Chapter 6
Managing Trades
Options traders can hold a position to expiration or close it prior to expiration (active management). Compared to holding a contract until expiration, an active management strategy should be considered for the following reasons:
It allows for more occurrences over a given time frame (if capital is redeployed).
It may allow for a more efficient use of portfolio buying power (if capital is redeployed).
It tends to reduce risk on a trade‐by‐trade basis.
Trades can be managed in any number of ways, but similar to choosing a contract duration,
consistency
is essential for reaching a large number of occurrences and realizing favorable long‐term averages. This book advocates for adopting a simple management strategy that is easily maintainable:
Closing a trade at a fixed point in the contract duration.
Closing a trade at a fixed profit or loss target.
Some combination of these strategies.
This chapter discusses different management strategies, compares trade‐by‐trade performance, and elaborates on the major factors to consider when choosing appropriate position management. Because management strategies impact the proportion of initial credit traders ultimately collect, the statistics will often be represented as an initial credit percentage rather than dollars. This chapter also predominantly focuses on undefined risk strategy management. Many of these principles also apply to defined risk positions, but defined risk positions are generally more forgiving from the perspective of trade management because they occupy a smaller percentage of portfolio buying power and have limited loss potential.
Managing According to DTE
As mentioned in
Chapters 3
and
5
, trade profit and loss (P/L) swings tend to become more volatile as options approach expiration. For a strangle, this increase generally results from the price of the underlying drifting toward one of the strikes throughout the contract duration. Consequently, closing a trade prior to expiration, whether at a fixed point in the contract duration or at a specific profit or loss target, tends to reduce ending P/L standard deviation and outlier risk exposure on a trade‐by‐trade basis. Managing trades actively also frees portfolio buying power from existing positions, which can then be allocated more strategically as opportunities arise. The freed capital can be redeployed to the same type of initial position (increasing the number of occurrences)
1
or
to a new position with more favorable short premium conditions (which may be a more efficient use of buying power).
Managing a trade according to days to expiration (DTE), such as closing a position halfway to expiration, offers the benefits described previously and is straightforward to execute. This technique has a clear management timeline and requires minimal portfolio supervision, particularly when portfolio positions have comparable durations.
The choice of management time greatly affects the profit potential and outlier risk exposure of a trade because trades managed closer to expiration are more likely to be profitable and have larger profits on average but are generally exposed to more tail risk. The trade‐by‐trade statistics shown in
Table 6.1
compare the performance of different management times for 45 DTE 16
SPY strangles.
Table 6.1
Statistics for 45 DTE 16
SPY strangles from 2005–2021 managed at different times in the contract duration.
16
SPY Strangle Statistics (2005–2021)
Management DTE
Probability of Profit (POP)
Average P/L
Average Daily P/L
P/L Standard Deviation
Conditional Value at Risk (CVaR) (5%)
40 DTE
67%
2.3%
$0.23
73%
–206%
30 DTE
73%
10%
$1.75
88%
–212%
21 DTE
79%
21%
$1.60
96%
–283%
15 DTE
78%
25%
$1.51
105%
–304%
5 DTE
a
82%
33%
$1.34
185%
–514%
Expiration
81%
28%
$1.29
247%
–708%
a
Strangles managed at 5 DTE seem to outperform strangles held to expiration because they have a higher POP and average P/L but lower P/L volatility and less tail risk. These results are specific to this strategy and data set, and were likely skewed by significant historical events. This trend is not generalizable across strategies, including the one presented in this table.
Table 6.1
shows that managing a trade prior to expiration is less likely to profit but also has less P/L standard deviation and less tail risk, and it also collects more daily, on average, compared to holding to expiration. These statistics also demonstrate that management time generally carries a trade‐off among profit potential, loss potential, and the number of occurrences. Compared to trades managed earlier in the contract duration, trades managed later have larger profits and losses and also allow for fewer occurrences. As early‐managed positions accommodate more occurrences and average more P/L per day than positions held to expiration, closing positions prior to expiration and redeploying capital to new positions is generally a more efficient use of capital compared to extracting more extrinsic value from an exi

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As early‐managed positions accommodate more occurrences and average more P/L per day than positions held to expiration, closing positions prior to expiration and redeploying capital to new positions is generally a more efficient use of capital compared to extracting more extrinsic value from an existing position.
If adopting this strategy, choose a management time that satisfies individual trade‐by‐trade risk tolerances, offers a suitable profit
potential, and occupies buying power for a reasonable amount of time. Remember that selling premium in any capacity carries tail risk exposure even when a position is closed almost immediately (see the 40 DTE results in
Table 6.1
). To achieve a decent amount of long‐term profit and justify the tail loss exposure, consider closing trades around the contract duration midpoint.
Managing According to a Profit or Loss Target
Compared to allowing a trade to expire, managing a position according to a profit target simplifies profit expectations and tends to reduce per‐trade P/L variance. Closing limit orders can be set by a trader and automatically executed by the broker, but this management strategy still requires some active maintenance. This is because trades may never reach the predetermined profit benchmark and may require alternative management prior to expiration. Additionally, there is some subtlety in choosing the profit target because that choice significantly impacts the profit and loss potential of a trade, as shown in
Tables 6.2
and
6.3
.
Managing at a profit threshold or expiration generally carries more P/L standard deviation and outlier risk exposure on a trade‐by‐trade basis than managing at 21 DTE, although it also comes with higher POPs and higher per‐trade profit potentials depending on the profit benchmark. Short options are highly likely to reach low profit targets early in the contract duration when P/L swings and tail risk are both fairly low. Therefore, managing a trade according to a low profit target yields a higher strategy POP, lower P/L standard deviation, and less outlier risk compared to managing at a high profit target. However, despite the higher average daily P/Ls, setting the profit threshold
too low
does not allow traders to collect a sufficient credit to justify the inherent tail risk of the position. Average P/Ls are well below the given profit target in all cases due to the tail loss potential. When using a 25% target, for example, the contract failed to reach the target only 4% of the time. Still, those losses were significant enough to bring down the P/L average by more than half. If this management strategy is adopted, a profit threshold between 50% and 75% of the initial credit is suitable to realize a reasonable amount of long‐term average profit and reduce the impact of outlier losses. Additionally, because these mid‐range profit targets tend to be reached near the contract midpoint or shortly after, these benchmarks also allow for a reasonable number of occurrences.
2
Table 6.2
Statistics for 45 DTE 16
SPY strangles from 2005–2021 managed at different profit targets. If the profit target is not reached during the contract duration, the strangle expires. The final row includes statistics for 45 DTE 16
SPY strangles managed around halfway to expiration (21 DTE) as a reference.
16
SPY Strangle Statistics (2005–2021)
Profit Target
POP
Average P/L
P/L Standard Deviation
Probability of
Reaching Target
CVaR (5%)
25% or Exp.
96%
11%
191%
96%
−522%
50% or Exp.
91%
16%
236%
90%
−654%
75% or Exp.
84%
22%
245%
80%
−699%
100% (Exp.)
81%
28%
247%
52%
−708%
21 DTE
79%
21%
96%
N/A
−283%
These tests did not account for whether a P/L target was reached throughout the trading day, but rather whether a target was reached by the end of the trading day. Therefore, these statistics are not entirely representative of this management technique.
Table 6.3
Average daily P/L and average duration for the contracts and management strategies described in
Table 6.2
.
16
SPY Strangle Statistics (2005–2021)
Profit Target
Average Daily P/L Over Average Duration
Average Duration (Days)
25% or Exp.
$1.75
15
50% or Exp.
$1.67
24
75% or Exp.
$1.49
34
100% (Exp.)
$1.29
44
21 DTE
$1.60
24
These tests did not account for whether a P/L target was reached throughout the trading day, but rather whether a target was reached by the end of the trading day. Therefore, these statistics are not entirely representative of this management technique. Additionally, because there can be significant variability in when a contract reaches a certain profit threshold, daily P/L estimates were derived from data over the average duration of the trade.
Just as trades can be managed according to a fixed profit target, they can also be managed according to a fixed loss limit (a stop loss). Defining a loss limit is trickier because option P/L swings are highly volatile. Small loss limits are reached commonly, but trades are also likely to recover. Implementing a very small loss limit may s


