rt back to along‐term baseline for each of the different assets, and it also demonstrates that elevated uncertainty is
unsustainable
in financial markets. Events may occur that spark fear in the market and drive up the demand for insurance, but as fear inevitably dissipates and the market adapts to the new conditions, IV deflates back down. This phenomenon has significant implications for short options traders. As stated in
Chapter 1
, it is controversial whether directional price assumptions are statistically valid or not as trading according to pricing forecasts has never been proven to consistently outperform the market. IV is assumed to eventually revert down following inflations from its stable volatility state unlike asset prices, which drift from their initial value with time. The timescale for these contractions is unpredictable, but this nonetheless indicates some statistical validity to make downward directional assumptions about volatility once it is elevated.
Figure 2.3
also shows how volatility profiles vary greatly across instruments. More volatile assets like Apple and Amazon stocks have higher IV averages, twice that of SPY and gold in this case, and experience expansion events more often. Single‐company factors, such as quarterly earnings reports, pending mergers, acquisitions, and executive changes can all cause volatility spikes not seen in diversified assets and portfolios. However, this increased volatility also comes with higher credits and more volatility contraction opportunities for premium sellers.
8
For an example of how the propensity for expansions and contractions differs between stocks with earnings and adiversified ETF, refer to
Figures 2.4
(a)–(c). Marked are the earnings report dates for each stock or the date when the company reported its quarterly profits (after‐tax net income).
Figure 2.3
IV indexes for different assets with their respective averages (dashed) from 2015–2021. Assets include (a) SPY (S&P 500 ETF), (b) GLD (gold commodity ETF), (c) AAPL (Apple stock), and (d) AMZN (Amazon stock).
Figure 2.4
Implied volatility indexes for different equities from 2017–2020 with earnings dates marked (if applicable). Assets include (a) AMZN (Amazon stock), (b) AAPL (Apple stock), and (c) SPY (S&P 500 ETF).
With tech stocks like AMZN and AAPL, it'scommon for IV to increase sharply prior to earnings and contract almost immediately afterward. The previous graphs show that sharp IV expansions happen less frequently with amore diversified market ETF, such as SPY. These figures indicate that when SPY does experience avolatility expansion, it generally takes much longer to contract. From 2017 to 2020, the VIX only rose above 35 two times and, in both situations, took roughly half amonth to contract down to its original level. Meanwhile, volatility levels of AMZN and AAPL rose above 40 many times and even had afew spikes above 50, or in the case of AMZN, almost 60.
Takeaways
IV is aproxy for the sentiment of market risk derived from supply and demand. When options prices increase, IV increases; when options prices decrease, IV decreases. IV also gives the perceived magnitude of future movement, and it is not directional.
Demand for options tends to increase when the historical volatility of an underlying increases unexpectedly, particularly with large moves to the downside. IV tends to be positively correlated with historical volatility and negatively correlated with price, but it is ultimately based on the
perceived
market risk and not directly on price information.
IV can be used to estimate the expected price range of an instrument. IV gives aone standard deviation
expected
range because it is based on how the market is using options to hedge against future periods of volatility.
Because stock returns are assumed to be normally distributed, theoretically, there is a 68.2% chance the price of an equity lands within its expected range over agiven time frame. However, historical data show that prices stay within their expected ranges more often than theoretically estimated. For example, market IV (estimated using the IV for SPY) overstated the realized move 87% of the time between 2016 and 2021.
Options sellers have the long‐term statistical advantage over options buyers, with the trade‐off of exposure to unlikely, potentially significant losses. Because IV is aproxy for the demand for options and the inflation of premium, it can be used to identify opportune times to sell insurance. Premium sellers can also use IV to structure positions so they are likely to expire worthless, the ideal outcome for the short position.
Volatility profiles differ significantly between assets, but all IV signals are assumed to revert back to some long‐term value following significant diversions. Stated differently, IV tends to contract back to along‐term value following significant expansions from its lull volatility state. This phenomenon indicates that there is some degree of statistical validity when


ls are assumed to revert back to some long‐term value following significant diversions. Stated differently, IV tends to contract back to along‐term value following significant expansions from its lull volatility state. This phenomenon indicates that there is some degree of statistical validity when making downward directional assumptions about volatility once it'sinflated.
Notes
1
Implied volatility (IV), like historical volatility, is apercentage and pertains to log returns. It is common to represent IV as either adecimal (0.X) or percentage (X%). An IV index, which is an instrument that tracks IV and will be introduced later in this chapter, is typically represented using points (X) but should be understood as apercentage (X%).
2
It is possible to get directional expected move information about an underlying by analyzing the IV across various strikes. This will be elaborated on more in the appendix.
3
IV yields arough approximation for the expected price range, but this is not how the expected range is typically calculated on most trading platforms. Refer to the appendix for more information about how expected range is calculated more precisely. For the time being, we are using this simplified formula since it is most intuitive.
4
When ignoring the risk‐free rate, the expected price range over
Tdays for astock with price
Sand volatility σ can be estimated by
. The formula in
Equation (2.2)
is an approximation because, for small
xvalues, ex
≈ 1 +
x
. This approximation becomes less valid when
xis large, meaning this expected range calculation is less accurate when IV is high. This will be explored more in the appendix.
5
Note that volatility indices, such as the VIX, will be represented using points but are meant to be understood as apercentage. For example, a VIX of 30 corresponds to an annualized implied volatility of 30%.
6
It'simportant to note that the threshold for high IV is different for every asset because each instrument is subject to unique risk factors. Evaluating IV can be difficult because there is so much variability between assets, but there will be amore in‐depth discussion of this in the following chapter.
7
The value that the signal reverts back to is roughly the long‐term mode of the distribution, or the volatility that has occurred most often historically.
8
Such underlyings can be used for earnings plays, which will be discussed in a
Chapter 9
.

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Chapter 3
Trading Short Premium
Options are highly versatile instruments. They can be used to hedge the directional risk of astock, or they can be used as asource of profits. As alluded to in the example of hurricane insurance, short premium positions can be used to generate small, consistent profits for those willing to accept the tail risk. The mechanics of short premium trading are subtle, but many of the core concepts can be introduced in an intuitive way with some simple gambling analogies. For example, when using options for profit generation (i.e., not risk mitigation), the long‐term performance of long and short options can be analogized with slot machines.
Buying Options for profit
is like playing the slot machines. Gamblers who play enough times may hit the jackpot and receive ahuge payout. However, despite the potential payouts, most players average aloss in the long run because they are taking small losses the majority of the time. Investors who buy options are betting on large, often directional moves in the underlying asset. Those assumptions
may be correct and yield significant profits occasionally, but underlying prices ultimately stay within their expected ranges most of the time. This results in small, frequent losses on unused contracts and an average loss over time.
Selling Options for profit
is like owning the slot machines. Casino owners have the long‐run statistical advantage for every game, an edge particularly high for slots. Owners may occasionally pay out large jackpots, but as long as people play enough and the payouts are manageable, they are compensated for taking on this risk with nearly guaranteed profit in the long term. Similarly, because short options carry tail risk but provide small, consistent profits from implied volatility (IV) overstatement, then they should average aprofit in the long run if risk is managed appropriately.
Long premium strategies have ahigh profit potential but cannot be consistently timed to ensure profit in the long term. This is because outlier underlying moves and IV expansions that benefit long premium positions are strongly linked to external events (such as natural disasters or political conflict), which are relatively difficult to reliably predict. Short premium strategies, on the other hand, profit more often and have the long‐term statistical advantage if investors manage risks appropriately.
Similar to the slot machine owner, ashort premium trader must reduce the impact of outlier losses to reach alarge number of occurrences (trades) and realize the positive long‐term averages. This is most effectively done by limiting position size and by adjusting portfolio exposure according to current market conditions. This chapter will, therefore, cover the following broader concepts in volatility trading:
Trading in high IV: Identifying favorable conditions for opening short premium trades.
Number of occurrences: Reaching the minimum number of trades required to achieve long‐term averages.
Portfolio allocation and position sizing: Establishing an appropriate level of risk for the given market conditions.
Active management and efficient capital allocation: Understanding the benefits of managing trades prior to expiration.
IV plays acrucial role in trading short premium. Remember that IV is ameasure of the
sentiment
of uncertainty in the market. It is aproxy for the amount of
fear
among premium buyers (or
excitement
, depending on your personality) and ameasure of
opportunity
for premium sellers. When market uncertainty increases, premium prices also increase, and premium sellers receive more compensation for being exposed to large losses. However, IV is also instrumental when managing exposure to extreme losses and establishing appropriate position sizes.
Background: A Note on Visualizing Option Risk
When discussing the risk‐reward trade‐off of trading short premium, it is helpful to contextualize concepts and statistics with respect to aspecific strategy. The next few chapters will focus on ashort strangle
, an options strategy consisting of ashort out‐of‐the‐money (OTM) call and ashort OTM put:
Ashort OTM call (the right to buy an asset at acertain price) has abearish directional assumption. The seller profits when the underlying price stays below the specified strike price.
Ashort OTM put (the right to sell an asset at acertain price) has abullish directional assumption. The seller profits when the underlying price stays above the specified strike price.
These two contracts combine to form astrangle. This is an example of an
undefined risk
strategy, where the loss is theoretically unlimited. The short call has undefined risk because stock prices can increase indefinitely, meaning the potential loss to the upside is unknown. Though short puts technically cannot lose more than 100 times the strike price, this potential loss is large enough that they are also considered undefined risk. Defined risk strategies, where the maximum loss is limited by the

