristics
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Future Characteristics
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MAX captures lottery qualities of stocks


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