What Does Risk-Neutral Skewness Tell Us About Future Stock Returns? University of Miami School of Business Stan Stilger, Alex Kostakis and Ser-Huang Poon MBS 23rd March 2015, Miami Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 1 / 31
Presentation Outline Motivation and related literature This paper and our contributions Methodology and dataset Relationship between risk-neutral skewness and future stock returns Mechanism to explain this relationship Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 2 / 31
Implied Volatility Surface Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 3 / 31
Implied Volatility Slope Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 4 / 31
Implied Volatility Slope and RNS Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 5 / 31
Motivation and Related Literature Option-implied information is inherently forward-looking, embedding investors expectations under Q (Bates, 1991, Jackwerth and Rubinstein, 1996) Option prices contain information for: 1 Future stock returns Xing et al. (2010): ve relation between steepness of implied vol smirk and future stock returns Cremers and Weinbaum (2010): +ve relation between call-put implied volatility spread and future stock returns Bali and Hovakimian (2009): no relation between RN volatility and future stock returns 2 Investment strategies Kostakis et al. (2011) use option-implied dbns for market timing De Miguel et al. (2014) use option-implied moments for asset allocation Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 6 / 31
Related studies on Risk-Neutral Skewness Bali and Murray (2013) nd portfolios returns ve relation between RNS and option Bali et al. (2014) nd +ve relation between RNS and expected stock returns derived from nancial analysts price targets Conrad et al. (2013) nd ve relation between past quarter averages of daily RNS values and future realized stock returns. Justify results using standard asset pricing results for (co)skewness under P. But RNS is extracted under Q )arguments not applicable. Rehman and Vilkov (2012) nd +ve relation between latest available RNS values and future realized stock returns. Conclusion: Highly ve RNS is a proxy for overvaluation. Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 7 / 31
This paper We nd signi cant +ve relation between RNS and future realized stock returns during 1996-2012. Long quintile with highest RNS/ short quintile with lowest RNS stocks) average alpha FFC of 55 bps per month (t-stat: 2.47) Decompose RNS into its systematic and unsystematic components and nd that the latter drives the +ve relation. Propose a mechanism to explain why/when highly ve RNS signals future stock underperformance and why the market does not immediately correct this mispricing. Mechanism consistent with demand-based option pricing framework (Bollen and Whaley, 2004, Garleanu et al., 2009). Stock overvaluation and short selling constraints are necessary conditions for ve RNS to signal underperformance. Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 8 / 31
Extracting Risk-Neutral Skewness Use model-free methodology of Bakshi et al. (2003) to calculate RN moments for the return distributrion of stock i using OTM call and put option prices. Approach based on the result of Bakshi and Madan (2000) that any (twice di erentiable) payo function H(S) can be spanned by a portfolio of zero-coupon bond, stock, and a continuum of OTM call and put options. From the above result, one can nd the prices V t, W t, and X t of τ-maturity volatility, cubic and quartic contracts with payo s equal to R (t, τ) 2, R (t, τ) 3, and R (t, τ) 4, respectively, as a function of OTM put and call prices (see Appendix A). Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 9 / 31
Extracting Risk-Neutral Skewness In this case, Bakshi et al. (2003) show that RNS is given by: RNS i,t (τ) = E Q t E Q t R (t, τ) E Q t 3 [R (t, τ)] 2 3/2 R (t, τ) Et Q [R (t, τ)] = er τ (W t (τ) 3µ t (τ) V t (τ)) + 2µ t (τ) 3 he r τ V t (τ) µ t (τ) 2i, where 3/2 µ t (τ) = e r τ 1 e r τ 2 V t (τ) e r τ 6 W t (τ) e r τ 24 X t (τ) Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 10 / 31