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rease indefinitely, meaning the potential loss to the upside is unknown. Though short puts technically cannot lose more than 100 times the strike price, this potential loss is large enough that they are also considered undefined risk. Defined risk strategies, where the maximum loss is limited by the construction of the trade, have pros and cons that will be discussed in
Chapter 5
. For simplicity, the strangle is used to formulate most examples in this book.
Strangles have aneutral directional assumption for the contract seller, meaning it is typically profitable when the price of the underlying stays
within the range defined by the short call strike and short put strike. Investors often define the strikes of astrangle according to the expected range of the underlying price (or some multiple of the expected range) over the contract duration. The one standard deviation expected range can be approximated with the current implied volatility of the underlying, as shown in
Chapter 2
.
Figure 3.1
The price of SPY in the last five months of 2019. Included is the 45‐day expected move cone calculated from the IV of SPY in December 2019. The edges of the cones are labeled according to appropriate strikes for an example strangle.
Figure 3.1
shows that SPY was priced at roughly $315 around December 2019, when the current IV for SPY was 12% (corresponding to a VIX level of 12). This means the price for SPY was forecasted to move between –4.2% and +4.2% over the next 45 days with a 68% certainty. This is equivalent to a 45‐day forecast of the price of SPY staying between $302 and $328 approximately. Acontract with astrike price corresponding to the
expected move range is approximately a 16
contract. In this scenario, a 45 days to expiration (DTE) short SPY call with astrike price of $328 is a –16
contract roughly, and a 45
DTE short SPY put with astrike price of $302 is approximately a 16
contract. The two positions combined form adelta‐neutral position known as a 45 DTE 16
SPY strangle.
1
The strangle buyer and seller are making different bets:
The strangle buyer assumes that SPY'sprice will move beyond expectation within the next 45 days, either to the upside or the downside. More specifically, the long strangle yields profit if the price of SPY significantly increases above $328 or decreases below $302 prior to expiration.
The strangle seller profits if the position expires when the underlying price is within or near its expected range or if the position is closed when the contract is trading for acheaper price than when it was opened (IV contraction).
Because there is a 68% chance the underlying will stay within its expected range, the short position theoretically has a 68% chance of being profitable. However, since the underlying price tends to stay in its expected range more often than theoretically predicted, this results in the probability of profit (POP) of short strangles held to expiration being much higher.
For example, consider the profit and loss (P/L) distributions for the short 45 DTE 16
SPY strangle in
Figures 3.2
(a)–(c). These distributions were generated using historical options data and are useful for visualizing the long‐term risk‐reward profile and likely trade‐by‐trade outcomes for this type of contract. Each occurrence in the histogram corresponds to the final P/Lof ashort strangle held to expiration.
2
P/Lcan be represented as araw dollar amount or as apercentage of initial credit (the fraction of option premium that the seller ultimately kept).
3
Figure 3.2
(a) Historical P/Ldistribution (% of initial credit) for short 45 DTE 16
SPY strangles, held to expiration from 2005–2021. (b) Historical P/Ldistribution ($) for short 45 DTE 16
SPY strangles, held to expiration from 2005–2021. (c) The same distribution as in (b) but zoomed in near $0. The percentage of occurrences on either side of $0 have been labeled.
Figure 3.2
(c) shows that 81% of occurrences are
positive
and only 19% are
negative
. This means this strategy has historically profited 81% of the time and only taken losses 19% of the time, significantly higher than the 68% POP that the simplified theory suggests. Over the long run, this strategy was
profitable
and averaged a P/Lof $44 (or 28% of the initial credit) per trade. However, notice the P/Ldistributions for this strategy are highly skewed and carry significant tail risk. As shown in
Figure 3.2
(a), these tail losses are unlikely but could potentially amount
to –1,000% or even –4,000% of the initial credit. In other words, if atrader receives $100 in initial credit for selling a SPY strangle, there is aslim chance of losing upward of $4,000 on that trade according to historical behavior. This is the trade‐off for the high POPs of short premium strategies.
The possibility of outlier losses should not be surprising because placing ashort premium trade is betting against large, unexpected price swings. For arelatively stable asset like SPY, these types of swings rarely happen. When t


. This is the trade‐off for the high POPs of short premium strategies.
The possibility of outlier losses should not be surprising because placing ashort premium trade is betting against large, unexpected price swings. For arelatively stable asset like SPY, these types of swings rarely happen. When they do, things can fly off the handle rapidly, such as during the 2008 recession or 2020 sell‐off. Consequently, the most important goals for ashort premium trader are to profit consistently enough to cover moderate, more likely losses and to construct aportfolio that can survive those unlikely extreme losses.
Background: A Note on Quantifying Option Risk
Approximating the historical risk of astock or exchange-traded fund (ETF) is relatively straightforward. Equity log returns distributions are fairly symmetric and resemble anormal distribution, thus justifying that standard deviation of returns (historical volatility) be used to approximate historical risk. However, ashort option P/Ldistribution is highly skewed and subject to substantial outlier risk. Due to this more complex risk profile, using option P/Lstandard deviation as alone proxy for risk
significantly
misrepresents the true risk of the strategy. Therefore, the following metrics will be used to more thoroughly discuss the risk of short options: standard deviation of P/L, skew, and conditional value at risk (CVaR).
4
The standard deviation of P/Lencompasses the range that the
majority
of endings P/Ls fall within for agiven strategy historically. The standard deviation for financial strategies is commonly interpreted relative to the normal distribution, where one standard deviation accounts for 34% of the distribution on either side of the mean. For options P/Ldistributions, however, the one standard deviation of P/Ltypically
accounts for more than 68% of the total occurrences and the density of occurrences is not symmetric about the mean. Again, consider the P/Ldistribution for the short 45 DTE 16
SPY strangle.
Figure 3.3
Historical P/Ldistribution ($) for 45 DTE 16
SPY strangles, held to expiration from 2005–2021. The distribution has been zoomed in near the mean (solid line), and the percentage of occurrences within
of the mean has been labeled.
For 45 DTE 16
SPY strangles from 2005–2021, the average P/Lwas $44, and the standard deviation of P/Lwas $614. As shown in
Figure 3.3
, the one standard deviation range accounts for nearly 96% of all occurrences, significantly higher than the
range for the normal distribution. Additionally, because the distribution is highly asymmetric, the P/Ls in the
range are less likely than the P/Ls in the
range. Due to these factors, the interpretation of standard deviation as ameasure of risk must be adjusted. Standard deviation
overestimates
the magnitude of the most likely losses (e.g., a $500 loss is unlikely, but the standard deviation range does not clarify that) and does not account
negative tail risk. It does yield arange for the
most likely
profits and losses on atrade‐by‐trade basis for agiven strategy. Therefore, traders can generally form more reliable P/Lexpectations for strategies with alower P/Lstandard deviation.
Skew and CVaR
are used to estimate the historical tail risk of astrategy. As covered in
Chapter 1
, skew is ameasure of the asymmetry of adistribution. Strategies with alarger magnitude of negative skew in their P/Ldistribution have more historical outlier loss exposure. CVaR gives an estimate of the potential loss of aposition over agiven time frame at aspecific likelihood level based on historical behavior. CVaR can be used to approximate the magnitude of an expected worst‐case loss and contextualize skew. For example, consider the two example short strangles outlined in
Table 3.1
.
Table 3.1
Two example short strangles. For Strangle A, CVaR estimates losing at least $200 at most 5% of the time. In this example, the time frame for this loss has not been specified, but one may assume the time frame is identical for both strategies.
Risk Factors
Strangle A
Strangle B
Skew
–5.0
–1.0
CVaR (5%)
–$200
–$2,000
Strangle Ahas alarger magnitude of negative skew, indicating that this strategy is more susceptible to tail risk and outlier losses compared to Strangle B. However, there is 10 times more capital at risk in an extreme loss scenario for Strangle Bcompared to Strangle Aperhaps because the underlying for Strangle Bis more expensive. Generally speaking, strategies with less skew are preferable because those strategies are less susceptible to large, unpredictable losses and perform more consistently. However, the optimal trade ultimately depends on the acceptable amount of per‐trade capital at risk according to the trader'spersonal preferences.
Also note it is difficult to accurately model outlier loss events because they happen rarely. P/Ldistributions can give an
idea
of the magnitude of extreme losses, but these statistics are averaged over abroad range of market conditions and volatility environm