to a fixed profit target, they can also be managed according to a fixed loss limit (a stop loss). Defining a loss limit is trickier because option P/L swings are highly volatile. Small loss limits are reached commonly, but trades are also likely to recover. Implementing a very small loss limit may significantly limit upside growth and make losses more likely. To understand this, see
Table 6.4
.
Table 6.4
Statistics for 45 DTE 16
SPY strangles from 2005–2021 managed at different loss limits. If the loss limit is not reached during the contract duration, the strangle expires. The final two rows reference other management strategies for comparison.
16
SPY Strangle Statistics (2005–2021)
Loss Limits
POP
Avg P/L
P/L Standard Deviation
Prob. of Reaching Target
CVaR (5%)
−50% or Exp.
58%
21%
90%
40%
−168%
−100% or Exp.
69%
25%
110%
25%
−238%
−200% or Exp.
76%
27%
131%
13%
−338%
−300% or Exp.
79%
27%
149%
8%
−450%
−400% or Exp.
79%
27%
160%
6%
–536%
None (Exp.)
81%
28%
247%
N/A
−708%
21 DTE
79%
21%
96%
N/A
−283%
50% Profit or Exp.
91%
16%
236%
90%
−654%
These tests did not account for whether or not a P/L amount was reached throughout the trading day, but rather whether it was reached by the end of the trading day. Therefore, these statistics are not entirely representative of this management technique.
Using a low stop loss threshold, –50% for example, results in lower P/L standard deviation and outlier risk compared to holding the contract to expiration. However, in this case, losses are more common and occur roughly 42% of the time since it is not uncommon for options to reach this loss threshold, although many positions ultimately recover prior to expiration (note the higher POPs for larger limits). Implementing a stop loss also does not necessarily eliminate
all
tail risk exceeding that threshold. For example, despite having a stop loss of –50%, a sudden implied volatility (IV) expansion or underlying price change may cause daily loss
to increase from –25% to –75%, resulting in the closure of the trade but with a final P/L past the loss threshold. Because upside potential is limited and some degree of tail exposure exists with a very small stop loss, a mid‐range stop loss of at least –200% is practical.
3
Using a stop loss and otherwise holding to expiration generally has a higher profit and larger loss potential than managing at the duration midpoint but tends to carry less tail risk than managing at a reasonable profit target. For more active trading, stop losses are not typically used alone but rather combined with another management strategy.
Comparing Management Techniques and Choosing a Strategy
The strangle management strategies presented thus far are relatively straightforward. These techniques can be ranked according to loss potential (from highest to lowest) and quantified using CVaR and P/L standard deviation of the positions studied:
Hold until expiration.
Manage at a profit target between 50% and 75%.
Manage at a loss limit of –200%.
Manage at 21 DTE (halfway to expiration).
Remember that consistency and ease of implementation are important factors to consider when choosing a management strategy. For traders who are comfortable with active trading, strategies can be combined and more precisely tuned according to individual preferences. For instance, suppose a trader of 45 DTE 16
SPY strangles wants a management strategy with a high POP, moderate P/L standard deviation, and moderate outlier exposure. One possibility is managing at 50% of the initial credit
or
at 21 DTE, whichever occurs first. The statistics for this strategy are outlined in
Table 6.5
.
Table 6.5
Statistics for 45 DTE 16
SPY strangles from 2005–2021 managed either at 50% of the initial credit
or
21 DTE, whichever comes first. Statistics for other strategies are given for comparison and ranked by CVaR.
16
SPY Strangle Statistics (2005–2021)
Management Strategy
POP
Average P/L
Average Daily P/L
P/L Standard Deviation
CVaR (5%)
21 DTE
79%
21%
$1.60
96%
–283%
21 DTE or 50% Profit
81%
18%
$1.67
96%
–288%
–200% Loss or Exp.
76%
27%
N/A
131%
–338%
50% Profit or Exp.
91%
16%
$1.67
236%
–654%
None (Exp.)
81%
28%
$1.29
247%
–708%
In this example, the duration and profit targets are moderate, resulting in a combined strategy with smaller but slightly more likely profits than 21 DTE management and significantly less loss potential than 50% profit management. This may be appealing to risk‐averse traders because it eliminates a large fraction of the historic losses and significantly reduces tail exposure with the benefit of a slightly higher POP and higher average daily P/L.
When choosing a management strategy, know that all management strategies come with trade‐offs among POP, average P/L, P/L standard deviation, and loss potential. How these factors are weighted depends on individual goals:
For
likely
profits, profit potential must be smaller or exposure to outlier losses must be larger.
For
large
profits, there must be fewer occurrences or mo


with trade‐offs among POP, average P/L, P/L standard deviation, and loss potential. How these factors are weighted depends on individual goals:
For
likely
profits, profit potential must be smaller or exposure to outlier losses must be larger.
For
large
profits, there must be fewer occurrences or more exposure to outlier losses.
For a
small
loss potential, profit potential must be smaller or profits must be less likely.
For a qualitative comparison of the different strategies, see
Table 6.6
.
As mentioned, a suitable management strategy depends on individual preferences for trading engagement, per‐trade P/L potential, P/L likelihood and number of occurrences. Following are example scenarios highlighting different management profiles:
Table 6.6
Qualitative comparison of different management strategies.
Management Strategy
21 DTE
50% or Exp.
–200% or Exp.
Exp.
Convenience
Med
High
a
High
High
POP
Med
High
Med
Med
Per‐Trade Loss Potential
Low
High
Low
High
Per‐Trade Profit Potential
Med
Low
High
High
Number of Occurrences
Med
Med
Low
Low
a
If limit orders are used, profit target management is very convenient.
For passive traders with portfolios that can accommodate more outlier risk, it may make more sense to use only a stop loss and otherwise hold trades to expiration to extract as much extrinsic value from existing positions as possible.
Active traders with portfolios that can accommodate more outlier risk may manage general positions at a fixed profit target and close higher‐risk, higher‐reward trades halfway to expiration.
Very active traders may manage all undefined risk contracts at either 50% of the initial credit
or
halfway through the contract duration because this method prioritizes moderating outlier risk and achieving likely profits of reasonable size.
Generally speaking, an active management approach is more suitable for retail traders because more occurrences can be achieved in a given time frame, it is a more efficient use of capital, average daily profits are higher, and the per‐trade loss potential is lower. It's critical to reiterate that this risk is on a
trade‐by‐trade
basis. Short premium losses happen infrequently and are often caused by unexpected events, making it difficult to precisely compare long‐term performance of strategies of varying timescales. The next section discusses in more detail why comparing the long‐term risks for management strategies is not straightforward.
A Note about Long‐Term Risk
As mentioned previously, contracts tend to have more volatile P/L swings as the contract approaches expiration. Managing trades prior to expiration, therefore, tends to have lower P/L standard deviation and outlier risk exposure on a trade‐by‐trade basis compared to holding the contract to expiration. But it's critical to note that this reduction in risk on a trade‐by‐trade basis
does not necessarily translate to a reduction in risk on a long‐term basis
. Though early management techniques reduce loss magnitude
per trade
, inherent risk factors arise from a larger number of occurrences. Consequently, one management strategy may have lower per‐trade exposure compared to another, but it may have more
cumulative
long‐term risk. Consider the scenarios outlined in
Figures 6.1
and
6.2
. Each scenario compares the performances of two portfolios, each with $100,000 of capital invested. Both portfolios consist of short 45 DTE 16
SPY strangles continuously traded, but the trades in one portfolio are managed halfway to expiration (21 DTE) and the trades in the other are managed at expiration. The unique market conditions in each scenario affect the performance of each management strategy.
4
The IV expansion during the 2020 sell‐off was one of the largest and most rapid expansions recorded in the past 20 years, producing historic losses for SPY strangles. Due to the timing and duration of this volatility expansion, 45 DTE contracts opened in February and closed at the end of the March expiration cycle experienced the majority of the expansion and were
especially
affected. Shown in
Figure 6.1
, the portfolio of contracts held to expiration was immediately wiped out by this extreme market volatility, and the portfolio of early‐managed contracts incurred a large drawdown of roughly 40% but ultimately survived. This scenario demonstrates how the loss potential for contracts held to expiration is significantly larger than for contracts managed early. However, this does not necessarily mean that holding to expiration results in more cumulative loss long term.
Figure 6.1
(a) Two portfolios, each with $100,000 in capital invested, trading short 45 DTE 16
SPY strangles from February 2020 to January 2021. One portfolio consists of strangles managed at 21 DTE (dashed line), and the other consists of strangles held until expiration (solid line). (b) The VIX from February 2020 to January 2021.
Figure 6.2
(a) Two portfolios, each with $100,000 in capital invested, trading short 45 DTE 16
SPY strangles from Septem


