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Equity Options

Can investors/speculators use equity options to boost return through buying and selling leverage (calls), and/or buying and selling insurance (puts)? If so, which strategies work best? These blog entries relate to trading equity options.

Option Valuation

How do market makers and sophisticated investors/traders determine option value? In his July 2019 essay entitled “Trading Volatility”, Emanuel Derman outlines the history and shortcomings of option valuation as described by the Black-Scholes model, which estimates the value of an option on an asset as a function of the asset’s price and volatility. He also addresses extensions of this model. Based on mathematical derivations and his knowledge of option markets, he concludes that:

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Best U.S. Equity Market Hedge Strategy?

What steps should investors consider to mitigate impact of inevitable large U.S. stock market corrections? In their May 2019 paper entitled “The Best of Strategies for the Worst of Times: Can Portfolios be Crisis Proofed?”, Campbell Harvey, Edward Hoyle, Sandy Rattray, Matthew Sargaison, Dan Taylor and Otto Van Hemert compare performances of an array of defensive strategies with focus on the eight worst drawdowns (deeper than -15%) and three NBER recessions during 1985 through 2018, including:

  1. Rolling near S&P 500 Index put options, measured via the CBOE S&P 500 PutWrite Index.
  2. Credit protection portfolio that is each day long (short) beta-adjusted returns of duration-matched U.S. Treasury futures (BofAML US Corp Master Total Return Index), scaled retrospectively to 10% full-sample volatility.
  3. 10-year U.S. Treasury notes (T-notes).
  4. Gold futures.
  5. Multi-class time-series (intrinsic or absolute) momentum portfolios applied to 50 futures contract series and reformed monthly, with:
    • Momentum measured for 1-month, 3-month and 12-month lookback intervals.
    • Risk adjustment by dividing momentum score by the standard deviation of security returns.
    • Risk allocations of 25% to currencies, 25% to equity indexes, 25% to bonds and 8.3% to each of agricultural products, energies and metals. Within each group, markets have equal risk allocations.
    • Overall scaling retrospectively to 10% full-sample volatility.
    • With or without long equity positions.
  6. Beta-neutral factor portfolios that are each day long (short) stocks of the highest (lowest) quality large-capitalization and mid-capitalization U.S. firms, based on profitability, growth, balance sheet safety and/or payout ratios.

They further test crash protection of varying allocations to the S&P 500 Index and a daily reformed hedge consisting of equal weights to: (1) a 3-month time series momentum component with no long equity positions and 0.7% annual trading frictions; and, (2) a quality factor component with 1.5% annual trading frictions. For this test, they scale retrospectively to 15% full-sample volatility. Throughout the paper, they assume cost of leverage is the risk-free rate. Using daily returns for the S&P 500 Index and inputs for the specified defensive strategies during 1985 through 2018, they find that:

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Stock Return Autocorrelations and Option Returns

Does return persistence of individual stocks predict associated option returns? In their March 2019 paper entitled “Stock Return Autocorrelations and the Cross Section of Option Returns”, Yoontae Jeon, Raymond Kan and Gang Li investigate relationships between equity option returns and return autocorrelations of underlying stocks. They consider call options, put options and straddles (long both a call and a put with the same strike price). Each month on standard option expiration date, they:

  • Measure one-step monthly stock return autocorrelations using a 36-month rolling window of monthly returns for U.S. stocks with over 20 monthly observations.
  • Rank stocks (and respective options) by autocorrelation into fifths (quintiles).
  • Construct a hedge portfolio that is long (short) the equal-weighted or market capitalization-weighted stocks in the top (bottom) quintile of autocorrelations, to calculate stock portfolio return as a control variable.
  • Construct corresponding hedge portfolios of call options, put options or straddles, limiting choices to reasonably liquid options with moneyness closest to 1.0 and time to expiration closest to 30 days. 
  • Hold these portfolios until the next standard option expiration date.