ng to the trader'spersonal preferences.
Also note it is difficult to accurately model outlier loss events because they happen rarely. P/Ldistributions can give an
idea
of the magnitude of extreme losses, but these statistics are averaged over abroad range of market conditions and volatility environments. They are
not necessarily representative of outlier risk at the present time. Buying power reduction (BPR), which will be covered in the next chapter, yields an estimate for the worst‐case loss of atrade according to current market conditions. Similar to implied volatility, BPR is aforward‐looking metric designed to encompass the most likely scope of losses for an undefined risk position.
Trading in High IV
Selling premium once IV is elevated comes with several advantages. Before that discussion, there are subtleties to note when evaluating “how high” the IV of an asset is. Contextualizing the current IV for an asset like SPY is somewhat straightforward because it has awell‐known and widely available IV index. The VIX has historically ranged from approximately 10 to 90, has an average of roughly 18, is typically below 20, and rarely surpasses 40. Therefore, atrader can intuitively interpret alevel of 15 as fairly low and alevel of 35 as fairly high relative to the long‐term behavior of the VIX. But how do traders contextualize the current IV relative to ashorter timescale, such as the last year? And how do traders contextualize the current IV for aless popular IV index with atotally different risk profile? For example, is 35 high for VXAZN, the IV index for AMZN?
One way to gauge the degree of IV elevation with respect to some timescale is by converting raw implied volatility into arelative measure such as IV percentile (IVP). IVP is the percentage of days in the past year where the IV was
below
the current IV level, calculated with the following equation. Note that 252 is the number of trading days in ayear.
(3.1)
IVP ranges from 0% to 100%, with ahigher number indicating ahigher relative IV. This metric normalizes raw IV to put the current level in context, and unlike raw IV, it is comparable between assets. For example, consider the raw IV indexes and the corresponding IVP values for SPY and AMZN shown in
Figure 3.4
.
Figure 3.4
The VIX (solid) and VXAZN (dashed) from 2015–2016. Labeled are the IVP values for each index at the end of 2015. When the VIX was roughly 18 SPY had an IVP of 74%, and VXAZN was roughly 36 AMZN had an IVP of 67%.
At the end of 2015, the VIX was near its long‐term average of 18 and would have been considered low. However, market IV was below average for the majority of 2015, and a VIX level of 18 was higher than nearly 74% of occurrences from the previous year. A SPY IVP of 74% indicates that IV is fairly elevated relative to the recent market conditions, suggesting that volatility may contract following this expansion period. Comparatively, the volatility index for AMZN at the end of 2015 was 37. This is significantly higher than the VIX at the time but is actually
less elevated
relative to its volatility history from the past year according to the AMZN IVP of 67%. SPY and AMZN have dramatically different volatility profiles, with VXAZN frequently exceeding 35 and the VIX rarely doing so. This makes raw IV apoor metric for comparing relative volatility and ametric like IVP necessary.
Another commonly used relative volatility metric is IV rank (IVR), which compares the current IV level to the historical implied volatility range for that underlying. It is calculated according to the following formula:
(3.2)
Similar to IVP, IVR normalizes raw IV on a 0% to 100% scale and is comparable between assets. IVR gives abetter direct metric for evaluating the price of an option compared to IVP. However, IVP is more robust than IVR because IVR is more sensitive to outlier moves and prone to skew.
Both metrics are suitable for practical decision making because they assist traders with evaluating current volatility levels and selecting asuitable strategy/underlying for those conditions. They are also useful for identifying suitable, high IV underlyings for aportfolio because most assets do not have well‐known volatility indices. However, both metrics are fairly unstable, sensitive to timescale, and can be skewed by prolonged outlier events such as sell‐offs. Raw IV, assuming that the characteristics of the volatility profile are well understood, is generally amore stable and reliable metric for analyzing long‐term trends. Because most studies throughout this book use SPY as abaseline underlying and span several years, raw IV will be used rather than arelative metric.
As previously mentioned, trading short premium when IV is elevated comes with the added benefits of higher credits and more profit potential for sellers. This is shown in
Figure 3.5
, which includes average credits for 16
SPY strangles from 2010–2020 in different volatility environments.
Trading short premium in elevated IV is an ef


hort premium when IV is elevated comes with the added benefits of higher credits and more profit potential for sellers. This is shown in
Figure 3.5
, which includes average credits for 16
SPY strangles from 2010–2020 in different volatility environments.
Trading short premium in elevated IV is an effective way to capitalize on higher premium prices and the increased likelihood of asignificant volatility contraction. Trading when credits are higher also means common losses tend to be larger (as adollar amount), but the exposure to outlier risk actually tends to be
lower
when IV is elevated compared to when it'scloser to equilibrium. This may seem counterintuitive: If market uncertainty is elevated and there is higher perceived risk, wouldn'tshort premium strategies carry more outlier risk? Although moves in the underlying tend to be more dramatic when IV is high, the expected range adjusts to account for the new volatility almost immediately, which in many cases reduces the risk of an outlier loss. To understand this, consider
Figures 3.6
(a) and (b), showing extreme losses for 16
SPY strangles from 2005–2021, with an emphasis on the 2008 recession.
Figure 3.5
SPY IV from 2010–2020. The average prices for 45 DTE 16
SPY strangles are labeled at different VIX levels: 10–20, 20–30, and 30–40. When the VIX was between 30 and 40, the average initial credit per one lot for the 16
SPY strangle was roughly 42% higher than when the VIX was between 10 and 20.
Ashort 16
SPY strangle rarely incurs aloss over $1,000. From 2005–2021, this occurred less than 1% of the time. However,
84%
of these losses occurred when the VIX was below 25. During the initial IV expansion of the 2008 recession (late August to early October), strangles incurred these large losses approximately 56% of the time. Notice in
Figure 3.6
that these extreme losses were confined to the initial IV expansion (when the VIX increased from roughly 20 to 35). This is because the market was not anticipating the large downside moves of the recession, as reflected by the VIX being near its long‐term average of 18. Because these large swings happened when the expected move range was tight, the historical volatility of the market well exceeded its expected range, and long strangles were highly profitable. Once market uncertainty adjusted to the new conditions and initial credits and expected ranges increased to reflect the perceived risks, the outlier losses for short strangles diminished.
Figure 3.6
(a) SPY IV from 2005–2021. Labeled are the extreme losses for 45 DTE 16
SPY strangles held to expiration, meaning losses that are worse than $1,000. (b) The same figure as shown in (a) but zoomed in to 2008–2010, during the 2008 recession.
These unexpected periods of high market volatility are the primary source of extreme loss for short premium positions. These events typically happen when there are large price swings in the underlying and the expected move range is tight (low IV). These extreme expansion events are rare, and trading short premium once IV is elevated tends to reduce this type of exposure. Another way to demonstrate this concept is to consider the amount of skew in the P/Ldistribution of the 16
SPY strangle at different IV levels.
Figures 3.7
(a)–(d) illustrate that strangle P/Ldistributions have less negative skew and smaller tail losses as IV increases. This means that, historically, the exposure
to negative tail risk was much higher when the VIX was closer to the lower end of its range compared to when the VIX already expanded. The P/Ldistribution becomes more symmetric as IV increases, indicated by the decreasing magnitude of negative skew. This means that higher IV conditions facilitate more dependable profit and loss expectations than lower IV conditions. As an important note, observe that there are significantly fewer occurrences when the VIX was over 35 (afew hundred occurrences) compared to when the VIX was between 0 and 25 (thousands of occurrences). This brings us to the next point to consider: How often should one trade?
Figure 3.7
Historical P/Ldistributions for 45 DTE 16
SPY strangles, held to expiration from 2005–2021: (a) Occurrences when the VIX is between 0 and 15 (1,603 occurrences total), (b) Occurrences when the VIX is between 15 and 25 (1,506 occurrences total). (c) Occurrences when the VIX is between 25 and 35 (416 occurrences total). (d) Occurrences when the VIX is above 35 (228 occurrences total).
Number of Occurrences
Table games at acasino typically have maximum bet sizes. The house has the statistical edge for every game in the casino, but the house will not necessarily profit from that edge unless patrons bet
often
. In blackjack, the house has an edge of 0.5% if the player'sstrategy is statistically optimized. So, if gamblers wager $100,000 on blackjack throughout the night, they should lose approximately $500 to the house after asufficiently large number of hands. If the opponent plays 10 hands at $10,000 per hand, they


ck, the house has an edge of 0.5% if the player'sstrategy is statistically optimized. So, if gamblers wager $100,000 on blackjack throughout the night, they should lose approximately $500 to the house after asufficiently large number of hands. If the opponent plays 10 hands at $10,000 per hand, they may win eight hands, three hands, or even all 10 hands. In this case, the variance of potential outcomes is fairly large, and the casino may have to pay fairly large payouts. However, if the opponent plays 1,000 hands at $100 per hand, it is more likely the player'sloss will amount to the expected $500.
By capping bet sizes, the casino aims to increase the number of occurrences from asingle gambler so the house is more likely to reach long‐run averages for each game, aconsequence of the law of large numbers and the central limit theorem. When asmall
number of events is randomly sampled from aprobability distribution repeatedly and the averages of those samples are compared, the variance of those averages tends to be quite large. But as the number of occurrences increases, the variance of the averages decreases and the sampled means converge to the expected value of the distribution.
5
Just as the casino aims to realize the long‐term edge of table games by capping bet sizes and increasing the number of plays, short premium traders should make many small trades to maximize their chances of realizing the positive long‐run expected averages of short premium strategies. For an example of why this is crucial, refer again to the P/Ldistribution of the 16
SPY strangle.
Figure 3.8
Historical P/Ldistribution for 45 DTE 16
SPY strangles, held to expiration from 2005–2021. The dotted line is the long‐term average P/Lof this strategy.
This strategy, shown in
Figure 3.8
, has an average P/Lper trade of roughly $44 and a POP of 81%. However, these long‐term averages were calculated using roughly 3,750 trades. Calculating averages with alarge pool of data provides the least amount of statistical error but does not model the occurrences retail traders can realistically achieve. What P/Lwould short premium traders have averaged if they only placed 10 trades from 2005 to 2021? 100 trades? 500 trades?
Figure 3.9
shows aplot of average P/Ls for acollection of sample portfolios, each with adifferent number of trades randomly selected from the P/Ldistribution of the 16
SPY strangle.
Figure 3.9
P/Laverages for portfolios with
Nnumber of trades, randomly sampled from the historical P/Ldistribution for 45 DTE 16
SPY strangles, held to expiration from 2005–2021. The variance among these portfolio averages is very large when asmall number of trades are sampled. As more trades are sampled, the averages converge to the long‐term average P/Lof this strategy.
As you can see, when asmall number of trades is sampled, 10 for example, the average P/Lranges from roughly –$900 to $200. This means that if two traders randomly traded 10 short strangles from 2005 to 2021, one trader may have profited by $2,000, and the other may have lost $9,000. As the number of occurrences increases, the variance of P/Laverages among these sample portfolios decreases, and the averages converge toward the long‐run expected value of this strategy. In other words, if two traders randomly traded 1,000 short strangles from 2005 to 2021, it would be fairly likely for both to average a P/Lnear $44 per trade, the historical long‐term average P/Lof this strategy.
Number of occurrences is acritical factor in achieving long‐term averages, and the minimum number of occurrences needed varies with the specific strategy'sstandard deviation of P/L. For practical purposes, aminimum of roughly 200 occurrences is necessary to reach long‐run
averages, and more is better. This puts short premium traders in abit of apredicament because, although trading short premium in high IV is ideal, high IV environments are very uncommon as shown in
Table 3.2
.
Table 3.2
How often the VIX fell in agiven range from 2005–2021.
VIX Data (2005–2021)
VIX Range
% of Occurrences
0–15
43%
15–25
40%
25–35
11%
35+
6%
The VIX is at the low end of its range 43% of the time and below 18.5, its long‐term average, the majority of the time. From 2005–2021, the VIX was only above 35 roughly 6% of the time, which does not leave much opportunity for trading short premium in very high IV. To optimize the likelihood of reaching the favorable long‐term expected values of this strategy, it is clearly necessary to trade in non‐ideal, low volatility conditions. The next section covers how to trade in all market conditions while mitigating the outlier risk in low volatility environments, specifically by maintaining small position sizes and limiting the capital exposed to outlier losses.
Portfolio Allocation and Position Sizing
In practice, short premium traders must strike abalance between being exposed to large losses and reaching asufficient number of occurrences. Trading in high IV tends to carry less exposure to outlier r


