Most investors are familiar with options as powerful hedging tools suitable for protecting equity or exchange-traded fund positions. Others have explored options further by enhancing their positions through call and put writing. Regardless of the approach, another attribute of options is that they allow investors to benefit from the power of leverage, providing notional exposure to an underlying for a fraction of the actual cost.
Before fully exploring the dynamics of this exposure, let us review some important elements of options trading. A common misconception is that the price change, known as delta, of a call relative to the underlying stock happens at a 1-1 ratio (delta = 1) for all underlying prices above the call’s strike. This is only the case very near to or at expiration or at strike prices at or further out than expected volatility. The reality is that with more time to expiration, underlying prices have a greater chance of deviating from their current price levels. Accordingly, the delta of the at-the-money (ATM) contract is 0.5 (a 0.5-1 ratio price move as compared with the underlying) and why any ATM trade is also referred to as the "50 delta trade." At a high level, the combination of the option contract moving deeper in the money and closer to expiration comes together to raise the contract’s delta toward 1. Consider Figures 1 and 2 (data provided as of authoring of article).
The only major difference between these two tables is the time to expiration. Figure 1 shows contracts 45 days from expiration, while Figure 2 shows contracts 10 days from expiration. What is interesting is that while the delta of the ATM strike is roughly the same for both expirations, the 145 strike delta is almost five times as much for the 45-day expiration as it is for the 10-day expiration. Also, it seems like the market is convinced that underlying prices equal to or less than 130 are not expected to be realized regardless of time frame.
In the above example, we see how delta represents the sensitivity of changes in an options contract’s price to changes in the price of the underlying. Three other options Greeks—vega, theta and rho—represent options price sensitivity to a 1 percent change in volatility, change in time to expiration and a 1 percent change in interest rates, respectively. The fifth and final Greek is gamma, which represents the rate of change of delta as underlying prices move. Out-of-the-money (OTM) contracts tend to have low delta and high gamma, while ATM and in-the-money (ITM) contracts have increasingly higher delta and lower gamma. Delta moving 0.05 from 0.05 to 0.10 equates to gamma of 1 ("100 gamma"), whereas delta moving 0.05 from 0.5 to 0.55 equates to gamma of 0.1 ("10 gamma").
How can the Greeks assist in explaining the observations made earlier in the comparison of Figures 1 and 2? Without devolving into yet another treatise on the Black-Scholes options pricing model, suffice it to say that while the price of the underlying, volatility of price of the underlying, time-to-expiration and prevailing interest rate all contribute to options contract price discovery, the volatility of underlying price changes drives this equation. Current observed, or historical, 10- and 45-day volatilities of SPY are each approximately 15 percent, which means that over any given 10- or 45-day period in the past year, investors could reasonably expect (68 percent of the time given a normal distribution) a 15 percent movement around any given price of SPY. In considering just the left tail of this distribution, this translates to an expected 7.70 percent move, or in this case, about $10 given the current $140 SPY price. This explains the 100 delta for contracts at or below the 130 strike regardless of time-to-expiration. Given that both observed volatilities in prices of SPY are held constant when considering any of the contracts in question, as are interest rates, the only variable left is time-to-expiration. That there is more time-to-expiration explains why the delta of the August 145 call is 0.05 while the delta of the September 145 call is 0.24: There is simply more time for the unknown to become known.
Consider a 100-share position of SPY at $140 per share. This position has a notional value of $14,000. What if an investor didn’t have or didn’t want to tie up $14,000 but still wanted exposure to the price movement of 100 shares of SPY? To participate in the upside of this trade for approximately the next month would require getting exposure to the ATM SPY call expiring as close to one month from now as possible. The call in question would be the SPY 140 September call. This contract is priced at $2.93 per share and, with option contracts almost always representing notional exposure of 100 shares per contract, the contract would cost $293. As the 140 strike call has a delta of roughly 0.5, investors would expect to observe roughly half of the price movement of the underlying reflected in the price of the option. To fully replicate exposure to 100 shares of SPY, an investor would have to purchase two calls in order to bring the overall position delta up to 1.
This concept is especially important when using options to hedge a position. Consider an existing position of 100 shares of SPY. The inexperienced investor seeking to fully hedge his position would purchase one ATM put and rest easy, until the anticipated downward move occurs and he is left pondering the source of his newly minted losses. It is only through hedging the portfolio on a delta basis (delta-hedging) that it will be fully protected.