olio consists of strangles managed at 21 DTE (dashed line), and the other consists of strangles held until expiration (solid line). (b) The VIX from February 2020 to January 2021.
Figure 6.2
(a) Two portfolios, each with $100,000 in capital invested, trading short 45 DTE 16
SPY strangles from September 2018 to September 2019. One portfolio consists of strangles managed at 21 DTE (dashed line), and the other consists of strangles held until expiration (solid line). (b) The VIX from September 2018 to September 2019.
These same strategies perform quite differently near the end of 2018 when the market experienced smaller, more frequent IV expansions. During this period, the 21 DTE management time for 45 DTE contracts consistently landed on IV peaks during this cycle of market volatility, causing the early‐managed portfolio to incur several consecutive losses. Comparatively, the 45 DTE expiration cycles were just long enough to evade these smaller peaks and the portfolio of contracts held to expiration had much stronger performance overall. This scenario demonstrates how having lower per‐trade loss potential does not guarantee stronger long‐term performance or smaller drawdowns.
Comparing the long‐term risks of strategies that occur over different timescales is complicated. These examples show potential trading strategies during unique macroeconomic conditions, but any number of factors could have impacted the realized experience of someone trading during these periods. For instance, if people began trading short 45 DTE 16
SPY strangles on February 3, 2020, they would have had a final P/L of –$717 if they managed at 21 DTE and a final P/L of –$8,087 if they held the contract to expiration. If they instead began trading the same strategy
one month later
on March 4, 2020, they would have had a final P/L of –$2,271 if they managed at 21 DTE and a final P/L of $518 if they held the contract to expiration. Strangle risk and performance, particularly during periods of extreme market volatility, are highly sensitive to changes in timescale and IV. There is as much variation in how people choose contract duration, manage positions, and apply stop losses as there are traders. This makes it difficult to model how people
would realistically trade
in a statistically rigorous way and, consequently, creates complications when evaluating the long‐term risk of different management strategies.
Rather than factor in long‐term risk when selecting a management strategy, the choice should ultimately be based on the following criteria:
Convenience/consistency.
Capital allocation preferences and desired number of occurrences.
Average P/L and outlier loss exposure
per trade
.
Takeaways
Traders should choose a
consistent
management strategy to increase the number of occurrences and the chances of achieving favorable long‐term averages. Some management strategies include closing a trade at a fixed point in the contract duration, closing a trade at a fixed profit or loss target, or some combination of the two.
Compared to trades managed early in the contract duration, trades managed later have larger profits and losses, higher POPs, and allow for fewer occurrences. Early‐managed positions accommodate more occurrences and average more P/L per day than positions held to expiration. Closing positions prior to expiration and redeploying capital to new positions is generally a more efficient use of capital compared to extracting more extrinsic value from an existing position.
If managing according to DTE, consider closing trades around the contract duration midpoint to achieve a decent amount of long‐term profit and justify the tail loss exposure of short premium.
To realize reasonable profits and reduce outlier losses, consider a profit threshold between 50% and 75% of the initial credit. A profit or loss target that is too small (say 25% of initial credit) reduces average P/L and per‐trade profit potential, and a profit or loss target that is too large does little to mitigate outlier risk.
If implementing a stop loss, a mid‐range stop loss threshold of at least −200% is practical because there is limited upside potential and still some degree of tail exposure with a very low stop loss.
A suitable management strategy depends on an individual's preferences for trade engagement, per‐trade average P/L, per‐trade outlier risk exposure, and the number of occurrences. Managing undefined risk contracts at 50% of the initial credit or halfway through the contract duration generally achieves reasonable, consistent profits and moderate outlier risk for those more comfortable with active trading. This policy of trading small and trading often also allows for more occurrences.
Comparing long‐term risks of trade management strategies is complicated because unexpected events, such as the 2020 sell‐off, affect short premium strategies differently depending on the contract duration. For this reason, compare the risk and rewards of different strategies on a t


more occurrences.
Comparing long‐term risks of trade management strategies is complicated because unexpected events, such as the 2020 sell‐off, affect short premium strategies differently depending on the contract duration. For this reason, compare the risk and rewards of different strategies on a trade‐by‐trade basis and choose one based on convenience and consistency, capital allocation preferences, tail exposure preferences, and profit goals.
The concepts outlined in this chapter are specific to undefined risk positions. These management principles can also be applied to defined risk positions, but defined risk positions are generally more forgiving because they have limited loss potential. It is not as essential to manage defined risk losses because the maximum loss is known, and in some cases, it may be better to allow a defined risk trade more time to recover rather than close the position at a loss.
Notes
1
This technique is commonly known as rolling.
2
For defined risk positions, a profit target of roughly 50% or lower is more suitable because P/L swings are less volatile and higher profit targets are less likely to be reached.
3
Stop losses are not suitable for defined risk strategies. As defined risk strategies have a fixed maximum loss, it is best to allow defined risk losers to expire rather than manage them at a specific loss threshold. This gives the position more opportunity to recover.
4
Options portfolio backtests should be taken with a grain of salt. Options are highly sensitive to changes in timescale, meaning that a concurrent portfolio with strangles opened on slightly different days, closed on slightly different days, or with slightly different durations may have performed quite differently than the ones shown here.