izes and limiting the capital exposed to outlier losses.
Portfolio Allocation and Position Sizing
In practice, short premium traders must strike abalance between being exposed to large losses and reaching asufficient number of occurrences. Trading in high IV tends to carry less exposure to outlier risk compared to trading in low IV, but trading in low IV is still profitable on average. Unlike long stocks, which are only profitable during bullish conditions, short options may be profitable in bullish, bearish, or neutral conditions and spanning all volatility environments. For the 16
SPY strangle from 2005–2021, for example, the majority of occurrences were profitable in all IV ranges. (See
Table 3.3
.)
Table 3.3
The POPs and average P/Ls in different IV ranges for 45 DTE 16
SPY strangles, held to expiration from 2005–2021.
16
SPY Strangle Data (2005–2021)
VIX Range
POP
Average P/L
0–15
82%
$20
15–25
78%
$7
25–35
86%
$159
35+
89%
$255
By trading short options strategies in all IV environments, profits accumulate more consistently, and the minimum number of occurrences is more achievable. To manage exposure to outlier risk throughout these environments, it'sessential
to keep position sizes small and limit the total amount of portfolio capital allocated to short premium positions, which can be scaled according to the current outlier risk. The percentage of portfolio capital allocated to short premium strategies should generally range from 25% to 50%, with the remaining capital either kept in cash or alow‐risk passive investment.
6
This is because allocating less than 25% severely limits upside growth, while allocating more than 50% may not leave enough capital for aportfolio to recover from an outlier loss event. Because the exposure to outlier risk tends to be higher when IV is low, scaling allocation down in low IV protects portfolio capital from the tail exposure of unexpected market volatility. Once IV increases, scaling short premium capital allocation up increases the potential to profit from higher credits, larger profits, and reduced outlier risk.
Table 3.4
Guidelines for allocating portfolio capital according to market IV.
VIX Range
Max Portfolio Allocation
0–15
25%
15–20
30%
20–30
35%
30–40
40%
40+
50%
Aportfolio should not be overly concentrated in short options strategies for the given market conditions, and the capital allocated to short premium should
also
not be overly concentrated in asingle position. An appropriately sized position should not occupy more than 5% to 7% of portfolio capital. The exact percentage varies depending on the POP of the strategies used, and this will be covered in more detail in
Chapter 8
.
To understand why it'scrucial to limit capital exposure and beneficial to scale portfolio allocation according to IV, look at aworst‐case scenario: the 2020 sell‐off. The 2020 sell‐off produced historic losses for short premium positions. From late February to late March 2020, the price of SPY crashed by roughly 34%. For 45 DTE 16
SPY strangles, the most extreme losses recorded for this position occurred throughout this time. A 16
SPY strangle opening on February 14, 2020, and expiring on March 20, 2020, had a P/Lper one lot of roughly –$8,974, the worst recorded loss in 16 years for this type of contract. If traders allocated different percentages of a $100,000 portfolio to short SPY strangles beginning with this worst‐case loss, how would those portfolios perform in regular market conditions compared to highly volatile conditions like the 2020 sell‐off? Compare three portfolio allocation strategies: allocation by IV guidelines (25–50%), amore conservative allocation (constant 15%), and amore aggressive allocation (constant 65%).
7
Unsurprisingly, the portfolios perform markedly differently in regular conditions compared to the 2020 sell‐off. From 2017 to February of 2020, the aggressive portfolio dramatically outperformed the conservative and IV‐allocated portfolios. Throughout this three‐year period, the conservative portfolio grew by 13% and the IV‐allocated portfolio by 28%, and the aggressive portfolio increased by 78%. Comparatively, from 2017–2020, SPY grew by 50%. This means that a $100,000 portfolio fully allocated to SPY shares would have outperformed the conservative and IV-allocated portfolios but underperformed the aggressive portfolio, though it would have required significantly more capital than any of them.
Figure 3.10
(a) Performances from 2017 to 2021, through the 2020 sell‐off. Each portfolio has different amounts of capital allocated to approximately 45 DTE 16
SPY strangles that are closed at expiration and reopened at the beginning of the expiration cycle. The portfolios are (a) IV‐allocated (solid), conservative (dashed), and aggressive (hashed). (b) SPY price from 2017 to 2021. (c) VIX throughout the same time frame.
Upon the onset of the highly volatile market conditions of 2020, the highly exposed aggressive portfolio was immediately wiped out. The conserva


lios are (a) IV‐allocated (solid), conservative (dashed), and aggressive (hashed). (b) SPY price from 2017 to 2021. (c) VIX throughout the same time frame.
Upon the onset of the highly volatile market conditions of 2020, the highly exposed aggressive portfolio was immediately wiped out. The conservative and IV‐allocated portfolios were also impacted by significant losses and declined by 35% and 24%, respectively, from February to March 2020. In all the previous scenarios, each portfolio experienced some degree of loss during the extreme market conditions of the 2020 sell‐off. The important thing to note is that portfolios with less capital exposure and position concentration ultimately had the capital to recover following these losses. Following the 2020 sell‐off, the conservative
portfolio recovered by 7% and the IV‐allocated by 20% because this portfolio was able to capitalize on the high IV and higher credits of the sell‐off recovery.
For profit goals to be reached
consistently
, it'scrucial to construct aportfolio that is robust in every type of market. Ahighly exposed portfolio takes extraordinary profits in more regular market conditions, but there is ahigh risk of going under in the rare event of asell‐off or major correction. Amore conservative portfolio is well suited for extreme market conditions, but upside profits are limited the majority of the time. Comparatively, scaling capital allocation according to market IV is an effective way to capitalize on higher profits when IV is high, protect capital from outlier losses when IV is low, and achieve reasonable growth with lower capital requirements than purchasing equities directly. More importantly, limiting capital exposure and maintaining appropriate position sizes are arguably the most effective ways to minimize the impact from extreme events. These concepts will be explored in more detail in
Chapter 7
.
Active Management and Efficient Capital Allocation
Up until now, this book has discussed option risk and profitability for contracts held to expiration. However, short premium traders can also close, or manage, their positions early by purchasing long options with the same underlying, strike, and date of expiration. This can often be profitable as aresult of partial theta decay and IV contractions, and it also tends to reduce P/Lvariability per trade. Options tend to have more P/Lfluctuations in the second half of the contract duration compared to the first half, aresult of increasing gamma risk. Gamma, as discussed in earlier chapters, is ameasure of how sensitive acontract'sdelta is to changes in the price of the underlying. Gamma increases for near‐the‐money options as expiration approaches, meaning that delta (and, therefore, the price sensitivity of the option) becomes more unstable in response to moves in the underlying toward the end of the contract.
Managing short positions actively, such as closing atrade prior to expiration and redeploying capital to new positions, is one way to reduce the P/Lswings throughout the trade duration, as well as the per‐trade
loss potential and ending P/Lstandard deviation. Early management strategies will not necessarily reduce risk in the long term because the cumulative losses of many shorter‐term trades may exceed the single loss of alonger‐term trade, but they do make per‐trade loss potentials more reasonable. This strategy effectively allows traders to assess the viability of atrade before P/Lswings become more extreme and assess whether it is an efficient use of portfolio capital to remain in the trade. Compare how the P/Ls of 45 DTE 16
SPY strangles are distributed when the contracts are held to expiration versus managed around halfway to expiration (21 DTE).
Table 3.5
Comparison of management strategies for 45 DTE 16
SPY strangles from 2005–2021 that are held to expiration and managed early. Statistics include POP, average P/L, standard deviation of P/L, and CVaR at the 5% likelihood level.
16
SPY Strangle Statistics (2005–2021)
Statistics
Held to Expiration
Managed at 21 DTE
POP
81%
79%
Average P/L
$44
$30
Average Daily P/L
$1.29
$1.60
Standard Deviation of P/L
$614
$260
CVaR (5%)
–$1,535
–$695
According to the statistics in
Table 3.5
, strangles managed at 21 DTE carry significantly less negative tail risk and P/Lstandard deviation on atrade‐by‐trade basis than strangles held to expiration. Additionally, although early‐managed contracts collect less on average per trade, they actually average
more
profit on adaily basis and allow for more occurrences due to the shorter duration.
Managing trades early has several benefits, most of which will be covered in
Chapter 6
. Much of this decision depends on the acceptable amount of capital to risk on asingle trade and whether it is an efficient use of capital to remain in the existing trade. Notice from this example that managed trades take 24 days (21 days remaining on a 45‐day duration trade corresponds to an elapsed duration of 24 days) to profit $30 o