They further explore out-of-sample use of results via modified mean-variance optimization of a portfolio consisting of the S&P 500 Index, the risk-free asset and equity options with bid-ask spreads no greater than 10% of price. They size individual option positions as a function of underlying stock volatility, variance risk premium and stock return autocorrelation. They assume investor utility derives from constant relative risk aversion level 3. For the frictionless case, they base option returns on the bid-ask midpoint. For the case with frictions, they assume buys (sells) occur at the ask (bid). Using specified stock and options data during January 1996 through December 2017, they find that: Keep Reading

Sell Equity Index OTM Put Options and ATM Straddles?

Does accounting for realistic trading frictions support beliefs that equity index out-of-the money (OTM) put options and at-the-money (ATM) straddles are systematically overpriced? In their October 2018 paper entitled “Index Option Anomalies: How Real Are They?”, Michal Czerwonko and Stylianos Perrakis re-examine assumptions and data used in several high-profile studies finding that OTM put options and ATM straddles for the S&P 500 Index are overpriced, and that shorting these positions is therefore reliably profitable. They focus on the following aspects of option pricing: accounting for realistic trading frictions (bid-ask spreads); differences in pricing of same-strike price puts and calls; and, inconsistency in pricing across maturities. Using groomed intraday prices and quotes for S&P 500 Index (cash-settled) options 28, 14, and seven days to maturity during January 1990 through February 2013 (278 settlement dates), they find that:

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Equity Index Options to Exploit Stock Market Volatility Spikes?

Under what conditions should speculators buy protective equity options when they expect realized stock market volatility to increase? In their September 2018 paper entitled “Being Right is Not Enough: Buying Options to Bet on Higher Realized Volatility”, Roni Israelov and Harsha Tummala analyze the relationship between: (1) long volatility return (delta-hedged options) and same-interval changes in realized volatility; and, (2) the volatility risk premium (VRP, implied volatility minus realized volatility) and same-interval changes in realized volatility. They specify long volatility as a portfolio of cash-settled equity index options, reformed monthly, that:

  • On each options expiration date, buys one-third of a -25 delta put option, one-third of a +25 delta call option and one-sixth each of at-the-money put and call options. All options initially have about a month to expiration.
  • Each day until expiration, hedges option deltas via equity index futures. 
  • Holds the options to expiration.

They also examine sensitivity of outcome to different portfolio initiation and termination points relative to significant volatility increases. They focus on the S&P 500 Index, using VIX as implied volatility and hedging via S&P 500 Index futures, during January 1996 through December 2016. They also consider for robustness testing corresponding data for Eurostoxx 50, FTSE 100 and Nikkei 225. Using daily data as specified, they find that:

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Shorting Equity Options to Automate Portfolio Rebalancing

Can investors refine portfolio rebalancing while capturing a volatility risk premium (VRP) by systematically shorting options matched to target allocations of the underlying asset? In their October 2017 paper entitled “An Alternative Option to Portfolio Rebalancing”, Roni Israelov and Harsha Tummala explore multi-asset class portfolio rebalancing via an option selling overlay. The overlay sells out-of-the-money options such that, if stocks rise (fall), counterparties exercise call (put) options and the portfolio must sell (buy) shares. They intend their approach to counter short-term momentum exposure between rebalancings (when the portfolio is overweight winners and underweight losers) with short-term reversal exposure inherent in short options. For testing, they assume: (1) a simple 60%-40% stocks-bonds portfolio; (2) bond returns are small compared to stock returns (so only the stock allocation requires rebalancing); and, (3) option settlement via share transfer, as for SPDR S&P 500 (SPY) as the stock/option positions. They each month sell nearest out-of-the-money S&P 500 Index  call and put options across multiple economically priced strikes and update the overlay intramonth if new economically priced strikes become available. Once sold, they hold the options to expiration. Using daily S&P 500 Total Return Index returns, Barclays US Aggregate Bond Index returns and closing bid/ask quotes for S&P 500 Index options equity options (with returns calculated in excess of the risk-free rate) during 1996 through 2015, they find that:

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Aggregate Stock Option Put-Call Ratio as Market Return Predictor

