# 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.

**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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**May 19, 2021** - Equity Options

Is systematically selling covered call options on equity indexes, as implemented by exchange-traded funds (ETF), attractive? To investigate, we consider four equity covered call ETFs:

- Invesco S&P 500 BuyWrite (PBP) – seeks to track the CBOE S&P 500 BuyWrite Index (BXM).
- Global X S&P 500 Covered Call (XYLD) – seeks to track BXM.
- Global X NASDAQ 100 Covered Call (QYLD) – seeks to track the CBOE Nasdaq-100 BuyWrite V2 Index (BXNT). We use CBOE NASDAQ-100 BuyWrite Index (BXN) based on availability of historical data.
- First Trust BuyWrite Income (FTHI) – holds U.S. stocks of all market capitalizations and sells at-the-money to slightly out-of-the-money covered calls on the S&P 500 Index up to 20% of fund assets, laddered with expirations of less than one year (we use BXM as a benchmark).

We focus on average monthly return, standard deviation of monthly returns, compound annual growth rate (CAGR) and maximum drawdown (MaxDD) based on monthly data. We consider SPDR S&P 500 (SPY) and Invesco QQQ Trust (QQQ) as underlying stock index proxies. Using monthly dividend-adjusted returns for the four covered call ETFs since inceptions and for all benchmarks/underlying index proxies through April 2021, *we find that:* Keep Reading

**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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**August 14, 2020** - Equity Options

Is systematically selling equity put options, as implemented by exchange-traded funds (ETF), attractive? To investigate, we consider four equity put-write ETFs, two dead and two living:

- US Equity High Volatility Put Write (HVPW) – oriented toward individual stocks (dead).
- ALPS Enhanced Put Write Strategy (PUTX) – index-oriented (dead).
- WisdomTree CBOE S&P500 PutWriteStrat (PUTW) – index-oriented (living).
- BMO US Put Write (ZPW.TO) – oriented toward individual stocks (living).

Because available samples are short, we focus on daily return correlation with SPY, average daily return, standard deviation of daily returns and daily reward/risk (average daily return divided by standard deviation of daily returns). We also look at compound annual growth rates (CAGR) and maximum drawdowns (MaxDD) based on daily data. We consider SPDR S&P 500 (SPY) and CBOE S&P 500 PutWrite Index (PUT) as benchmarks. Using daily returns for the four ETFs as available through late July 2020, and contemporaneous daily returns for SPY and PUT, *we find that:* Keep Reading

**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

**December 19, 2018** - Equity Options

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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