Chapter 7
Basic Portfolio Management
Whether adopting an equity, option, or hybrid portfolio, building a portfolio is nontrivial. Identifying a suitable collection of elements, calculating optimal portfolio weights, and maintaining that balance easily becomes hairy. Though countless ways to approach this process exist, the portfolio management tactics discussed in this book are fairly back‐of‐the‐envelope and divided between two chapters. This chapter covers
necessary
guidelines in portfolio management, and the following chapter covers advanced portfolio management including
supplementary
techniques for portfolio optimization. Basic portfolio management includes the following concepts:
Capital allocation guidelines
Diversification
Maintaining portfolio Greeks
Capital Allocation and Position Sizing
The purpose of the dynamic allocation guidelines first introduced in
Chapter 3
is to limit portfolio tail exposure while also allowing for reasonable long‐term growth by scaling capital allocation according to the current risks and opportunities in the market. Recall that the amount of portfolio buying power allotted to short premium positions, such as short strangles and short iron condors, should range from 25% to 50%, depending on the current market volatility, with the remaining capital either kept in cash or a low‐risk passive investment. Of the amount allocated to short premium, at least 75% should be reserved for undefined risk trades (with less than 7% of portfolio buying power allocated to a single position) and at most 25% reserved for defined risk strategies (with less than 5% of portfolio buying power allocated to a single position), although there are exceptions for high probability of profit (POP), defined risk strategies. It's worth mentioning that it is not always feasible to strictly abide by the position size caps of 5% to 7%. If a portfolio has only $10,000 in buying power and implied volatility (IV) is low (i.e., VIX<15), this rule limits the maximum per‐trade buying power reduction (BPR) to $700 for an undefined risk trade at a time when BPRs tend to be high. This guideline would severely limit the opportunities available for small accounts. Though total portfolio allocation guidelines
must
be followed, there is more leniency for the per‐trade allocation guidelines in smaller accounts.
These guidelines limit the amount of capital exposed to outlier losses, but how capital is allocated depends on personal profit goals and loss tolerances. An options portfolio is typically composed of two types of positions: core and supplemental. Core positions are usually high‐POP trades with moderate profit and loss (P/L) standard deviation. These types of positions should offer consistent, fairly reliable profits and reasonable outlier exposure although they will vary by risk tolerance. Consider the following examples:
Riskier core position: a 45 days to expiration (DTE) 20
strangle (undefined risk trade) with a diversified exchange‐traded fund (ETF) underlying, such as SPY or QQQ.
More conservative core position: a 45 DTE 16
SPY iron condor with 6
wings (high‐POP, defined risk trade) with a diversified ETF underlying, such as SPY or QQQ.
Core positions should comprise the majority of a portfolio and be diversified across sectors to develop more reliable portfolio profit and loss expectations and resilience to market volatility. Supplemental positions are not necessarily dependable sources of profit but rather tools for market engagement. These positions are typically higher‐risk, higher‐reward trades meant to capitalize on dynamic opportunities in the market. Some examples of supplemental positions include earnings trades (which will be discussed in more detail in
Chapter 9
) or strangles with stock underlyings, such as a 45 DTE 16
AAPL strangle. When trading stock underlyings, defined risk supplemental positions would be suitable for more risk‐averse traders. These types of positions have significantly more P/L variability than positions with ETF underlyings, resulting in more per‐trade profit potential and more loss potential with less dependable profit and loss expectations.
The expected returns, P/L variability, and tail exposure of a portfolio overall primarily depend on the types of core positions, types of supplemental positions, and the ratio of core positions to supplemental positions. Portfolios for more risk‐tolerant traders may include a larger percentage of supplemental positions. However, mitigating tail risk remains the highest priority, particularly if the portfolio underlyings are not diversified well. This is why, generally speaking, at most 25% of the capital allocated to short premium should go toward supplemental positions. For example, if the VIX is valued at 45 and 50% of portfolio buying power is allotted to short premium positions (per the allocation guidelines), then at most 25% of the 50% portfolio buying power (or 12.5%) should be allocated to supplemental positions. See
Table 7.

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o toward supplemental positions. For example, if the VIX is valued at 45 and 50% of portfolio buying power is allotted to short premium positions (per the allocation guidelines), then at most 25% of the 50% portfolio buying power (or 12.5%) should be allocated to supplemental positions. See
Table 7.1
for some numerical context.
Compared to core positions, such as SPY or QQQ strangles, the supplemental positions above have significantly more profit potential, loss potential, and tail risk exposure. The average profit is larger partially as the result of supplemental underlying assets having higher per share prices. This was the case with GOOGL and AMZN, which cost more than the other equity underlyings throughout the entire backtest period. However, these instruments also carry larger profit potentials as option underlyings because they are subject to company‐specific risk factors that often inflate the values of their respective options. This was particularly the case with AAPL, which had a
lower
per share value than SPY, QQQ, and GLD throughout this backtest period but more option volatility.
Table 7.1
Statistics for 45 DTE 16
strangles from 2011–2020, managed at expiration. Included are examples for core and supplemental position underlyings.
16
Strangle Statistics (2011–2020)
Underlying
POP
Average Profit
Average Loss
Conditional Value at Risk (CVaR) (5%)
Core
SLV
84%
$32
−$88
−$201
QQQ
74%
$109
−$183
−$454
SPY
80%
$162
−$320
−$800
GLD
81%
$119
−$456
−$1,100
Supplemental
AAPL
74%
$425
−$1,443
−$4,771
GOOGL
80%
$1,174
−$2,955
−$6,593
AMZN
77%
$1,235
−$2,513
−$6,810
These statistics do not account for IV or stock‐specific factors, such as earnings or dividends.
Due to these single‐stock risk factors and the variance reflected in the option P/Ls, stocks are generally unsuitable underlyings for core positions. Their high profit potentials make them appealing supplemental position underlyings for opportunistic investors, but mitigating the tail risk exposure from supplemental positions is key for portfolio longevity. The most effective way to accomplish this is by strictly limiting the portfolio capital allocated to high‐risk positions.
To summarize, core positions should provide somewhat reliable expectations around P/L and be diversified across sectors. Supplemental positions should comprise a smaller percent of a portfolio because they bring higher profit potentials but also more risk. Diversification, particularly when trading options, is another crucial risk management strategy that can significantly reduce portfolio P/L variability and outlier exposure.
The Basics of Diversification
All financial instruments are subject to some degree of risk, with the risk profiles of some instruments being more flexible than others. A single equity has an immutable risk profile, and an option's risk profile can be
adjusted according to multiple parameters. However in either scenario, traders are subject to the risk factors of the particular position. When trading a
portfolio
of assets, a trader may offset the risks of individual positions using complementary positions. Spreading portfolio capital across a variety of assets is known as diversification.
Risk is divided into two broad categories: idiosyncratic and systemic. Idiosyncratic risk is specific to an individual asset, sector, or position and can be minimized using diversification. For example, a portfolio containing only Apple stock is subject to risk factors specific to Apple and the tech sector. Some of those risks can be offset with the addition of an uncorrelated or inversely correlated asset, such as a commodity ETF like GLD. In this more diversified scenario, some hypothetical company‐specific risk factors causing AAPL stock to depreciate may be reduced by the performance of GLD, which has relatively independent dynamics.
Comparatively, systemic risk is inherent to the market as a whole and cannot be diversified away. All traded assets are subject to systemic risk because every economy, market, sector, and company has the potential to fail. No amount of diversification will ever remove that element of uncertainty. Instead, the purpose of diversification is to construct a robust portfolio with minimal sensitivity to company‐, sector‐, or market‐specific risk factors.
The process of building a diversified portfolio depends on the types of assets comprising the target portfolio. For an equity portfolio, the most effective way to diversify against idiosyncratic risk is to distribute portfolio capital across assets that have low or inversely correlated price movements. This is because the primary concern when trading equities is the directional movement of the underlying, specifically to the downside. Diversifying portfolio assets, typically using instruments for a variety of companies, sectors, and markets, reduces some of this directional concentration and improves the stability of the portfolio.
To understand the effectiveness of diversification by this met