Do aggregate positions in put and call options on individual stocks, as indicators of sentiment of informed traders, predict future market returns? In their July 2017 paper entitled “Stock Return Predictability: Consider Your Open Options”, Farhang Farazmand and Andre de Souza examine the power of average value-weighted put option open interest divided by average value-weighted call option open interest in individual U.S. stocks (PC-OI) to predict U.S. stock market returns. Specifically, they:

  • Compute for each stock each day total put option open interest and total call option open interest.
  • Average daily values for each stock by month and weight by market capitalization.
  • Calculate PC-OI by dividing the sum of monthly capitalization-weighted average put option open interest by the sum of monthly capitalization-weighted call option open interest.
  • Each month, relate via regression monthly PC-OI to stock market return the next three months to determine the sign of the future return coefficient.
  • Each month, create a net signal from the sum of the signs of these coefficients from the last three monthly regressions. A positive (negative) sum indicates a long (short) position in the stock market and an offsetting short (long) position in the risk-free asset.

They further test whether PC-OI predictive power concentrates in stocks with unique informativeness as represented by high idiosyncratic volatility (individual stock return volatility unexplained via regression versus market returns). For comparison, they also test their model with S&P 500 index options. Using daily open interest for options on AMEX, NYSE and NASDAQ common stocks and on the S&P 500 Index with moneyness 0.8-1.2 and maturities 30-90 days, associated stock characteristics, and contemporaneous U.S. stock market returns during January 1996 through August 2014, they find that:

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Covered Equity Index Calls Worldwide

How well do stock index covered call strategies work across markets worldwide? In their June 2017 paper entitled “Covering the World: Global Evidence on Covered Calls”, Roni Israelov, Matthew Klein and Harsha Tummala test covered call strategies for 11 global equity indexes. They measure overall returns and return contributions from equity exposure, short volatility exposure and equity timing. They also test a risk-managed covered call strategy that sells at-the-money covered calls with hedging of estimated dynamic equity exposure deviations from 0.5 (from an option pricing model) using index futures. Using call options data for the 11 equity indexes as available (all by January 2006) through September 2015, along with associated index values and futures returns, they find that: Keep Reading

Best Index Options to Sell?

Which short index options offer the best overall performance? In their June 2017 paper entitled “Which Index Options Should You Sell?”, Roni Israelov and Harsha Tummala explore return and risk properties of short delta-hedged out-of-the-money S&P 500 Index put and call options of various moneyness and maturities. They consider moneyness of -2.5 to +1.0 standard deviations relative to the forward index price. They consider maturities of one, two, three, six and 12 months. They assume daily delta-hedge rebalancing with S&P 500 Index futures to isolate volatility and time effects. They calculate average returns and estimate alphas and betas relative to S&P 500 Index returns. They then calculate three beta-adjusted risk metrics for the returns: (1) volatility; (2) stress-test losses (specified for a 20% one-day adverse S&P 500 Index move as on October 19, 1987); and, (3) 0.1% value at risk (VAR), which approximately translates to a once-in-four-years worst loss. Using daily data for S&P 500 Index options with standard monthly expiration dates (3rd Friday of the month) and for the index itself during late March 1996 through December 2015, they find that:

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Do Protective Equity Index Puts Work Well?

Is the conventional wisdom that equity index put options are effective tail risk hedges for a stock portfolio correct? In his March 2017 paper entitled “Pathetic Protection: The Elusive Benefits of Protective Puts”, Roni Israelov compares the hedging properties of put protection strategies with those of daily rebalanced stocks-cash (divested) portfolios that generate the same compound annualized return in excess of cash. He considers put protection portfolios based on: (1) the CBOE S&P 500 5% Put Protection Index (PPUT), which systematically purchases monthly put options that are 5% out of the money; and, (2) Monte Carlo simulations with and without a volatility risk premium (difference between implied and realized volatilities). For simulations, he assumes compound annualized equity return 4% with 20% annualized volatility, zero risk-free rate and dividend yield and monthly purchases of 5% out-of-the-money put options held to expiration. For simulations with a volatility risk premium, he assumes annualized implied volatility 22%. Using monthly PPUT and S&P 500 Total Return Index (SPTR) returns during July 1986 through mid-May 2016, he finds that: Keep Reading

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