These positions are examples of debit strategies, or strategies that leave investors’ accounts with debits as they are paying for access to these positions. Credit strategies are those trades that produce a net credit in investors’ accounts as they involve the writing, or selling, of option contracts.
Writing or selling options has been a strategy that is becoming increasingly popular with investors as a way to enhance returns on their existing positions. However, writing options obligates the writer to deliver or take receipt of underlying shares if the contract is exercised or assigned. If options are written against existing positions (covered either by shares or cash), then the investor may be forced to either deliver his position against the open written call or receive (purchase from the holder of the put contract) shares to close out the written put. If options are written without any collateral, they are said to be "naked." Writing naked options can quickly lead to great financial success, as the writer could end up keeping the entire collected premium as the contracts written expire worthless, or to financial ruin as the writer could be on the hook for the difference between the underlying share price less the contract strike less collected premium. Theoretically, this obligation could be infinite.
Consider the ATM September 140 SPY call. If an investor were convinced that SPY was destined to trade off sharply, he might consider selling this call. If he is correct, he realizes a gain of $293 at expiration for each contract sold. If he is incorrect, he must deliver 100 shares of SPY at $140 per share regardless of the prevailing price. For example, if SPY is trading at $160 at any point prior to expiration, he would have to purchase shares in the open market at $160 and deliver (sell) them to the buyer of his contract for only $140. Multiply this scenario by 10 and you can see why the possibility of earning $2,930 is quickly outweighed by the possibility of having to source $160,000 and immediately lose $17,070 ($20,000-$2,930) on the transaction. This is why most brokerage houses permission their clients’ options activity in tiers, with naked option writing being one of the highest-level activities allowed.
An easy way to mitigate the risk of this lopsided trade is through a spread trade. Spread trades can take any number of forms, such as vertical spreads, horizontal (calendar) spreads, back spreads or ratio spreads, to name a few. We are going to consider the vertical spread trade; specifically, the vertical bear call spread and the vertical bull put spread.
The vertical bear call spread is a neutral-to-bearish multileg options strategy (Figure 3). Premium is collected through the sale of a call (obligation to deliver the underlying stock). Part of the premium received is used to buy a call (right to buy the underlying stock) at a higher strike price. Selling a call theoretically represents unlimited risk. Buying a call limits the risk to the difference between the sold and bought strike prices (strike spread) less any premium collected. For example:
SLD: SPY NOV 140 CALL @ 4.20 (receive $420)
BOT: SPY NOV 143 CALL @ 2.62 (pay $262)
Net Credit: $420 - $262 = $158
$-At-Risk: Difference in Strikes – Net Credit ((143 – 140) x 100) - $158 = $142
MAX Gain/Loss: Max Gain = $158 (52.67%) / Max Loss = $142 (-47.33%)
Collateral for this position would generally be determined by the strike spread. Collateral of $300 would be required to establish this position and is the basis for all gain/loss calculations.
The vertical bull put spread is a neutral-to-bullish multileg options strategy (Figure 4). Premium is collected through the sale of a put (obligation to receive the underlying stock). Part of the premium received is used to buy a put (right to sell the underlying stock) at a lower strike price. Selling a put theoretically represents risk equal to the contract strike price. Buying a put limits the risk to the difference between the sold and bought strike prices (strike spread) less any premium collected. For example:
SLD: SPY NOV 140 PUT @ 4.55 (receive $455)
BOT: SPY SEP 137 PUT @ 3.45 (pay $345)
Net Credit: $455 - $345 = $110
$-At-Risk: Difference in Strikes – Net Credit ((140 – 137) x 100) - $110 = $190
MAX Gain/Loss: Max Gain = $110 (36.67%) / Max Loss = $193 (-63.33%)
Collateral for this position would generally be determined by the strike spread. Collateral of $300 would be required to establish this position and is the basis for all G/L calculations.
Benchmarking Options Strategies
The ISE Options Overlay indexes provide benchmarks for investors looking to track the performance of a diversified portfolio of exchange-listed options utilizing the vertical spread strategy. As indicated by the name, each index solely includes option contracts on the SPDR S&P 500 exchange-traded fund (NYSE Arca: SPY).