lying, specifically to the downside. Diversifying portfolio assets, typically using instruments for a variety of companies, sectors, and markets, reduces some of this directional concentration and improves the stability of the portfolio.
To understand the effectiveness of diversification by this method, consider the example outlined next.
Table 7.2
shows different portfolio allocation percentages for two equity portfolios,
Table 7.3
shows the correlation of the assets in both portfolios, and
Figure 7.1
shows the comparative performance of the two portfolios. The historical directional tendencies are often estimated using the correlation coefficient,
which quantifies the strength of the historical linear relationship between two variables. Recall that the correlation coefficient ranges from –1 to 1, with 1 corresponding to perfect positive correlation, –1 corresponding to perfect inverse correlation, and 0 corresponding to no measured correlation.
Table 7.2
Two sample portfolios, each containing some percentage of market ETFs for reliable portfolio growth (SPY, QQQ), low volatility assets for diversification (GLD, TLT), and high volatility assets for increased profit potential (AMZN, AAPL).
% Portfolio Allocation
Portfolio A
Portfolio B
Market ETFs
40%
50%
Low Volatility Assets
50%
0
High Volatility Assets
10%
50%
These portfolio weights were determined intuitively and not by any particular quantitative methodology. This example demonstrates the effectiveness of diversification rather than providing a specific framework for achieving diversification in equity portfolios.
Table 7.3
The five‐year correlation history for the assets in Portfolios A and B. Though these relationships fluctuate with time over short timescales, they are assumed to remain relatively constant long term.
Correlation (2015–2020)
SPY
QQQ
GLD
TLT
AMZN
AAPL
Market
SPY
1.0
0.89
−0.13
−0.33
0.62
0.64
ETFs
QQQ
0.89
1.0
−0.12
−0.26
0.75
0.74
Low
Volatility
GLD
−0.13
−0.12
1.0
0.39
−0.12
−0.11
Assets
TLT
−0.33
−0.26
0.39
1.0
−0.18
−0.22
High
Volatility
AMZN
0.62
0.75
−0.12
−0.18
1.0
0.50
Assets
AAPL
0.64
0.74
−0.11
−0.22
0.50
1.0
Table 7.2
outlines two portfolios: Portfolio A is a relatively diversified portfolio with conservative risk tolerances and moderate profit expectations, while Portfolio B is a risk tolerant and fairly concentrated portfolio.
Table 7.3
shows how the elements in Portfolio B (SPY, QQQ, AMZN, AAPL) have fairly high mutual historic correlations and therefore similar
directional tendencies. Comparatively, half of Portfolio A is allocated to low volatility assets that are uncorrelated or inversely correlated with the market ETFs and high volatility assets. Therefore, due to the diversifying contributions of those relatively independent assets, Portfolio A is less sensitive to outlier market events.
Figure 7.1
shows how these portfolios would have performed from 2020–2021, importantly including the 2020 sell‐off and subsequent recovery.
Figure 7.1
Performance comparison for Portfolios A and B from 2020 to 2021. Each portfolio begins with $100,000 in initial capital.
Historic correlations have become
stronger
during financial crashes and sell‐offs. Stated differently, assets have become more correlated or more inversely correlated during volatile market periods. The correlations in
Table 7.2
, therefore,
underestimate
the correlation magnitudes that would have been measured from 2020–2021.
As a result of the COVID‐19 pandemic, market ETFs and highly correlated assets, such as large cap tech stocks incurred significant drawdowns. Portfolio B, half of which was high volatile tech stocks, crashed by roughly 25% from February to late March 2020. Comparatively,
Portfolio A still experienced massive drawdowns but only declined by 14% during the same period. Portfolio B is significantly more exposed to market volatility than Portfolio A, resulting in a more rapid, but unstable recovery following the 2020 sell‐off. Throughout this year, Portfolio B grew by roughly 90% from its minimum in March while Portfolio A was growing by 44%, but Portfolio B was nearly twice as volatile. Nondiversified portfolios are generally more sensitive to sector‐ or market‐specific fluctuations compared to diversified portfolios. Diversifying a portfolio across asset classes reduces position concentration risk and tends to reduce loss potential in the event of turbulent market conditions. However,
Figure 7.1
shows how more volatile, higher‐risk portfolios can pay off with higher profits.
Due to their complex risk profiles, options are inherently more diversified relative to one another compared to their equity counterparts. Unlike equities, where the primary concern is directional risk, several factors may affect option P/L:
Directional movement in the underlying price.
Changes in IV.
Changes in time to expiration.
Because exposure to each of these variables can be controlled according to the contract parameters, varying factors, such as duration/management


rn is directional risk, several factors may affect option P/L:
Directional movement in the underlying price.
Changes in IV.
Changes in time to expiration.
Because exposure to each of these variables can be controlled according to the contract parameters, varying factors, such as duration/management time, underlying, and strategy creates an additional reduction in P/L correlation that is not possible when trading equities exclusively. However, diversifying against directional risk of the underlyings remains most essential from the perspective of risk management, particularly outlier risk management. Diversifying against nondirectional risk by varying strategy or contract duration is supplemental.
To understand why it is so essential to diversify the option underlyings of a portfolio, consider two market ETFs: SPY and QQQ. These assets have historically had highly correlated price dynamics and IV dynamics, as shown in the correlation matrix in
Table 7.4
.
The equity underlyings and IV indices are highly correlated, meaning that IV expansion events and outlier price moves tend to happen simultaneously for these two assets. When such events do occur, short premium positions with these two underlyings may experience simultaneous tail losses. To get an idea of how often these positions have incurred simultaneous outlier losses historically, refer to the strangle statistics shown in
Table 7.5
.
Table 7.4
Historic correlations between two market ETFs (SPY, QQQ) and the correlations between their implied volatility indices (VIX, VXN) from 2011 to 2020. Also included is the correlation between each market index and the respective VIX, for reference.
Equity Price and IV Index Correlation (2011–2020)
SPY
QQQ
VIX
VXN
Equities
SPY
1.0
0.89
−0.80
QQQ
0.89
1.0
−0.76
Volatility
VIX
−0.80
1.0
0.89
Indices
VXN
−0.76
0.89
1.0
Table 7.5
The probability of outlier losses (worse than 200% of the initial credit) occurring simultaneously for 16
SPY strangles and 16
QQQ strangles from 2011 to 2020. All contracts have approximately the same duration (45 DTE), start date, and expiration date. The diagonal entries (SPY Strangle‐SPY Strangle, QQQ Strangle‐QQQ Strangle) indicate the probability of a strategy incurring an outlier loss individually, and the off‐diagonal entries correspond to the probability of the pair incurring outlier losses simultaneously.
Probability of Loss Worse than 200% (2011–2020)
SPY Strangle
QQQ Strangle
SPY Strangle
5.8%
3.9%
QQQ Strangle
3.9%
8.7%
Table 7.5
shows that it is reasonably unlikely for the pair of strategies to incur outlier losses simultaneously having occurred only 3.9% of
the time. However, if these events were completely independent, then these compound losses would have occurred less than 1% of the time:
. Additionally, when considering the outlier loss probability for each strategy on an individual basis, the effects of trading strangles with correlated underlyings becomes a bit clearer.
For example, the probability of a SPY strangle incurring an outlier loss is 5.8%. What is the probability a QQQ strangle will incur a simultaneous outlier loss given that a SPY strangle has taken an outlier loss? To calculate this, one can use conditional probability.
1
In other words, SPY strangles and QQQ strangles may only have simultaneous outlier losses 3.9% of the time, but when a SPY strangle incurs an outlier loss, there is a
67%
chance
that a QQQ strangle also will.
2
Generally, the probability of a compound loss is fairly low, but when one short premium position takes a loss there is often a high likelihood an equivalent position with a correlated underlying will experience a loss of comparable magnitude. Because the loss potential of these compound occurrences is so large, it is essential to diversify underlying equities and maintain appropriate position sizes for correlated options to reduce the likelihood and impact of compounding outlier losses.
Now consider two market ETFs (SPY and QQQ) and two diversifying ETFs that have been uncorrelated or inversely correlated to the market (GLD, TLT). The historic correlations are shown in
Table 7.6
and the probability of outlier losses occurring simultaneously are shown in
Table 7.7
.
Table 7.6
Historic correlations among two market ETFs (SPY and QQQ), a gold ETF (GLD), and a bond ETF (TLT) from 2011 to 2020.
Equity Price Correlation (2011–2020)
SPY
QQQ
GLD
TLT
SPY
1.0
0.89
−0.03
−0.41
QQQ
0.89
1.0
−0.04
−0.34
GLD
−0.03
−0.04
1.0
0.23
TLT
−0.41
−0.34
0.23
1.0
Table 7.7
The probability of outlier losses (worse than 200% of the initial credit) occurring simultaneously for different types of 16
strangles held to expiration from 2011 to 2020. All contracts have approximately the same duration (45 DTE), open and close dates. The diagonal entries correspond to the probability of the specific strategy incurring an outlier loss individually, and the off‐diagonal entries correspond to the probability of the pair incurring outlier losses simultaneously.
Probability