acceptable amount of capital to risk on asingle trade and whether it is an efficient use of capital to remain in the existing trade. Notice from this example that managed trades take 24 days (21 days remaining on a 45‐day duration trade corresponds to an elapsed duration of 24 days) to profit $30 on average and held contracts 45 days to make $44 on average. Trades may accumulate the majority of their profit potential well before expiration,
depending on the market and staying in the position for the remainder of the duration may limit upside potential. Closing trades prior to expiration and redeploying capital to anew position in the same underlying is an effective method for increasing the number of occurrences in agiven time frame. Redeploying that capital to aposition in adifferent underlying with more favorable characteristics (such as higher IV) can be amore efficient use of capital and can offer elements of risk reduction in certain situations. Taking an active approach to investing and trade management provides more control over portfolio capital allocation and the flexibility to modify trades given new information.
Takeaways
Compared to long premium strategies, short premium strategies yield more consistent profits and have the long‐term statistical advantage. The trade‐off for receiving consistent profits is exposure to large and sometimes undefined losses, which is why the most important goals of ashort premium trader are to (1) profit consistently enough to cover moderate and more likely losses and (2) to construct aportfolio that can survive unlikely extreme losses.
Unexpected periods of high market volatility are the primary source of extreme loss for short premium positions. These events are highly unlikely but typically happen when large price swings occur in the underlying while the expected move range is tight (low IV). Trading short premium once IV is elevated is one way to consistently reduce this exposure.
The profitability of short options strategies depends on having alarge number of occurrences to reach positive statistical averages. At minimum, approximately 200 occurrences are needed for the average P/Lof astrategy to converge to long‐term profit targets and more is better.
Although trading short premium in high IV is ideal, high IV environments are somewhat uncommon. This means that short premium traders must strike abalance between being exposed to large losses and reaching asufficient number of occurrences. Trading short options strategies in all IV environments accumulates profits more
consistently and makes it more likely to reach the minimum number of occurrences. To manage exposure to outlier risk when adopting this strategy, it'sessential to maintain small position sizes and limit the amount of capital allocated to short premium positions. This strategy can also be improved by scaling the amount of capital allocated to short premium according to the current market conditions.
Managing positions actively is one way to reduce P/Luncertainty on atrade‐by‐trade basis, use capital more efficiently, and achieve more occurrences in agiven time frame. The choice of whether to close aposition early and redeploy capital depends on the acceptable amount of capital to risk on asingle trade and whether it is an efficient use of capital to remain in the existing trade. These concepts will be explored more in
Chapter 6
.
Notes
1
These are approximate strikes for the 16Δ SPY strangle calculated using the equation from
Chapter 2
. The actual strikes for a 16Δ SPY strangle are calculated using more complex estimations for expected range, which will be touched on in the appendix.
2
It is difficult to make aone‐to‐one comparison between equity returns and option P/Ls because these instruments operate over different timescales. The closest option analog to an equity returns distribution is adistribution for the ending P/Ls of aparticular strategy.
3
Statistics represented as apercentage of initial credit are more representative of long‐term values than those represented with dollars. Equity prices drift with time, meaning the prices for their options do as well. Normalizing P/Lstatistics by the initial credit makes them more robust to changes in time but also makes comparisons between strategies less intuitive. This book will often represent option statistics in dollars, but remember these statistics are averaged over fairly long time frames.
4
These are past‐looking risk metrics. Metrics of forward‐looking risk include implied volatility and buying power reduction (BPR), which will be covered in the following chapter. Forward‐looking metrics are the focus of this book and more relevant in applied trading, but past‐looking metrics are still included for the sake of completeness and education.
5
Specifically, the standard deviation of the average of
nindependent occurrences is
times the standard deviation of asingle occurrence.
6
More specifically, the portfolio capital being referred to here is


Chapter 4
Buying Power Reduction
Having discussed the nature of implied volatility (IV) and the general risk‐reward profile of short premium positions, it'stime to introduce some elements of short volatility trading in practice. Because short options are subject to significant tail risk, brokers must reserve acertain amount of capital to cover the potential losses of each position. The capital required to place and maintain ashort premium trade is called the buying power reduction (BPR), and the total amount of portfolio capital available for trading is the portfolio buying power.
BPR is the amount of capital required to be set aside in the account to insure ashort option position, similar to escrow. BPR is used to evaluate short premium risk on atrade‐by‐trade basis in two ways:
BPR acts as afairly reliable metric for the worst‐case loss for an undefined risk position in current market conditions.
BPR is used to determine if aposition is appropriate for aportfolio with acertain buying power.
Though BPR is the option counterpart of stock margin, the distinction between the two
cannot be overstated
, as short options positions can never be traded with borrowed money. BPR is
not
borrowed money nor does it accrue interest. It is
your
capital that is out of play for the duration of the short option trade. Margin, mostly used for stock trading, is money borrowed from brokers to purchase stock valued beyond the cash in an account. Interest
does
accrue on margin (usually between a 5% to 7% annual rate), and traders are required to pay back the margin plus interest regardless of whether the stock trade was profitable. Margin and BPR are conceptually different: Margin amplifies stock purchasing power, and BPR lowers purchasing power to account for the additional risk of short options.
The definition of BPR and its usage differs depending on whether the strategy is long or short and whether the strategy has defined or undefined risk. For long options, the maximum loss is simply the cost of the option, so that is the BPR. Defining the BPR for short options is more complicated, particularly for undefined risk positions, because the loss is theoretically unlimited. Defined risk trades, which will be covered in the next chapter, are short premium trades with aknown maximum loss. These are simply short premium contracts (undefined risk trades) combined with cheaper, long premium contracts that will cap the excess losses when the underlying price moves past the further strike. BPR
is
the maximum loss for adefined risk strategy, but only an estimate for maximum loss for an undefined risk trade. Because the undefined risk case is more complicated, this chapter explains the BPR as it relates to undefined risk strategies, specifically short strangles.
Up until now, options trading has predominantly been discussed within the context of strangles, an undefined risk strategy with limited gain and theoretically unlimited loss. In this case, the BPR is calculated such that it is unlikely that the loss of aposition will exceed that threshold. More specifically, BPR is intended to account for roughly 95% of potential losses with exchange-traded fund (ETF) underlyings and 90% of potential losses with stock underlyings.
1
The historical effectiveness of BPR for an ETF underlying is seen in
Figure 4.1
by looking at losses for 45 days to expiration (DTE) 16
SPY strangle from 2005–2021.
Figure 4.1
Loss as a % of BPR for 45 DTE 16
SPY strangles held to expiration from 2005–2021.
In this example, most losses ranged from 0% to 20% of the BPR. Roughly 95% of all these losses were accounted for by the BPR when this position was held to expiration, as expected. Though BPR did not always capture the full extent of realized losses, it is an effective proxy for worst‐case loss on atrade‐by‐trade basis in most cases. This metric works fairly well for SPY strangles, but strangles with more volatile underlyings and strangles with tighter strikes may be more likely to have losses that breach BPR (hence the 90% efficacy rate for stocks).
BPR corresponds to the capital required to place atrade, and that quantity varies depending on the specific strategy. The BPR for short strangles can be approximated as 20% of the price of the underlying, but mathematically, BPR depends on three variables: the stock price,
put/call prices, and the put/call strike prices.
2
Because the strangle is composed of the short out‐of‐the‐money (OTM) call and short OTM put, the BPR required to sell astrangle is simply the larger of the short put BPR and the short call BPR. The short call/put BPR is the largest of three different values:
, which is the expected loss from a 20% move in the underlying price.
, which is the expected loss from a 10% strike breach.
, which ensures that there is aminimum BPR for cheap options.
As BPR is intended to encompass the largest likely loss for an undefined risk contract, the largest of these values is taken. This can be mathematically represen

eBooks\The Unlucky Investor_s Guide to Options Trading\The Unlucky Investor_s Guide to Options Trading.epub#section:c04.xhtml


the underlying price.
, which is the expected loss from a 10% strike breach.
, which ensures that there is aminimum BPR for cheap options.
As BPR is intended to encompass the largest likely loss for an undefined risk contract, the largest of these values is taken. This can be mathematically represented using the
max
function, which takes the largest of the given values:
(4.1)
(4.2)
Combining these formulas, the BPR of the strangle is given by:
(4.3)
Clearly, this equation is hairy, but using some numerical examples, one can infer how strangle BPR and, therefore, option risk changes with more intuitive variables, such as the historical and implied volatility of the underlying. Consider three potential strangle trades outlined in
Table 4.1
.
Table 4.1
Three examples of approximate 45 DTE 16
strangle trades with different parameters and the resulting BPR.
Scenario A
Scenario B
Scenario C
Stock Price
$150
$150
$300
Call Strike
$160
$175
$320
Put Strike
$140
$130
$280
Call Price
$1
$2
$2
Put Price
$1
$2
$2
BPR
$2,000
$1,750
$4,000
IV
20%
45%
20%
The underlying in Scenario Bis priced the same as that of Scenario A, but the strikes for the 16
strangle are further apart (consistent with ahigher implied volatility). The underlying in Scenario Cis twice as expensive as the underlyings in Scenarios Aand B, but the IV in Scenario Cis the same as that of Scenario A.
Because the BPR is higher in Scenario Ccompared to Scenario A (but the implied volatility and contract delta are the same), traders can deduce that strangle BPR tends to increase with the price of the underlying.
Technically
, BPR is inversely correlated with option price, but the BPR still tends to increase with the price of the underlying because more expensive instruments have larger volatilities (as adollar amount) and, therefore, higher potential losses. BPR also decreases as the IV of the underlying increases, and both relationships can be seen in
Figure 4.2
looking at BPR for 45 DTE 16
SPY strangles from 2005–2021.
These charts show astrong linear relationship between BPR and underlying price and aslightly messier inverse relationship between BPR and underlying IV. This relationship is largely driven by the strikes moving further OTM for afixed
as IV increases. BPR tends to decrease exponentially as the IV of the underlying increases, and because BPR is arough estimate for worst‐case loss, this relationship illustrates how the magnitude of potential outlier losses tends to decrease when IV increases.
3
Figure 4.2
Data from 45 DTE 16
SPY strangles from 2005–2021. (a) BPR as afunction of underlying price. (b) BPR as afunction of underlying IV.
Short premium positions carry higher credits and larger profit potentials when IV is high, but the reduction in BPR also allows more short premium positions to be placed compared to when IV is low. Because average profit and loss (P/L) is higher on atrade‐by‐trade basis
and
more potentially profitable positions can be opened, it is essential to reserve alarge percentage of portfolio buying power for high IV conditions. This additionally justifies increasing the percentage of portfolio capital allocated to short premium BPR as IV increases. These crucial high‐IV profits improve portfolio performance but also cushion potential future losses. Historically, when the VIX has been over 40 compared to under 15, the same amount of capital has covered the BPR of roughly twice as many 16Δ SPY strangles. The difference between the number of short premium trades allowed in these two volatility environments is even larger when taking portfolio allocation guidelines into account. For context, consider the scenarios outlined in
Table 4.2
.
Table 4.2
Two portfolios with the same net liquidity but different amounts of market volatility, using SPY strangle data from 2005–2021.
Scenario A
Scenario B
Net Portfolio Liquidity
$100,000
$100,000
Current VIX
> 40
< 15
Portfolio Allocation
$50,000
$25,000
Approx. 16
SPY Strangle BPR
$1,500
$3,300
Max Number of Strangles
33
7
It'simportant to note that BPR can be used to compare the capital at risk for variations of the same type of strategy, but it
cannot
be used to compare the risk between defined risk strategies and undefined risk strategies. For example, if the BPR required to trade ashort strangle with underlying Awas twice the BPR required to trade ashort strangle with underlying Band otherwise had identical parameters, we can conclude that Ais twice as risky as B. This is avalid comparison because we are considering two trades with the same risk profile, but BPR
cannot
be used to compare strategies with different risk profiles (say, ashort strangle versus ashort put) because it does not account for factors like the probability of profit or the probability of incurring alarge loss. This subtlety will be discussed in more detail in the following chapter.
Understanding BPR is crucial when transitioning from options theory to applied options trading because it corresponds to the actual c