Extracting Risk-Neutral Skewness Formulae based on a continuum of OTM option prices (not available) We require 2 OTM put and 2 OTM call options per stock for a given maturity on each trading day to calculate RN moments Interpolate implied volatility between lowest and highest available moneyness using piecewise cubic Hermite polynomial Extrapolate implied volatility outside the lowest and highest available moneyness using boundaries values. Moneyness range: 1/3 to 3. Convert back to option prices using B-S and compute RN moments via numerical integration Robustness check: Alternatively use trapezoidal approximation of Dennis and Mayhew (2002) Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 11 / 31
Dataset Daily option data with maturities between 10 and 180 days from OptionMetrics during 1996-2012 Discard options with zero open interest, negative strike, zero bid price and prices < $0.50 Filter out rms with < 2 OTM put/ call options for a given maturity Choose the set of OTM options with shortest maturity Discard rms with illiquid options (<10 daily RNS obs in a month) Benchmark results: 128,960 RNS observations on the last trading day of the month CRSP, Compustat and ExecuComp used for rm characteristics Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 12 / 31
Descriptive statistics Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 13 / 31
RNS-sorted Portfolios: Characteristics Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 14 / 31
RNS-sorted Portfolios: Performance Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 15 / 31
Robustness checks Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 16 / 31
Fama-MacBeth regressions Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 17 / 31
Further results Nonsynchroneity bias (Battalio and Schultz, 2006) RNS may not be available before the close of the stock market Compute monthly portfolio returns using opening prices on the rst trading day of the post-ranking month Benchmark results are robust Long-term performance of t sorted RNS portfolios Compute portfolio returns in month t + k, k = 1, 2,..., 6. Spread is signi cant only in month t + 1 Market corrects RNS-signalled temporary mispricing within 1 month Examine the impact of option liquidity Additional option liquidity controls Exclude RNS estimates from low volume/ open interest OTM options Examine the impact of short sale ban period (Sep-Oct 2008) Exclude the short sale ban period/ post-aug 2008 sample Interact RNS with dummy for rms that were subject to the ban Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 18 / 31
Decomposing RNS Following Bakshi et al. (2003), we further decompose RNS into its systematic and unsystematic components. Starting from the single-index model under Q, Bakshi et al. (2003) show that: RNS i,d,systematic = b 3 i RNV 3/2 m,d RNS m,d /RNV 3/2 i,d, where b i is the risk-neutral beta of stock i, and RNS i,d,unsystematic = RNS i,d RNS i,d,systematic Construct portfolios on the basis of systematic and unsystematic RNS estimates on the last trading day of month t. Alternative decomposition into RN Coskewness and idiosyncratic RNS Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 19 / 31
Systematic RNS-sorted portfolios Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 20 / 31
Unsystematic RNS-sorted portfolios Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 21 / 31
Conjectured Mechanism 1 Why portfolios with highly ve RNS stocks subsequently underperform? 2 Do all stocks with highly ve RNS subsequently underperform? If not, which? 3 Why the market does not correct this pattern? Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 22 / 31