oximately the same duration (45 DTE), open and close dates. The diagonal entries correspond to the probability of the specific strategy incurring an outlier loss individually, and the off‐diagonal entries correspond to the probability of the pair incurring outlier losses simultaneously.
Probability of Loss Worse than 200% for Different Strangles (2011–2020)
SPY
QQQ
GLD
TLT
SPY
5.8%
3.9%
2.1%
1.9%
QQQ
3.9%
8.7%
1.9%
1.7%
GLD
2.1%
1.9%
12%
4.8%
TLT
1.9%
1.7%
4.8%
12%
Again, it is relatively unlikely for any pair to incur simultaneous outlier losses, but this table shows the significant reduction in the
conditional
outlier probability when the underlying assets are uncorrelated or inversely correlated. Consider the following:
If a SPY strangle incurs an outlier loss, there is a 67% chance of a compounding loss with a QQQ strangle.
If a SPY strangle incurs an outlier loss, there is a 36% chance of a compounding loss with a GLD strangle.
If a QQQ strangle incurs an outlier loss, there is a 20% chance of a compounding loss with a TLT strangle.
Compound losses still occur when the underlying assets have low or inversely correlated price movements, but this reduction in likelihood is crucial nonetheless. Having a portfolio that includes uncorrelated or inversely correlated assets is particularly meaningful during periods of unexpected market volatility when most assets develop a stronger correlation to the market and there are widespread expansions in IV. Though options can be diversified with respect to several variables, diversifying the underlying assets is one of the most effective ways to reduce the impact of outlier events on a portfolio. Because diversification does not entirely remove the risk of compounding outlier losses, so maintaining small position sizes (at most 5% to 7% of portfolio capital allocated to a single position) remains critical.
Maintaining Portfolio Greeks
The Greeks form a set of risk measures that quantify different dimensions of exposure for options. Each contract has its own specific set of Greeks, but some Greeks have the convenient property of being additive across positions with different underlyings. Consequently, these metrics can be used to summarize the various sources of risk for a portfolio and guide adjustments. The following portfolio Greeks will be the focus of this section:
Beta‐weighted delta (
): Recall from
Chapter 1
that beta is a measure of systematic risk and specifically quantifies the directional tendency of the stock relative to that of the overall market. Stocks with positive correlation to the market have positive beta and stocks with negative correlation have negative beta.
is similar to delta, which is the expected change in the option price given a $1 change in the price of the underlying. When delta is beta‐weighted, the adjusted value corresponds to the expected change in the option price given a $1 change in some reference index, such as SPY.
Theta (
): The decline in an option's value due to the passage of time, all else being equal. This is generally represented as the expected decrease in an option's value per day.
Maintaining the balance of these two variables is crucial for the long‐term health of a short options portfolio.
represents the amount of directional exposure a position has relative to some index rather than the underlying itself. The cumulative portfolio
delta represents the overall directional exposure of the portfolio relative to the market assuming that the beta index is a market ETF like SPY. Normalizing delta according to a standard underlying allows delta to be additive across all portfolio positions. This
cannot
be done with unweighted delta because $1 moves across different underlyings are not comparable, i.e., trying to add deltas of different positions is like adding inches and ounces. For example, a 50
sensitivity to underlying A and a 25
sensitivity to underlying B does not imply a 75
sensitivity to anything, unless A and B happen to be perfectly correlated.
neutral portfolios are attractive to short premium traders because the portfolio is relatively insensitive to changes in the market, and profit is primarily driven by changes in IV and time. Adopting
neutrality also simplifies aspects of the diversification process because a near‐zero
indicates low directional market exposure. As the delta of a position drifts throughout the contract duration, the overall delta of the portfolio is skewed. To maintain
neutrality, existing positions can be re‐centered (where the current trade is closed and reopened with a new delta), existing positions can be closed entirely, or new positions can be added. The most appropriate strategy depends on the current portfolio theta.
Theta is also additive across positions because the units of theta are identical for all options ($/day). Because short premium traders consistently profit from time decay, the total theta across positions gives a reliable estimate for the expected daily growth of the por


he current portfolio theta.
Theta is also additive across positions because the units of theta are identical for all options ($/day). Because short premium traders consistently profit from time decay, the total theta across positions gives a reliable estimate for the expected daily growth of the portfolio. The theta ratio (
) estimates the expected daily profit per unit of capital for a short premium portfolio. Options portfolios are subject to significant tail risk, so the expected daily profit should be significantly higher than a portfolio passively invested in the market to justify that risk. Therefore, one can determine the benchmark profit goals of an equivalent short options portfolio by referring to the daily P/L performance of a passively invested SPY portfolio as shown below in
Table 7.8
.
Table 7.8
Daily performance statistics for five portfolios passively invested in SPY from 2011–2021. Each portfolio has $100,000 in initial capital, and the amount of capital allocated in each portfolio ranges from 25% to 50%.
SPY Allocation Percentage
Daily Portfolio P/L (2011–2021)
25%
0.013%
30%
0.015%
35%
0.017%
40%
0.020%
50%
0.025%
From 2011–2021, a passively invested SPY portfolio collected between 0.013% and 0.025% daily depending on the percentage of capital allocated. In other words, these portfolios had daily profits between $13 and $25 per $100,000 of capital over the past 10 years (
). However, the expected daily profit per unit of capital for a short options portfolio should be
significantly
higher than this benchmark. For most traders, the minimum theta ratio should range from 0.05% to 0.1% of portfolio net liquidity to justify the tail risks of short premium. In other words, short premium portfolios should have a daily expected profit between $50 and $100 per $100,000 of portfolio buying power from
decay.
The theta ratio should not exceed 0.2%. A higher theta ratio is preferable, but it should not be too high due to hidden gamma risk. Gamma (
) is the expected change in the option's delta given a $1 change in the price of the underlying. Delta neutral positions are rarely gamma neutral, and if the gamma of a position is especially high, then the delta of the trade is highly sensitive to changes in the underlying price and is generally unstable. A position with high delta sensitivity can easily affect the overall
neutrality of a portfolio.
The gammas of different derivatives cannot be compared across underlyings for similar reasons as to why raw delta cannot be compared across underlyings. Gamma cannot be accurately beta‐weighted as delta can; however, a positive relationship
between gamma and theta presents a solution to this problem. Positions with large amounts of theta, such as trades with strikes that are close to at‐the‐money (ATM) or trades that are near expiration, typically also have large amounts of gamma risk. Because theta is additive across portfolio positions, the theta ratio is the most direct indicator of excessive gamma risk. This relationship between gamma and theta also demonstrates how short premium traders must balance the profitability of time decay with the P/L fluctuations resulting from gamma.
To summarize, the theta ratio for an options portfolio should range from 0.05% to 0.1% and should not exceed 0.2%. Based on the theta ratio and the amount of capital currently allocated, existing positions should then be re‐centered, short premium positions should be added, or short premium positions should be removed. Given these benchmarks for expected daily profits, the procedure for modifying portfolio positions can be summarized as follows:
If a properly allocated, a well‐diversified portfolio is
neutral but does not provide a sufficient amount of theta, then the positions in the portfolio should be reevaluated. In this case, perhaps some defined risk trades should be replaced with undefined risk trades or undefined risk positions should be rolled to higher deltas. New delta neutral positions can also be added, such as strangles and iron condors, for example. IV and theta are also highly correlated, meaning that higher IV underlyings could also be considered if theta is too low. These measures can be reversed if the portfolio has too much theta exposure while being
neutral.
If the theta ratio is too low (<0.1%), then either existing positions should be re‐centered/tightened or new short premium positions should be added.
If the
is too large and positive (bullish), then add new negative
positions (e.g., add short calls on positive beta underlyings or add short puts on negative beta underlyings).
If the
is too large and negative (bearish), then add new positive
positions (e.g., add short puts on positive beta underlyings).
If the theta ratio is too large (>0.2%), then either existing positions should be re‐centered/widened or short premium positions should be removed.
If the
is too large and positive (bullish), then remove positive
positions (e.g., remove short puts on positive be