count for factors like the probability of profit or the probability of incurring alarge loss. This subtlety will be discussed in more detail in the following chapter.
Understanding BPR is crucial when transitioning from options theory to applied options trading because it corresponds to the actual capital requirements of trading short options. BPR is also necessary to discuss the capital efficiency of options (option leverage) in entirety. Consider astock trading at $100 with avolatility of 20%, and suppose atrader wanted to invest in this asset with abullish directional assumption. The trader could achieve abullish directional exposure to this underlying in afew different ways as shown with the examples in
Table 4.3
.
Table 4.3
Example trades that offer bullish directional exposure. Assume that the 50
(ATM) call and put contracts have 45 DTE durations and cover 100 shares of stock.
Strategy
Capital Required
Max Profit
Max Loss
Probability of Profit (POP)
50 Shares of Long Stock
$5,000
∞
$5,000
50%
Long 50
Call
$280
∞
$280
30%
Short 50
Put
$2,000 (BPR)
$280
$9,720
60%
In this one‐to‐one comparison, the effects of option leverage are clear because the long call position achieves the same profit potential as the long stock position with 94% less capital at risk. The short put position is capable of losing several times the initial investment of the trade but has ahigher POP than the long stock position and requires 60% less capital. Suppose that the price of the stock increases to $105 after 45 days. The resulting profits and corresponding returns for these different positions is given below:
Long stock:
Long ATM call:
Short ATM put:
In this example, the long call position was able to achieve 88% of the long stock profit with 94% less capital, and the short put position was able to achieve 12%
more
profit than the long stock position with 60% less capital.
Takeaways
Because short premiums are subject to significant tail risk, brokers must reserve capital to cover the potential losses of each position. This capital is called BPR. The total amount of portfolio capital available for trading is called portfolio buying power.
BPR is used to evaluate short premium risk on atrade‐by‐trade basis in two ways: BPR is afairly reliable metric for worst‐case loss of an undefined risk position, and BPR is used to determine if aposition is appropriate for aportfolio based on its buying power.
For long options, BPR is the cost of the option. For short strangles, the BPR is roughly 20% of the price of the underlying. BPR for short options encompasses roughly 95% of potential losses for ETF underlyings and 90% of losses for stock underlyings.
Strangle BPR tends to increase linearly with the price of the underlying because more expensive instruments have larger volatilities (as adollar amount) and, therefore, higher potential losses. There is an inverse relationship between strangle BPR and underlying IV; more specifically, it approximately decreases exponentially as the IV of the underlying increases. This demonstrates the advantages of trading short when IV is high because more short strangles can be opened with the same amount of capital as in low IV, and the outlier loss potential is generally lower.
BPR can be used to compare capital at risk for variations of the same strategy, but it cannot be used to compare the risk of different strategies with different risk profiles.
The leveraged nature of options allows traders to achieve adesired risk‐return profile with significantly less capital than an equivalent stock position.
Notes
1
This statistic will vary with the IV of the underlying, but this is asuitable approximation for general cases.
2
This is the FINRA (Financial Industry Regulatory Authority) regulatory minimum. Brokers typically follow this formula, but occasionally (especially when IV is very high) they will increase the capital requirements for contracts on specific underlyings.
3
This relationship between BPR and IV is specific to strangles. The next chapter discusses how these relationships may differ for certain defined risk strategies.


Chapter 5
Constructing a Trade
This book has covered anumber of topics but how does one tie all these concepts together and actually build atrade? Options are unique in that they have
tunable
risk‐reward profiles, and the type of strategy and choice of contract parameters hugely impact the characteristics of that profile. This chapter describes some common short premium strategies and how varying each contract feature tends to alter the risk‐reward properties of ashort position. Some basic guidelines are also included, but the ideal trade selection ultimately depends on personal profit goals, loss tolerances, account size, and the existing positions in aportfolio. Each new trade should complement existing positions, ideally contributing some degree of diversification to the overall risk profile. However, first this chapter outlines the mechanics of building individual trades; portfolio management will be discussed later.
The general procedure for constructing atrade can be summarized as follows:
Choose an asset universe.
Choose an underlying.
Choose acontract duration.
Choose adefined or undefined risk strategy.
Choose adirectional assumption.
Choose adelta.
All these factors impact the overall profile of atrade, and strategies are rarely constructed in alinear manner. Traders build trades according to their personal preferences and the size of their account, making the process of constructing aposition unique. For instance, if the priority is an
undefined risk
trade, the choice of underlying will have more constraints. If the priority is trading aparticular underlying under acertain directional assumption
, the delta and the risk definition will have more constraints.
Choose an Asset Universe
Before choosing an underlying, it'simportant to start with an appropriate asset universe or aset of tradable securities with desirable characteristics. The assets suitable for retail options trading must have highly liquid options markets, meaning the contracts for the security can be easily converted into cash without significantly affecting market price. To understand why liquidity is crucial, consider an example of an
illiquid
asset, such as ahouse. Selling ahome at fair market value in asaturated housing market requires significant time and effort. Sellers run the additional risk of having to reduce the asking price significantly to secure abuyer quickly. Options illiquidity carries risk for similar reasons, and selectively trading assets with liquid options markets ensures that contract orders will be filled efficiently and at afair market price.
Options liquidity is not equivalent to underlying liquidity. An underlying is considered liquid if it has the following characteristics:
Ahigh daily volume, meaning many shares traded daily (>1 million).
Atight bid‐ask spread, meaning asmall difference between the maximum abuyer is willing to pay and the minimum aseller is willing to take (<0.1% of the asset price).
Some examples of liquid underlyings include AMZN, IBM, SPY, and TSLA, as shown in
Table 5.1
below.
Table 5.1
Pricing, bid‐ask spread, and daily volume data for different equities collected on February 10, 2020, at 1 p.m.
Asset
Previous Closing Price
Bid‐Ask Spread
Spread/Close (% of Closing Price)
Daily Trading Volume
AMZN
$3,322.94
$0.32
0.01%
1,240,935
IBM
$121.98
$0.05
0.04%
2,484,505
SPY
$390.51
$0.02
0.005%
16,619,920
TSLA
$863.42
$0.51
0.06%
9,371,760
It is relatively straightforward to verify underlying liquidity using daily volume and bid‐ask spread as apercentage of closing price. However, aliquid underlying may not have an equally liquid options market. Sufficiently liquid options underlyings must have
contract prices
with tight bid‐ask spreads and high daily volumes. The options selection should also offer flexible time frames and strike prices. An underlying with aliquid options market is thus classified by the following properties:
Ahigh open interest or volume across strikes (at least afew hundred per strike).
Atight bid‐ask spread (<1% of the contract price).
Available contracts with several strike prices and expiration dates.
Options liquidity ensures that traders have awide selection of contracts to choose from and that short premium positions can be opened (i.e., contracts can be sold to abuyer) easily. Additionally, liquidity minimizes the risk of being stuck in aposition because it allows traders to close short premium positions (i.e., identical contracts can be bought back) quickly.
The asset universe presented in this book is equity‐based and mostly consists of stock and exchange‐traded fund (ETF) underlyings, recalling that astock represents ashare of ownership for asingle company, and an ETF tracks aspecific set of securities, such as asector, commodity, or market index. However, asset universes are generally product indifferent and can include any instruments with liquid options that present opportunities, such as commodities, digital currencies, and futures.
Choose an Underlying
The

eBooks\The Unlucky Investor_s Guide to Options Trading\The Unlucky Investor_s Guide to Options Trading.epub#section:c05.xhtml