The spreads described here are typical in that this trade is usually constructed to sell the ATM and use the proceeds to purchase insurance a certain percentage away from ATM. This is a classic, risk-controlled trade. ISE took the framework of this trade and blended it with modern portfolio theory to develop a truly diversified portfolio of vertical spread trades to help transform a trading vehicle into a potential investment vehicle.
Spread pairs that are very close to or ATM are more likely to have the underlying stock trade through them and incur maximum losses (high delta/low gamma). Pairs that are further away from ATM are less attractive from a net credit perspective, but require larger moves of the underlying to put the position at risk (mid delta/mid gamma). Pairs that are quite far away from ATM exhibit higher levels of price volatility (low delta/high gamma) due to the low absolute-price levels at which they trade. Being positioned too close or too far away from ATM presents unique risks for each. We identified optimal spreads from each of these categories and combine them into a single basket. In doing so, we created the ISE SPY Bear Options Overlay Index (VCS) and the ISE SPY Bull Options Overlay Index (VPS).
The following steps are taken to select spread pair components for each index:
i) Establish total population of available SPY option contracts for the front and second month.
ii) Refine selection universe based on eligibility/liquidity requirements.
iii) Create all possible ATM vertical spread pairs.
iv) Create and equal-weight overall rank for each pair by calculating and ranking on various criteria based on factors such as strike spread and net credit.
v) Based on the sold leg of each spread, determine the distance away from ATM (money-ness).
vi) Allocate spread pairs along proprietary money-ness and expiration criteria.
vii) Apply an equal weighting to all spread pairs.
Index components are evaluated using bid/ask pricing. Midpoint pricing is used for the real-time and end-of-day index level calculation. The index is rebalanced monthly in conjunction with the regular options expiration calendar.
To manage downside volatility, each index employs loss floors at the individual spread level. Once a spread pair has priced through the floor on an end-of-day basis, the component’s weight in the index is allocated away from the spread pair and moved to a cash proxy until the next rebalance cycle. While this approach is effective in managing downside risk over a few days or in between rebalance cycles, it is ineffective in controlling any one-day market event. Managing downside risk in this manner not only limits losses but mitigates the risk of any positions being assigned and forcing the delivery of shares of the underlying for any investor following the index.
Figure 5 shows this loss floor in action. This graph highlights the complete options cycle for December 2011 (11/18/2011 to 12/16/2011). In the December period, SPY trades off early in the cycle and we see the bullish index trading off as well. What is hidden is the loss-floor mechanism. Figure 6 provides an analysis of index components during this period.
The loss-floor mechanism allows for those positions that could cause more drag on performance to be allocated to cash, and without significant lag. It sometimes is the case with sharp moves in SPY that the entire index spends some time during the expiration cycle allocated completely to the cash proxy, but as mentioned earlier, the cash proxy weight is reallocated to new spread pairs in the next rebalance cycle. The example given represents one period and is unique, meaning it will not always be the case that a -2.21 percent move in SPY will result in 27 spread pairs being reallocated to the cash proxy, or more generically, that an aggregate move of X percent in the underlying will always result in a particular action occurring in the index.
Unlike other options strategy indexes, these indexes solely include options contracts and do not contain any underlying security as a component. In designing these indexes, we realized that investors looking for option-overlay products wanted just that—an option overlay. It did not make sense to force investors to double-up on the existing underlying stock positions or have to incur transaction costs or create taxable events in order to get exposure to these strategies.
Figure 7 shows some periodic returns of each of the indexes as compared with the underlying (SPY) for each calendar year since the indexes’ inception. Figure 8 shows the historical trend lines for the indexes versus SPY. While the indexes’ base dates are both Jan. 21, 2005, the indexes commenced operation on Sept. 16, 2011, and all prior index levels are backtested. As component selection for these indexes is a purely quantitative process, there should be no concerns regarding survivorship bias or other forms of "cherry-picking" that could influence any backtested results. The base date of Jan. 21, 2005 was chosen as it was the date that ISE and the other U.S. options exchanges first listed options contracts on SPY.
The development of the VCS and VPS indexes began as an academic exercise, but they have real-world potential to help investors gain exposure to options in a sophisticated—yet straightforward—approach. Composed of option contracts that are centrally cleared, exchange listed, continuously quoted and among the most liquid and heavily traded contracts in the marketplace, the indexes could provide investors access to a truly unique and useful way to express their opinions on the market.