Conjectured Mechanism Certain stocks seem relatively overvalued but are too costly/ risky to sell short, hindering the price correction mechanism (Miller, 1977) ) Investors resort to the options market buying (selling) OTM puts (calls) and/or constructing synthetic short stock positions to hedge their exposure/ trade on their pessimistic expectations ) Drive up (down) OTM puts (calls) prices, leading to highly negative RNS values, since risk-averse market makers cannot perfectly hedge their positions (Garleanu et al., 2009) ) RNS contains information not already embedded in stock prices, consistent with the sequential trade model of Easley et al. (1998) and the noisy rational expectations model of An et al. (2014) Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 23 / 31
Hedging Motive and Risk-Neutral Skewness Stocks with stronger hedging motive exhibit more ve RNS Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 24 / 31
Proxies for relative overvaluation Reasons for relative stock overvaluation: Over-optimistic growth expectations/ investors with strong preference for lottery-like payo s drive up their prices Such stocks may subsequently underperform if the price correction mechanism reverses overvaluation Proxies: 1 EIS P : Expected Idiosyncratic Skewness of realized stock returns (Boyer et al., 2011) 2 Max: Maximum daily stock return in past month (Bali et al., 2011) 3 Probability of a Jackpot (>100%) stock return over next year (Conrad et al., 2014) Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 25 / 31
The role of overvaluation: Conditional sorts Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 26 / 31
The role of overvaluation: Reverse conditional sorts Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 27 / 31
The role of short selling constraints: Conditional sorts Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 28 / 31
Short selling constraints: Reverse conditional sorts Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 29 / 31
Trivariate independent portfolio sorts Overvaluation proxy EIS P Max Jackpot Short selling constraints proxy ESF RSI IVol P ESF RSI IVol P ESF RSI IVol P P1 RNS L & Overvaluation L & Constraints L 0.13 (0.89) 0.17 (1.30) 0.03 (0.28) 0.19 (1.52) 0.21* (1.75) 0.07 (0.65) 0.05 (0.42) 0.11 (0.93) 0.03 (0.31) P2 RNS L & Overvaluation L & Constraints H 0.27 ( 1.34) 0.35* ( 1.81) 0.10 ( 0.41) 0.30* ( 1.71) 0.36* ( 1.89) 0.00 ( 0.02) 0.35* ( 1.66) 0.63*** ( 3.01) 0.05 (0.14) P3 RNS L & Overvaluation H & Constraints L 0.05 ( 0.28) 0.15 (0.99) 0.03 ( 0.20) 0.12 ( 0.73) 0.12 ( 0.71) 0.49*** ( 2.58) 0.19 (0.73) 0.29 (0.90) 0.11 ( 0.42) P4 RNS L & Overvaluation H & Constraints H 0.49** ( 2.45) 0.61*** ( 3.18) 0.87*** ( 3.48) 0.65*** ( 3.20) 0.64*** ( 3.33) 0.76*** ( 2.73) 0.63*** ( 3.15) 0.57*** ( 2.89) 0.66** ( 2.46) P5 RNS H & Overvaluation L & Constraints L 0.30 (1.52) 0.32 (1.58) 0.48*** (3.26) 0.50*** (2.76) 0.52*** (2.73) 0.36** (2.50) 0.40** (2.03) 0.41* (1.95) 0.26 (1.58) P6 RNS H & Overvaluation L & Constraints H 0.15 (0.65) 0.16 (0.70) 0.07 (0.27) 0.09 (0.41) 0.12 (0.65) 0.31 (1.10) 0.09 (0.33) 0.00 ( 0.02) 0.07 ( 0.22) P7 RNS H & Overvaluation H & Constraints L 0.36 (1.60) 0.11 (0.43) 0.27* (1.65) 0.12 (0.54) 0.07 (0.28) 0.06 (0.26) 0.31 (1.15) 0.40 (1.35) 0.30 (1.19) P8 RNS H & Overvaluation H & Constraints H 0.41* ( 1.85) 0.22 ( 1.09) 0.28 ( 1.23) 0.47** ( 2.12) 0.38* ( 1.80) 0.31 ( 1.31) 0.37 ( 1.63) 0.31 ( 1.40) 0.07 ( 0.29) Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 30 / 31
Conclusions We document a signi cantly +ve relation between RNS on the last trading day of the month and future stock returns This relation is mainly driven by the underperformance of stocks with highly ve RNS values However, RNS per se is not a good proxy for overvaluation as not all highly ve RNS stocks subsequently underperform Propose a "limits-to-arbitrage" mechanism to explain this pattern: For stocks perceived as overvalued but costly/ risky to sell short ) Investors resort to options market to hedge/ speculate but their trades have an impact on put/call prices driving down RNS ) Stocks with highly ve RNS, relatively overvalued and hard to sell short subsequently underperform Option prices contain information that is not embedded in stock prices ) fruitful research agenda Alex Kostakis (MBS) RNS and Stock Returns 23rd March 2015, Miami 31 / 31