tracks aspecific set of securities, such as asector, commodity, or market index. However, asset universes are generally product indifferent and can include any instruments with liquid options that present opportunities, such as commodities, digital currencies, and futures.
Choose an Underlying
The choice of underlying from auniverse of sufficiently liquid assets is somewhat arbitrary, but traders often choose to trade short options on instruments for apreferred company, sector, or market under specific directional beliefs. Though this is aperfectly fine way to trade, it'salso important to select an underlying with an appropriate amount of risk for agiven account size. The two broad classes of instruments in the example asset universe, stocks and ETFs generally have different volatility profiles, and there are pros and cons to trading each, summarized in
Table 5.2
.
Table 5.2
General pros and cons for stock and ETF underlyings.
Stocks
ETFs
Pros
Cons
Pros
Cons
Tend to have options with higher credits and higher profit potentials
Frequent high implied volatility (IV) conditions
Single‐company risk factors
Earnings and dividend risk
Tend to have options with higher buying power reductions (BPRs)
Inherently diversified across sectors or markets
Tend to have options with lower BPRs and are still highly liquid
Limited selection compared to stocks
High IV conditions are not common
When choosing an underlying, the capital requirement of the trade is alimiting factor. Asingle position should generally occupy no more than 5% to 7% of portfolio capital, meaning that stock underlyings may not be suitable for small accounts because they are more expensive to trade. However, since selling premium when IV is elevated has several benefits, stock underlyings may be preferable underlyings in certain circumstances. As stocks are subject to company‐ and sector‐specific risks, they tend to have higher IVs compared to ETFs and tend to present elevated IV opportunities more often. Note that if trading stock options, investors should also be aware of the contextual information (e.g., earnings reports dates, company announcements) that may be driving these periods of IV inflation because it may impact the
strategy choice.
1
This practice is less important when trading options with ETF underlyings.
The additional risk factors (coupled with the fact that liquid stocks are often more expensive than ETFs) result in stock options generally having much larger profit and loss (P/L) swings throughout the contract duration, more ending P/Lvariability, and more tail risk. If the capital requirements of the trade are not excessive and the IV of the underlying is favorable, then these will be the next factors to consider. Overall, stock options are usually riskier but also carry ahigher profit potential than ETF options. Consider the statistics outlined in
Table 5.3
.
Table 5.3
Options P/Land probability of profit (POP) statistics 45 days to expiration (DTE) 16
strangles with six different underlyings, held to expiration, from 2009–2020. Assets include SPY (S&P 500 ETF), GLD (gold commodity ETF), SLV (silver commodity ETF), AAPL (Apple stock), GOOGL (Google stock), and AMZN (Amazon stock).
16
Strangle Statistics, Held to Expiration (2009–2020)
Underlying
Average Profit
Average Loss
POP
ETFs
SPY
$160
–$297
82%
GLD
$125
–$424
83%
SLV
$33
–$103
81%
Stocks
AAPL
$431
–$1,425
76%
GOOGL
$1,108
–$2,886
80%
AMZN
$1,041
–$2,215
78%
The tolerance for P/Lswings, ending P/Lvariability, and tail exposure depends mostly on account size and personal risk preferences. If atrade approximately satisfies those preferences and the constraints previously stated, then the choice of underlying is somewhat irrelevant because of aconcept called product indifference. Because IV is derived from option price, if two assets have the same IV, their options will have roughly the same price (as apercentage of underlying price).
Consequently, one underlying will not give more edge with respect to options pricing inefficiencies compared to another, provided they have similarly liquid options markets. To visualize this, consider the example in
Table 5.4
.
Table 5.4
Two sample options underlyings with the same IV but differing stock and put prices.
Option Parameters
Scenario A
Scenario B
Stock Price
$100
$200
IV
33%
33%
45 DTE 16
Put Price
$1
$2
In Scenario A, the put is $1 (1% of the underlying price). Due to the efficient nature of options pricing, the short put in Scenario Bwill also cost 1% of the underlying price, as both assets have the same IV. Product indifference suggests that no one (liquid) underlying is inherently superior to another, merely that there are proportional trade‐offs among different assets. The high‐risk, high‐reward nature of stocks is not inherently better or worse than the relatively stable nature of ETFs, but some assets may be more suitable for an individual trader than others. We can, thus, conclude that the choice of an underlying essentially depen


e‐offs among different assets. The high‐risk, high‐reward nature of stocks is not inherently better or worse than the relatively stable nature of ETFs, but some assets may be more suitable for an individual trader than others. We can, thus, conclude that the choice of an underlying essentially depends on five main factors (in order of significance):
The liquidity of the options market
The BPR of the trade relative to account size
2
The IV of the underlying
3
The preferred magnitude of P/Lswings, ending P/Lvariability, and tail exposure per trade
The preferred company, sector, or market exposure
Choose a Contract Duration
There are many ways to choose acontract duration, but this book approaches this process from aqualitative perspective. The three primary goals when choosing acontract duration are summarized as follows:
Using portfolio buying power effectively.
Maintaining consistency and reaching alarge number of occurrences.
Selecting asuitable time frame given contextual information.
It is essential to determine what contract duration is the most effective use of portfolio buying power without exceeding risk tolerances. Premium prices tend to be more sensitive to changes in underlying price (higher gamma) for contracts that are near expiration (5 DTE) compared to contracts that are far from expiration (120 DTE). Consequently, short‐term contracts tend to have significant P/Ls swings for alarger portion of their duration compared to longer‐term contracts, which initially have more moderate P/Lswings and gradually become more volatile. Most contracts also tend to exhibit an increase in P/Linstability as they near expiration, which is also aconsequence of higher gamma. The gamma of acontract tends to increase throughout acontract'sduration, usually the result of the underlying price drifting closer to one of the strangle strikes over time.
Figure 5.1
illustrates these concepts by comparing the standard deviation of daily P/Ls for different durations of the same type of contract.
All of these strangles exhibit adecrease in P/Lswings right before expiration. This is because options rapidly lose their extrinsic value near expiration, presuming they are not in‐the‐money (ITM), which is usually the case because 16Δ options often expire worthless. Near expiration, this exponential decline in premium from theta decay outweighs the magnitude of the P/Lswings.
The P/Lswings at the beginning of the contract vary greatly based on the contract duration. On day seven, the daily P/Lfor the 15 DTE contract has ahigh variance, and the 30 DTE, 45 DTE, and 60 DTE contracts have much lower P/Lswings around the seven‐day mark. This is because the 16
strikes in the 15 DTE contract are much closer to the at‐the‐money (ATM) than the 16
strikes in the 30+ DTE contracts. This is shown numerically in
Table 5.5
.
4
Figure 5.1
Standard deviation of daily P/Ls (in dollars) for 16
SPY strangles with various durations from 2005–2021. Included are durations of (a) 15 DTE, (b) 30 DTE, (c) 45 DTE and (d) 60 DTE.
Table 5.5
illustrates how the 16
strikes are closer to the stock price for the 15 DTE contract compared to longer duration strangles. Therefore, small changes in the price of the underlying will have alarger impact on the option'sdelta compared to contracts with longer durations and further out strike prices. The 30+ DTE contracts tend to experience larger P/Lswings once they near expiration because the underlying price often drifts toward one of the strikes over time.
Longer contract durations, because their P/Lswings are manageable for alonger period of time, give traders more time to assess the trade and adjust to changes in market conditions. However, trade durations that are too long are not necessarily effective uses of buying power because they do not allow for as many occurrences and take alonger time to generate profits. To summarize, longer‐term contracts, which don'ttypically experience large changes in P/Luntil the latter half of their duration, tie up buying power for along time without generating significant profit most of that time. By comparison, shorter‐term contracts exhibit volatile P/Lswings for the majority of their duration and leave little time to react to new conditions. Amiddle ground contract duration, one between 30 and 60 days on amonthly expiration cycle,
5
is considered asuitable use of buying power. Middle ground durations offer aperiod of manageable P/Lswings while providing afair amount of daily premium decay and areasonable timescale for profit. This buffer time allows traders to evaluate the viability of atrade before P/Lswings become more volatile. It also allows traders to incorporate different trade management strategies, which will be covered in the next chapter.
Table 5.5
Data for 16
SPY strangles with different durations from April 20, 2021. The first row is the distance between the strike for a 16
put and the price of the underlying for different contract durations (i.e., if the price of the


anagement strategies, which will be covered in the next chapter.
Table 5.5
Data for 16
SPY strangles with different durations from April 20, 2021. The first row is the distance between the strike for a 16
put and the price of the underlying for different contract durations (i.e., if the price of the underlying is $100 and the strike for a 16
put is $95, then the put distance is ($100 – $95)/$100 = 5%). The second row is the distance between the strike for a 16
call and the price of the underlying for different contract durations.
16
SPY Option Distance from ATM
Option Type
15 DTE
30 DTE
45 DTE
Put Distance
3.9%
6.5%
8.0%
Call Distance
2.4%
3.9%
4.9%
Another important factor to consider when choosing acontract duration is consistency and the number of occurrences. Consistently choosing similar contract time frames increases the number of occurrences and simplifies portfolio management because expiration and management times will roughly align for the majority of short premium trades in aportfolio. As discussed in
Chapter 3
, alarge number of occurrences is required to reduce the variance of portfolio averages and maximize the likelihood of realizing long‐term expected values.
For profit and risk expectations to be dependable, it is essential to choose contract durations (and management strategies) that allow for areasonable number of occurrences and to do so consistently. Therefore, it'sgood practice to choose acontract time frame that is convenient to maintain and short enough to allow for several trades to be placed throughout the trading year, presuming the duration maintains amanageable amount of tail risk exposure.
The final major factor when choosing acontract duration is contextual information, particularly when trading stock options. Contextual information, such as an approaching election, earnings report date, or forecasted natural disaster cannot necessarily be used to consistently forecast price direction, but it may indicate apredictable change in price volatility. There is, therefore, utility in taking contextual information into account when choosing acontract time frame. This will be discussed in more detail in
Chapter 9
.
Choose Defined or Undefined Risk
Long options strategies are defined risk trades, as the maximum loss is capped by the price of the contract. Short options positions may have defined or undefined risk profiles.
Defined risk strategies have afixed maximum loss, but capping downside risk has drawbacks. Undefined risk strategies have unlimited downside risk, meaning the maximum loss on atrade-by-trade basis is potentially unlimited. The pros and cons of defined and undefined risk strategies are outlined in
Table 5.6
.
Table 5.6
Comparison of defined and undefined risk strategies.
Undefined Risk
Defined Risk
Pros
Cons
Pros
Cons
Higher POPs
Higher profit potentials
Unlimited downside risk
Higher BPRs (more expensive to trade)
Limited downside risk
Lower BPRs (less expensive to trade)
Lower POPs
Lower profit potentials
Can run into liquidity issues
aa
Defined risk trades, because they consist of short premium and long premium contracts, require more contracts to be filled than equivalent undefined risk trades. There is, therefore, ahigher risk that adefined risk order will be unable to close at agood price compared to an equivalent undefined risk position.
Defined risk strategies have aknown maximum loss (i.e., the BPR of the trade) and will typically have alower BPR than an undefined risk strategy with similar parameters (underlying, contract duration, strikes). Although defined risk positions expose less capital than equivalent undefined risk positions, this does not imply they carry less risk.
Recall from the discussion of option risk in
Chapter 3
that there are several ways to quantify the risk of an options strategy. Though defined risk strategies avoid carrying
outlier risk
, they are more likely to lose most or all their BPR when losses do occur. It's, therefore,
essential
to recognize that BPR is mathematically and functionally different for defined and undefined risk trades, and it
cannot
be used as acomparative risk metric between them. This will be discussed later in the chapter.
Due to the differences in POP and profit potential between risk profiles, the maximum amount of portfolio capital allocated should differ depending on whether the strategy is defined or undefined risk. For undefined risk strategies, traders are compensated for the significant tail risk with high profit potentials and high POPs. It is generally recommended that undefined risk strategies constitute the majority of portfolio capital allocated to short premium strategies. More specifically,
at least
75% of allocated capital should be in undefined risk strategies (with amaximum of 7% allocated per trade) and at most 25% of allocated capital should be in defined risk strategies (with amaximum of 5% allocated per trade). For anumerical example, consider the allocation scenarios for a $100,000 portfoli


