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Motivation

Option Returns and Individual Stock Volatility Jie Cao, Chinese University of Hong Kong Bing Han, University of Texas at Austin Presented by Jie Cao 2010 NTU International Conference on Finance December 10, 2010. Motivation. Equity o ption market is big and grows very fast

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Motivation

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  1. Option Returns and Individual Stock VolatilityJie Cao, Chinese University of Hong KongBing Han, University of Texas at Austin Presented by Jie Cao2010 NTU International Conference on FinanceDecember 10, 2010

  2. Motivation • Equity option market is big and grows very fast • Most option research focuses on pricing options relative to the underlying stock, given the stock price • But not much is known about the returns investors can expect to receive from holding various stock options • We examine the cross-sectional determinants of expected equity option returns • Focus on the role of volatility • Study delta-hedged options (control for the price movement of underlying stocks), which are most sensitive to volatility risk • Use a large sample of individual stock options rather than index options

  3. Related Literature • Index options • Coval and Shumway (2001) study index option returns and argue that some other systematic factor, such as stochastic volatility, might be priced by the market • Following stochastic volatility model, Bakshi and Kapadia (2003a) examine delta-hedged returns of S&P 500 index options, and find a negative market volatility risk premium (time-series tests) • Individual options • Bakshi and Kapadia (2003b) study 25 individual options, and argue that 1) individual stock option prices also embed a negative market volatility risk premium, 2) but idiosyncratic volatility is not priced • Duarte and Jones (2007) study individual options, and find that beta to the market volatility risk conditionally matters in the cross-section • With a large sample, we study how total and idiosyncratic volatility affect the cross-sectional delta-hedged individual option returns

  4. Daily Rebalanced Delta-Hedged Gains • Delta-hedged gain: following Bakshi and Kapadia (2003a) • Changes in the value of a portfolio of a long call position, and hedged by a short position in the underlying stock, with the net investment earning risk-free rate • Discrete version: daily rebalancing for empirical analysis • Normalized: the gain is scaled by stock (or option) price

  5. Under Stochastic Volatility Model • Under Black-Scholes model: • Under Stochastic Volatility model : • Volatility follows: • Bakshi and Kapadia (2003a) show: • is the market price of volatility risk • Assuming (Heston (1993)), is linear in total volatility

  6. Data and Sample • Data and Sample • Options daily data from Option-Metrics • Underlying stock data obtained from CRSP, COMPUSTAT • Each month, construct a cross-section of at-the-money options with a common short-term maturity (around 50 calendar days) • Apply several filters to ensure data quality: exclude options if • Paying dividend, or violate no-arbitrage conditions • Bid = 0, or (Bid + Ask)/2 < 1/8, or zero volume • Moneyness (S/K) < 0.8 or > 1.2, or non-common maturity • Final sample: Jan 1996 – Dec 2006 • 5,255 stocks, average 1,394 per month • 159,346 obs for call and 139,285 obs for put

  7. Summary Statistics

  8. Delta-Hedged Gains and Volatility • Fama-MacBeth Regressions • Dependent variable: delta-hedged gain till maturity / stock price • Stock volatility • Total volatility: VOL -- s.t.d of previous month daily returns • Idiosyncratic volatility: IVOL -- AHXZ (2006): FF-3 factors • Systematic volatility measures • SysVOL = sqrt (VOL2 - IVOL2) • Betas to MKTRF, SMB, HML, and change in VIX • Key results • The delta-hedged gains decrease with total volatility • The result is driven entirely by idiosyncratic volatility • Consistent with stochastic volatility model prediction

  9. Determinants of Delta-Hedged Option Returns: Volatility

  10. Robustness • The results hold after controlling • for vega (moneyness) • for contemporaneous stock returns • for jump risk – option implied Skewness & Kurtosis • for volatility-related mispricing (Goyal and Saretto (2009)) • for past stock returns over different horizons • for stock liquidity and transaction costs • for option demand pressure and transaction costs • The results hold using alternative volatility measures: • Expected idiosyncratic volatility from EGARCH (1,1) • Implied total volatility • The results hold for delta-hedged gain till month-end, or scaled by the option price • The results hold for both call options and put options

  11. More Controls

  12. Put Options

  13. Monthly Rebalanced Delta-Hedged Returns • Daily rebalancing is very costly in practice • Delta-hedged gain scaled by stock or option price is not a proper measure for return • Construct a return measure from covered call writing • At the beginning of each month, sell one call and buy delta-unit stocks: cost Vt = (∆t*S t - C t)>0 • At the end of each month buy the call and sell the stocks: gain Vt+1 =(∆t*S t+1 - C t+1) • Rt = (Vt+1 - Vt )/ Vt • R should increase with total or idiosyncratic volatility in the cross-section

  14. Returns of Covered Call Writing Sorted on Volatility

  15. Portfolio Returns Sorted on VOL: Subsamples

  16. Time-Series of the (5-1) Spreads Sorted on VOL 1996-1999 2000-2003 2004-2006

  17. Impact of Transaction Costs and Liquidity • Option bid-ask spread is relatively high • The effective bid-ask spread (ESPR) is a subset of quoted bid-ask spread (QSPR)

  18. Economic Interpretations of Negative Risk Premium • Compensation for option sellers • Volatility premium could be compensation for option sellers who are unable to eliminate volatility risk through hedging and diversification • Even if they could perfectly hedge the option’s exposure to underlying stock, they are exposed to volatility risk, which are higher for more volatile stocks • Options on high volatility stocks are overvalued • These options attract investors who like to gamble or who prefer positive skewness in payoffs • Overconfident investors overreact to recent increase in volatility of these stocks

  19. Conclusion • This paper provides a comprehensive study of individual option returns, after delta-hedging their exposure to the underlying stock returns • The average delta-hedged stock option returns are negative • These returns decrease with the volatility of the underlying stock. The result is driven by idiosyncratic volatility • Individual stock options embed a negative premium for the underlying stock’s stochastic volatility • This premium could be compensation for option sellers, or reflect the overvaluation created by option investors

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