# 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.

**December 1, 2017** - Equity Options, Strategic Allocation, Volatility Effects

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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**August 10, 2017** - Equity Options, Equity Premium

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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**July 19, 2017** - Equity Options

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

**July 18, 2017** - Equity Options

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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**April 13, 2017** - Equity Options

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

**March 21, 2017** - Equity Options, Momentum Investing

Are strategies that exploit return autocorrelation good places to look for complementary (diversifying) return streams? In the March 2017 version of their paper entitled “Momentum and Covered Calls almost Everywhere”, Stephen Choi, Gil-Lyeol Jeong and Hogun Park examine trend following and covered call strategies at the asset class level both separately and in combination. Their asset class universe consists of three equity indexes, three bond indexes, three commodity indexes and one real estate investment trust (REIT) index. Their trend following (or time series momentum) strategy, which exploits positive autocorrelation of monthly index returns, is long (short) an index when its end-of-month level is above (below) its 12-month simple moving average. Their covered call strategy, which exploits negative autocorrelation (reversion) of index returns, is continuous, such as specified for the CBOE S&P 500 BuyWrite Index. They compare trend following and covered call strategies, separately and in combination, with buy-and-hold for single-class indexes and for multi-class portfolios of indexes. They consider three ways to construct multi-class portfolios (see “Tests of Strategic Allocations Based on Risk Metrics”): (1) maximum diversification (MDR), which maximizes the ratio of the sum of volatilities for individual assets divided by overall portfolio volatility; (2) equal risk contribution (ERC), a form of risk parity with adjustments for correlation; and, (3) equal weight (EW). They rebalance these portfolios quarterly, with volatility/correlation inputs for MDR and ERC based on a 3-year rolling window of historical data. They focus portfolio testing for only 10 years (2007-2016) based on availability of data for covered call indexes. Using the specified data as available from the end of 1971 through 2016, *they find that:* Keep Reading

**March 2, 2017** - Equity Options, Volatility Effects

Does option-implied correlation, a measure of the expected average correlation between a stock index and its components over a specified horizon, predict stock market behavior? In their January 2017 paper entitled “Option-Implied Correlations, Factor Models, and Market Risk”, Adrian Buss, Lorenzo Schoenleber and Grigory Vilkov examine option-implied correlation as a stock market return predictor. They consider expected average correlations between:

- Major U.S. stock indexes (S&P 500, S&P 100 and Dow Jones Industrial Average) and their respective component stocks.
- Major U.S. stock indexes the nine Select Sector SPDR exchange-traded funds (ETF).
- The nine Select Sector SPDR ETFs and their respective component stocks.

They calculate a correlation risk premium (CRP) as the implied average correlation minus realized average correlation measured over the past month, quarter or year. For comparison, they also calculate variance risk premium (VRP) as the difference between option-implied and realized return variances. Using daily returns for the specified indexes and ETFs (and component stocks of all) and for associated near-the-money options with 30, 91 and 365 days to maturity since January 1996 for S&P 500 and S&P 100 index, since October 1997 for DJIA and since mid-December 1998 for sector ETFs, all through August 2015, *they find that:* Keep Reading

**February 23, 2017** - Equity Options, Short Selling

“When to Sell Equity Index Put Options” summarizes research finding that the “insurance” premium from systematically selling equity index out-of-the-money (OTM) put options concentrates during the last few days before expiration. An ancillary finding is that a similar, though weaker and more volatile, pattern holds for selling at-the-month (ATM) put options. To test the general finding, we therefore look at the monthly return pattern for the CBOE S&P 500 PutWrite Index (PUT). PUT sells a sequence of one-month, fully collateralized (cash covered) ATM S&P 500 Index put options and holds these options to expiration (cash settlement). Per the referenced research, PUT gains should noticeably concentrate in the week before monthly option expiration. Using daily levels of PUT during mid-July 1986 through mid-February 2017, *we find that:* Keep Reading

**February 22, 2017** - Equity Options, Short Selling

Can speculators squeeze the “insurance” premium from shorting equity index put options in just the few days before expiration? In their January 2017 paper entitled “The Timing of Option Returns”, Adriano Tosi and Alexandre Ziegler investigate the timing of returns from shorting out-of-the-money (OTM) S&P 500 Index put options. Specifically, they compute daily excess returns (accruing return on cash for open short positions) for the two front contracts (“front-month” and “back-month”) up through expiration. They translate findings into strategies that open equally weighted short positions in the most liquid OTM puts a certain number of days before expiration and hold to the cash-settled expiration. They also consider delta-hedged positions via long S&P 500 Index futures. In most calculations, they account for market frictions by opening (closing) short positions at the bid (ask). Using daily data for S&P 500 Index levels, options and futures, and contemporaneous stock and option pricing model factors, as available during January 1996 through August 2015, *they find that:* Keep Reading

**December 15, 2016** - Calendar Effects, Equity Options

Do retail investors tend to underprice equity options in monthly series when the interval between expirations from third Friday to third Friday is five weeks instead of the more frequent (65% versus 35%) four weeks? In their November 2016 paper entitled “Inattention in the Options Market”, Assaf Eisdorfer, Ronnie Sadka and Alexei Zhdanov examine differences in U.S. equity option return behaviors for “months” with five weeks versus four weeks. They focus on stocks and exchange-traded funds (ETFs) with liquid options (relatively large size and high institutional ownership) and exclude options not expiring on the third Friday. Specifically, they each month on the third Friday form equally weighted portfolios of one-month-to-expiration, at-the-money long straddles (call and put with same strike price), delta-hedged calls and delta-hedged puts (both short the underlying stocks) and hold to maturity on the third Friday of the next month. They also run regressions of average weekly returns for these portfolios versus expiration interval and several control variables found in prior research to affect option returns (index option return, gap between implied and historical volatilities, return skewness and kurtosis, firm size, firm book-to-market ratio, past stock return and idiosyncratic volatility. Using daily returns (from closing bid-ask midpoints for options) for the specified options and underlying stocks/ETFs during 1996 through 2014, *they find that:* Keep Reading