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1/19 Motivation Framework Data Regressions Portfolio Sorts Conclusion 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

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2/19 Motivation Framework Data Regressions Portfolio Sorts Conclusion 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

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3/19 Motivation Framework Data Regressions Portfolio Sorts Conclusion 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

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4/19 Motivation Framework Data Regressions Portfolio Sorts Conclusion 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

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5/19 Motivation Framework Data Regressions Portfolio Sorts Conclusion 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 Under Stochastic Volatility Model

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6/19 Motivation Framework Data Regressions Portfolio Sorts Conclusion 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) 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

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7/19 Motivation Framework Data Regressions Portfolio Sorts Conclusion Summary Statistics

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8/19 Motivation Framework Data Regressions Portfolio Sorts Conclusion 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 (VOL 2 - IVOL 2 ) 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

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9/19 Motivation Framework Data Regressions Portfolio Sorts Conclusion Determinants of Delta-Hedged Option Returns: Volatility

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10/19 Motivation Framework Data Regressions Portfolio Sorts Conclusion 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

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11/19 Motivation Framework Data Regressions Portfolio Sorts Conclusion More Controls

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12/19 Motivation Framework Data Regressions Portfolio Sorts Conclusion Put Options

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13/19 Motivation Framework Data Regressions Portfolio Sorts Conclusion 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 V t = (∆ t *S t - C t )>0 At the end of each month buy the call and sell the stocks: gain V t+1 =(∆ t *S t+1 - C t+1 ) R t = (V t+1 - V t )/ V t R should increase with total or idiosyncratic volatility in the cross- section

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14/19 Motivation Framework Data Regressions Portfolio Sorts Conclusion Returns of Covered Call Writing Sorted on Volatility

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15/19 Motivation Framework Data Regressions Portfolio Sorts Conclusion Portfolio Returns Sorted on VOL: Subsamples

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16/19 Motivation Framework Data Regressions Portfolio Sorts Conclusion Time-Series of the (5-1) Spreads Sorted on VOL 1996-19992004-20062000-2003

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17/19 Motivation Framework Data Regressions Portfolio Sorts Conclusion 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)

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18/19 Motivation Framework Data Regressions Portfolio Sorts Conclusion 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

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19/19 Motivation Framework Data Regressions Portfolio Sorts Conclusion 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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McGraw-Hill/Irwin Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 21 Option Valuation.

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