# 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.

**May 9, 2022** - Equity Options

Do simple stock index option strategies (stock-covered calls, cash-covered puts and collars) outperform the underlying index? To investigate, we examine performances of:

- CBOE S&P 500 BuyWrite Index (BXM),CBOE S&P 500 PutWrite Index (PUT) and CBOE S&P 500 95-110 Collar Index (CLL), with S&P 500 Total Return Index (SPTR) as a benchmark.
- Invesco S&P 500 BuyWrite ETF (PBP), designed to track BXM, and WisdomTree CBOE S&P 500 PutWrite Strategy Fund (PUTW), designed to track PUT, with SPDR S&P 500 ETF Trust (SPY) as a benchmark.

We focus on monthly return statistics, compound annual growth rates (CAGR) and maximum drawdowns (MaxDD) for comparisons. Using end-of-month levels for SPTR, BXM, PUT and CLL since June 1986, total returns for SPY and PBP since December 2007 (limited by PBP) and total returns for SPY and PUTW since February 2016 (limited by PUTW), all through March 2022, *we find that:*

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**March 28, 2022** - Calendar Effects, Equity Options

Are there anomalies for U.S. stock market returns around equity option expiration (OE) days (normally the third Friday of each month, but the preceding Thursday when the market is closed on the third Friday)? To investigate, we examine close-to-close S&P 500 Index returns from five trading days before through five trading days after a moderately large sample of OE days. Using daily closing prices for the index during January 1990 through February 2022 (386 OE days), *we find that:*

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**August 19, 2021** - Commodity Futures, Equity Options, Investing Expertise

How well do derivatives traders perform, and why? In the July 2021 version of their paper entitled “Derivatives Leverage is a Double-Edged Sword”, Avanidhar Subrahmanyam, Ke Tang, Jingyuan Wang and Xuewei Yang study the performance of Chinese derivatives (futures) traders across 1,086 contracts on 51 underlying assets. They consider gross and net daily trader returns, turnover and degree of leverage implied by contracts held. They further investigate sources of profits/losses for these traders. To identify clearly skilled (unskilled) traders, they identify those in the top (bottom) 5% of Sharpe ratios who trade on at least 24 days during the first year of the sample period and isolate those with statistically extreme performance. They then analyze trading behaviors and results for these extreme performers the next two years. Using data from a major futures broker in China, including transaction histories, end-of-day holdings and account flows (injections and withdrawals) for 10,822 traders (315 institutional) during January 2014 through December 2016, *they find that:*

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**July 1, 2021** - Equity Options, Individual Investing, Investing Expertise

Overall, how do retail option traders perform compared to institutional counterparts, and what accounts for any performance difference? In their June 2021 paper entitled “Who Profits From Trading Options?”, Jianfeng Hu, Antonia Kirilova, Seongkyu Park and Doojin Ryu use account-level transaction data to examine trading styles and profitability by investor category for KOSPI 200 index options and futures. There are no restrictions in Korean derivatives markets on retail investor participation, and retail participation is high. Using anonymized account-level (153,835 domestic retail, 5,904 domestic institutional, 667 foreign institutional and 604 foreign retail) data for all KOSPI 200 index options and futures trades during January 2010 through June 2014, *they find that:*

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**April 15, 2021** - Equity Options

What is the latest evidence on attractiveness of selling covered calls or buying protective puts on the U.S. stock market? In his February 2021 paper entitled “Revisiting Covered Calls and Protective Puts: A Tale of Two Strategies”, Bryan Foltice examines raw and risk-adjusted returns from systematically selling covered calls and buying protective puts on SPDR S&P 500 ETF Trust (SPY) as a proxy for the stock market. Specifically, at the beginning of each month, he sells fully hedged calls or buys fully hedged puts on SPY with one month to expiration. He estimates option prices via the Black-Scholes option pricing model, using the CBOE VIX Index for SPY volatility and accounting for dividends. He considers a range of option moneyness, ranging from 5% out-of-the-money (OTM) to 5% in-the-money (ITM) in 1% increments. Using monthly SPY price, VIX level and risk-free rate during March 1993 through September 2020, *he finds that:*

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**December 9, 2020** - Calendar Effects, Equity Options, Momentum Investing

Do options of individual stocks exhibit momentum and seasonality patterns? In their November 2020 paper entitled “Momentum, Reversal, and Seasonality in Option Returns”, Christopher Jones, Mehdi Khorram and Haitao Mo investigate momentum and seasonality effects for options on U.S. common stocks. They focus on performance of straddles, combining a put and a call with the same strike price and expiration date. They balance needs for liquidity and sample size by requiring positive open interest during the holding period but not the momentum calculation interval. Specifically, on each monthly option expiration date, they:

- Form two straddles from near-the-money options expiring next month for each for each stock: (1) the pair with call delta closest to 0.5 for calculating momentum; and, (2) the pair with call delta closest to 0.5 and with positive open interest for both the put and the call when selected for calculating momentum portfolio return.
- Construct from these pairs zero-delta straddles using bid-ask midpoints as prices and calculate monthly straddle excess returns relative to the 1-month Treasury bill yield. This process generates about 1,600 straddles per month with average monthly excess return -5.6% and very large standard deviations.
- Calculate momentum as average monthly excess return over a specified lookback interval (rather than cumulative return, to suppress effects of return outliers).
- Rank straddle returns into equal-weighted fifths (quintiles) based on momentum and calculate average return for each quintile and for a portfolio that is long the top quintile and short the bottom quintile.

Using end-of-day open interest and bid-ask quotes for call and put options on U.S. common stocks from OptionMetric and trading data for underlying stocks during January 1996 through June 2019, *they find that:* Keep Reading

**August 28, 2020** - Equity Options

Does nominal stock price matter for associated option returns? In their May 2020 paper entitled “Cheap Options Are Expensive”, Assaf Eisdorfer, Amit Goyal and Alexei Zhdanov evaluate option returns across the range of U.S. stock prices. For each stock each month, they:

- Pick a single call option and a single put option closest to at-the-money and expiring the third Friday of the month, excluding those with zero open interest or zero trading volume to ensure liquidity.
- Sort options into tenths (deciles) based on underlying stock price.
- Construct equal-weighted delta-hedged call and put portfolios and hold to option expiration, computing returns from option quote midpoints (zero effective bid-ask spread).

Using price and characteristics data for 257,107 call options and 204,123 put options on a broad sample of U.S. common stocks during 1996 through 2017, *they find that:*

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**September 5, 2019** - Equity Options

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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**June 24, 2019** - Bonds, Equity Options, Gold, Momentum Investing, Strategic Allocation

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:

- Rolling near S&P 500 Index put options, measured via the CBOE S&P 500 PutWrite Index.
- 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.
- 10-year U.S. Treasury notes (T-notes).
- Gold futures.
- 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.

- 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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**May 15, 2019** - Equity Options, Momentum Investing

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