of allocated capital should be in undefined risk strategies (with amaximum of 7% allocated per trade) and at most 25% of allocated capital should be in defined risk strategies (with amaximum of 5% allocated per trade). For anumerical example, consider the allocation scenarios for a $100,000 portfolio described in
Table 5.7
.
Table 5.7
Portfolio allocation for defined and undefined risk strategies with a $100,000 portfolio at different VIX levels.
VIX Level
Maximum Portfolio Allocation
Minimum Undefined Risk Allocation
Maximum Defined Risk Allocation
20
$30,000
$22,500 ($7,000 max BPR per trade)
$7,500 ($5,000 max BPR per trade)
40
$50,000
$37,500 ($7,000 max BPR per trade)
$12,500 ($5,000 max BPR per trade)
These differences will be elaborated on in the next section, but to summarize, the following five factors are generally the most important to consider when comparing defined and undefined risk trades:
The amount of BPR required for atrade relative to the net liquidity of the portfolio.
The likelihood of profiting from aposition.
The preferred amount of downside risk.
The preferred ending P/Lvariability and preferred magnitude of P/Lswings throughout the contract duration.
The profit targets.
Defined risk trades typically require less capital, have more moderate P/Lswings throughout the trade, and have less ending P/Lstandard deviation compared to undefined risk trades. Consequently, defined risk trades may be preferable for small accounts and relatively new traders. Undefined risk trades are statistically favorable and have, therefore, been the focus of this book. However, the following section discusses how to construct defined risk trades that behave like undefined risk trades while offering protection against extreme losses. For these types of strategies, and only these types of strategies, defined risk trades can be substituted for undefined risk trades in the portfolio allocation guidelines.
Choose a Directional Assumption
After choosing acontract underlying, duration, and risk profile, the next steps are determining the directional assumption for the price of the underlying asset and selecting astrategy consistent with that belief and the preferred risk profile. The directional assumption may be bullish, bearish or neutral, and the optimal choice is subjective and depends on one'sinterpretation of the efficient market hypothesis (EMH). Recall that the EMH assumes that current prices reflect some degree of available information and comes in three main forms:
Weak EMH: Current prices reflect all past price information.
Semi‐strong EMH: Current prices reflect all publicly available information.
Strong EMH: Current prices reflect all possible information.
Each form of the EMH implies some degree of limitation with respect to price predictability:
Weak EMH: Past price information cannot be used to consistently predict future price information, which invalidates technical analysis.
Semi‐strong EMH: Any publicly available information cannot be used to consistently predict future price information, which invalidates fundamental analysis.
Strong EMH: No information can be used to consistently predict future price information, which invalidates insider trading.
No form of the EMH is universally accepted or rejected, and the ideal form to trade under (if any) depends on personal preference. This book takes asemi‐strong approach to market predictability, assuming equity and option prices effectively reflect available information and that few directional assumptions are valid (e.g., the market trends bullish in the long term). As volatility reverts back to along‐term value following significant deviations, it is more valid to make directional assumptions on IV once it'sinflated rather than directional assumptions around equity prices. This book, therefore, typically focuses on directionally
neutral
strategies, such as the short strangle, because these types of positions profit from changes in volatility and time and are relatively insensitive to price changes. However, that is apersonal choice. Multiple strategies are outlined in
Table 5.8
.
For reasons discussed in earlier chapters, all these strategies perform best in high IV. However, the POPs of these trades remain relatively high in all volatility environments, justifying that some percentage of capital should be allocated in all IV conditions.
To elaborate on the differences between defined and undefined risk, compare statistics for the two neutral strategies: the iron condor and the strangle. An iron condor consists of ashort out-of-the-money (OTM) vertical call spread and ashort OTM vertical put spread (introduced in
Table 5.8
). This trade is effectively ashort strangle paired with along strangle having strikes that are further OTM (typically called wings). As with strangles, iron condors are profitable when the underlying price stays within the range defined by the short strikes or when there is asignificant IV contraction or time decay. For example,


ort strangle paired with along strangle having strikes that are further OTM (typically called wings). As with strangles, iron condors are profitable when the underlying price stays within the range defined by the short strikes or when there is asignificant IV contraction or time decay. For example, a 16
strangle can be turned into a 16
iron condor with 10
wings
6
with the addition of along call and along put with the same duration, further from OTM (the long contracts are 10
in this case). An example of an iron condor is shown in
Table 5.9
and
Figure 5.2
.
Table 5.8
Examples of popular short options strategies with the same delta of approximately 20.
a
Strategy
Composition
Defined or Undefined Risk
Directional Assumption
POP
b
Naked Option
Short OTM put
Undefined
Bullish
80%
Short OTM call
Undefined
Bearish
80%
Vertical Spread
Short OTM put, long further OTM put
Defined
Bullish
77%
Short OTM call, long further OTM put
Defined
Bearish
77%
Strangle
Short OTM put, short OTM call
Undefined
Neutral
70%
Iron Condor
Short OTM vertical call spread, short OTM vertical put spread
Defined
Neutral
60%
a
The directional assumption will be flipped for the long side of anon‐neutral position. For along neutral position, the assumption is that the underlying price will move outside of the price range defined by the contract strikes. The POP of the long side is given by 1 – (short POP).
b
These POPs are approximate. The POP of adefined risk strategy depends heavily on the choice of long delta(s). Contracts with wider long deltas will generally have higher POPs. This will be explored more later in the chapter.
The long wings of the iron condor cap the maximum loss as either the difference between the strike prices of the vertical put spread or vertical call spread (whichever is greater) times the number of shares in the contract (typically 100) minus the net credit. The maximum loss of the short iron condor is equivalently the BPR required to open the trade.
It can be summarized by the following formula:
(5.1)
Continuing with the same example as shown in
Table 5.9
, we apply this formula to calculate some statistics for these two trades in
Table 5.10
.
Table 5.9
Example of a 16
SPY strangle and a 16
SPY iron condor with 10
wings when the price of SPY is $315 and its IV is 12%. All contracts must have the same duration.
Contract Strikes
16
Strangle
16
Iron Condor with 10
Wings
Long Call Strike
‐‐‐
$332
Short Call Strike
$328
$328
Short Put Strike
$302
$302
Long Put Strike
‐‐‐
$298
The short strikes were approximated with the expected range formula and the long strikes for the iron condor wings were approximated with the Black‐Scholes formula. Underlyings are often subject to strike skew, not to be confused with distribution skew, which neither of these methods really consider. This means that the strikes (both long and short) are typically not equidistant (as adollar amount) from the price of the underlying although they were approximated in this example as such. This concept will be explored more later in the chapter.
Figure 5.2
Graphical representation of the iron condor described in
Table 5.9
. The 10
wings correspond to long strikes that are $17 from ATM, which is further OTM than the 16
short strikes that are $13 from ATM.
Table 5.10
Initial credits for the 16
SPY strangle and the 16
SPY iron condor with 10
wings outlined in
Table 5.9
. Because the difference between the vertical call spread strikes ($332–$328) and the vertical put spread strikes ($302–$298) is the same ($4), this value is used when calculating the maximum loss.
Contract Credits
16
Strangle
16
Iron Condor with 10
Wings
Long Call Debit
‐‐‐
−$69
Short Call Credit
$122
$122
Short Put Credit
$108
$108
Long Put Debit
‐‐‐
−$57
Net Credit
$230
$104
Max Loss
∞
BPR
$5,000
$296
The choice of wing width depends on personal profit targets and the threshold for extreme loss. Large losses generally occur once the long put or call strikes are breached by the price of the underlying, so wings that are further from ATM are exposed to larger outlier moves but are more likely to be profitable. Wings that are closer to ATM are more expensive but also reduce the maximum loss of atrade. To summarize, wings that are further out yield iron condors with alarger profit potential and ahigher probability of profit but also larger possible losses. For some numerical examples, refer to the statistics in
Table 5.11
.
Table 5.11
Statistical comparison of 45 DTE 16
SPY iron condors with different wing widths, held to expiration from 2005–2021. Wings that have asmaller delta are further from ATM compared to wings with alarger delta. Included are 45 DTE 16
SPY strangle statistics held to expiration from 2005–2021 for comparison.
16
Iron Condor Statistics (2005–2021)
16
Strangle Statistics (2005–2021)
Statistics
5
Wings
10
Wings
13
Wings
POP
79%
75%
73%
81%
Average P/L
$35
$15
$6
$44
Standard Deviation of P/L
$251
$132
$74
$614
Conditional Value at Risk (CVaR) (5%)
−$771
−$399
−$220
−$1,535