t puts on positive beta underlyings).
If the theta ratio is too large (>0.2%), then either existing positions should be re‐centered/widened or short premium positions should be removed.
If the
is too large and positive (bullish), then remove positive
positions (e.g., remove short puts on positive beta underlyings).
If the
is too large and negative (bearish), then remove negative
positions (e.g., remove short calls on positive beta underlyings).
If a properly allocated, well-diversified portfolio provides a sufficient amount of theta but is not
neutral, then existing positions should be reevaluated. For example, skewed positions could be closed and re‐centered or replaced with new delta-neutral positions that offer comparable amounts of theta.
Takeaways
The amount of portfolio buying power allotted to short premium positions should range from 25% to 50% depending on the current market volatility, with the remaining capital either kept in cash or a low‐risk passive investment. Of the amount allocated, at least 75% should be reserved for undefined risk trades (with no more than 7% allocated to a single position), and at most 25% should be reserved for defined risk strategies (with no more than 5% allocated to a single position). The total portfolio allocation guidelines
must
be followed, but there is more leniency for the per‐trade allocation guidelines, especially in smaller accounts.
An options portfolio is typically composed of two types of positions: core and supplemental. Core positions are usually high‐POP trades with moderate P/L variance that offer consistent profits and reasonable outlier exposure. Supplemental positions are not necessarily dependable sources of profit but rather tools for market engagement. At most 25% of the capital allocated to short premium should go toward supplemental positions.
Unlike equity portfolios, options portfolios can be diversified with respect to multiple variables, such as duration/management time, underlying, and strategy. Diversifying the underlyings of an options portfolio remains the most essential diversification tool for portfolio risk management, particularly outlier risk management.
Beta‐weighted delta (
) represents the amount of directional exposure a position has relative to some index rather than the underlying itself. Portfolio theta (
) represents the expected daily growth of the portfolio. The minimum theta ratio for an options portfolio should range from 0.05% to 0.1% and should not exceed 0.2%. Maintaining the balance of these two Greeks ensures the risk‐reward profile of an options portfolio remains as close to the target as possible.
Notes
1
For an introduction to conditional probability, refer to the appendix.
2
A 67% conditional probability of a compound loss is very high but lower than the compound loss probability when trading the equivalent equities. SPY and QQQ are
highly
correlated and experience near‐identical drawdowns in periods of market turbulence. Therefore, that these options incur compound outlier losses only 70% of the time demonstrates the inherent diversification of options alluded to earlier.


Chapter 8
Advanced Portfolio Management
Having covered the necessary basics of portfolio management, this chapter discusses supplemental optimization techniques for traders who can accommodate more active trading. The capital allocation guidelines, underlying diversification, and Greeks of a portfolio are essential to maintain and are relatively straightforward to employ. This chapter will introduce some less essential strategies:
Additional option diversification techniques.
Weighting assets according to probability of profit (POP).
Advanced Diversification
As stated in the previous chapter, one of the biggest strategic differences between equity portfolios and options portfolios is the ability to diversify
risk with respect to factors other than price. Diversifying with respect to the underlying is the most effective way to reduce the effect of outlier events on a portfolio. Diversifying with respect to other variables, such as time and strategy, requires more active management but tends to reduce the profit and loss (P/L) correlation between positions. For example, consider the per‐day standard deviation of P/L for SPY strangles with different durations as shown in
Figure 8.1
.
Figure 8.1
Standard deviation of daily P/Ls (in dollars) for 16
SPY strangles with various durations from 2005–2021. Included are durations of (a) 15 days to expiration (DTE), (b) 30 DTE, (c) 45 DTE, and (d) 60 DTE.
Short premium trades tend to have more volatile P/L swings as they approach expiration, a result of the position becoming more sensitive to changes in time and underlying price (larger gamma and theta). Because contracts with different durations have varying sensitivities to these
factors at a given time, diversifying the timescales of portfolio positions reduces the correlations among their P/L dynamics. Because trading consistent contract durations is important for reaching many occurrences, the most effective way to diversify with respect to time is by trading contracts with consistent durations but a variety of expiration dates. This strategy achieves an assortment of contract durations in a portfolio at a given time without compromising the number of occurrences. Despite its efficacy, diversification with respect to time will not be thoroughly covered in this chapter because it is difficult to maintain conveniently and consistently.
Strategy diversification, while not as essential as underlying diversification, is another risk management technique that is more straightforward than time diversification. This method effectively spreads portfolio capital across different risk profiles while maintaining the same directional assumption for a given underlying (or a highly correlated underlying). This lets traders capitalize on the directional dynamics of an asset while protecting a proportion of portfolio capital from outlier losses. To see an example of the diversification potential for this method, consider a backtest of three different portfolios. Each portfolio contains some combination of two directionally neutral SPY strategies: strangles and iron condors. The performance of these portfolios in this long‐term backtest is shown in
Figure 8.2
and analyzed in
Table 8.1
. The purpose of this backtest is not to demonstrate the profit or loss potential associated with combining SPY strangles and iron condors but rather to illustrate the possible effects of strategy diversification on portfolio risk according to one sample of outcomes.
The impact of diversification is immediately clear, particularly when emphasizing the drawdowns of the 2020 sell‐off. Strangles and iron condors experienced massive drawdowns in early 2020 even though defined risk trades are lower‐risk, lower‐reward trades. The cumulative drawdowns as a percentage of portfolio capital are approximately the same across all three portfolios (roughly 150%). However, the drawdowns as a raw dollar amount were significantly larger for the strangle portfolio compared to the combined portfolio. During more regular market conditions, the combined portfolio also had a much larger POP and profit potential than the iron condor portfolio and less P/L variability and outlier risk than the strangle portfolio.
Figure 8.2
Cumulative P/L of three different portfolios containing some combination of SPY strangles and SPY iron condors, held to expiration from 2005–2021. The strangle portfolio contains 10 strangles, the combined portfolio contains five strangles and five iron condors, and the iron condor portfolio contains 10 iron condors. All contracts are traded once per expiration cycle, opened at the beginning of the expiration cycle and closed at expiration. These positions have the same short delta (16
), approximately the same duration (45 DTE), and the same open and close dates. The long strikes of the iron condors are roughly 10
.
This example demonstrates how diversifying portfolio capital across defined and undefined risk strategies lets a trader capitalize on the di

eBooks\The Unlucky Investor_s Guide to Options Trading\The Unlucky Investor_s Guide to Options Trading.epub#section:c08.xhtml


the same short delta (16
), approximately the same duration (45 DTE), and the same open and close dates. The long strikes of the iron condors are roughly 10
.
This example demonstrates how diversifying portfolio capital across defined and undefined risk strategies lets a trader capitalize on the directional tendencies of an underlying asset (or several highly correlated underlyings) while protecting a fraction of capital from unlikely outlier events. However, this example combines strategies in a highly simplified way as market implied volatility (IV), capital allocation guidelines, alternative management techniques, and strategy‐specific factors are not considered. In practice, defined and undefined risk strategies reach P/L targets at different rates and often require different management strategies. The percentage of capital allocated to a single position also depends on a number of factors, including the buying power reduction (BPR) of the trade (maximum of 5% for defined risk trades and 7% for undefined risk) and the correlation with the existing positions in a portfolio. For traders interested in a more quantitative approach to positional capital allocation, allocation weights can be estimated from the probability of profit of the strategy.
Table 8.1
Statistical analysis of the three portfolios illustrated in
Figure 8.2
. The first four statistics (POP, average P/L, standard deviation of P/L, and conditional value at risk (CVaR)) gauge portfolio performance during more regular market conditions (2005–2020). The final column gives the worst‐case drawdown from the 2020 sell‐off (the cumulative losses from February to March 2020).
2005–2020
2020 Sell‐Off
Portfolio Type
POP
Average P/L
Standard Deviation of P/L
CVaR (5%)
Worst‐Case Drawdowns
Strangle
76%
$379
$1,803
−$5,174
−$77,520
Combined
75%
$221
$1,275
−$3,648
−$45,080
Iron Condor
67%
$64
$799
−$2,324
−$12,640
Balancing Capital According to POP
The proportion of capital to allocate to a position can be estimated from the POP of the strategy. An appropriate percentage of buying power can be estimated using the following formula, derived from the Kelly Criterion:
1
(8.1)
where
r
is the annualized risk‐free rate of return, DTE is days to expiration or the contract duration (in calendar days), and POP is the
probability of profit of the strategy.
2
Approximating the risk‐free rate is not straightforward because it is an unobservable market‐wide constant, but the long‐term bond rate is commonly used as a conservative estimate. For the remainder of this chapter, the risk‐free rate will be estimated at roughly 3% for the sake of simplicity. To see some examples of portfolio allocation percentages calculated using this equation, see
Table 8.2
.
Table 8.2
POPs and allocation percentages of buying power for 45 DTE 16
SPY, QQQ, and GLD strangles from 2011–2018.
Strangle Statistics (2011–2018)
POP
Allocation Percentages
SPY Strangle
79%
1.4%
QQQ Strangle
73%
1.0%
GLD Strangle
84%
1.9%
The equation above suggests that the amount of portfolio buying power allocated to these positions should range from 1.0% to 1.9%, but those calculations don't take correlations between positions into account. Strategies with perfectly correlated underlyings should be counted against the same percentage of portfolio capital because
Equation (8.1)
requires that trades be independent of one another. In this example, because SPY and QQQ are highly correlated to each other but mutually uncorrelated with GLD, GLD strangles can occupy an entire 1.9% of portfolio buying power, and SPY strangles and QQQ strangles
combined
should occupy around 1.4% (the larger of the two allocation percentages). Because SPY and QQQ are not perfectly correlated, this is a conservative lower bound.
Overall, these allocation percentages are fairly low because the Kelly Criterion advocates for placing many small, uncorrelated bets. When aiming to allocate between 25% and 50% of portfolio buying power, strictly abiding by these bet sizes is somewhat impractical; there just aren't enough uncorrelated underlyings. The value of the risk‐free rate
provides a
conservative
estimate for the ideal capital allocation, so scaling these percentages up and adopting a more aggressive approach is justified. To scale up these percentages without violating the capital allocation guidelines, these bet sizes can be used as a heuristic to estimate
proportions
of capital allocation rather than the explicit percentages. For example, rather than allocating according to POP weights, a more heuristic approach would be as follows:
According to initial estimates, 1.4% of portfolio buying power should be allocated to SPY strangles and 1.9% to GLD strangles.
Dividing by 1.9, these weights correspond to a ratio of approximately 0.74:1.0.
This means that SPY strangles should occupy roughly 0.74 times the portfolio buying power of GLD strangles.
If the maximum per‐trade allocation of 7% goes toward GLD strangles, then approximately 5.2% (der


GLD strangles.
Dividing by 1.9, these weights correspond to a ratio of approximately 0.74:1.0.
This means that SPY strangles should occupy roughly 0.74 times the portfolio buying power of GLD strangles.
If the maximum per‐trade allocation of 7% goes toward GLD strangles, then approximately 5.2% (derived from
) should be allocated to SPY strangles.
To continue this example, suppose that the capital allocated to SPY strangles is further split between SPY strangles and QQQ strangles. Although these underlyings are correlated, splitting capital between these positions achieves more diversification than allocating the entire 5.2% to one underlying. This process can also be estimated using the POP weights:
According to initial estimates, 1.4% of portfolio buying power should be allocated to SPY strangles and 1.0% to QQQ strangles.
Dividing by 2.4% (from
), these weights correspond to a ratio of approximately 0.58:0.42.
This means that SPY strangles should occupy 58% of the capital allocation and QQQ strangles should occupy 42%.
If a maximum of 5.2% can be allocated toward these positions, then 3.0% of portfolio capital should go toward SPY strangles and 2.2% to QQQ strangles.
This scaling formula, when combined with position sizing caps of the capital allocation guidelines, allows traders to construct portfolio weights that scale with the POP of a strategy without overexposing
capital to outlier risk. These two concepts form a simple but effective basis for options portfolio construction.
Constructing a Sample Portfolio
Throughout this section, simplified capital allocation guidelines, option diversification, and POP‐weighting are combined to create a sample portfolio. The sample portfolio shown here will be constructed using data from January 2011 to January 01, 2018 and backtested with data from January 02, 2018 to September 2019. This backtest will focus on implementing some of the portfolio construction techniques outlined in
Chapters 7
and 8. This sample portfolio has six different core positions (all strangles), each occupying a constant amount of portfolio capital determined by the POP‐weight scaling method described in the previous section. The following three simplifications are made for ease of analysis and understanding:
Neither market IV nor underlying IV will be considered. Scaling portfolio allocation up when market IV increases is an effective way to capitalize on higher premium prices, as is focusing on underlyings with inflated implied volatilities. Because a constant 30% of portfolio capital will be allotted to the same short premium positions throughout this backtest, profit potential will be significantly limited. Therefore, the focus of this analysis is risk management.
This study only uses strangles with exchange‐traded fund (ETF) underlyings instead of a combination of strategies. This makes the portfolio approximately delta neutral and eliminates the need to justify specific directional assumptions or risk profiles for individual assets. By disregarding stock underlyings, stock‐specific binary events, such as earnings and dividends do not apply. This also means that the added profit potential from supplemental positions (which tend to be higher risk and include stock underlyings) will not be accounted for in this backtest.
Rather than managing trades at fixed profit targets, all the trades shown in this backtest will be approximately opened on the first of the month and closed at the end of the month.
Step 1:
Identify suitable underlyings using past data. Core positions should have moderate P/L standard deviations and well‐diversified
underlying assets. ETFs, such as the ones in
Table 8.3
, are viable candidates for core position underlyings. Though the market ETFs are highly correlated, a sufficient number of uncorrelated and inversely correlated assets can achieve a reasonable reduction in idiosyncratic risk.
Table 8.3
Correlations between different ETFs from 2011–2018. Included are two market ETFs (SPY, QQQ), a gold ETF (GLD), a bond ETF (TLT), a currency ETF (FXE ‐ Euro), and a utilities ETF (XLU).
Correlation (2011–2018)
SPY
QQQ
GLD
TLT
FXE
XLU
Market ETFs
SPY
1.0
0.88
−0.02
−0.44
0.16
0.49
QQQ
0.88
1.0
−0.03
−0.36
0.12
0.35
Diversifying ETFs
GLD
−0.02
−0.03
1.0
0.19
0.34
0.08
TLT
−0.44
−0.36
0.19
1.0
−0.03
−0.04
FXE
0.16
0.12
0.34
−0.03
1.0
0.18
XLU
0.49
0.35
0.08
−0.04
0.18
1.0
Step 2:
Calculate the percentage of portfolio capital that should be allocated to each position. These percentages can be estimated with
Equation (8.1)
and scaled according to the methodology described in the previous section, as shown in
Table 8.4
.
The core positions shown in
Table 8.4
are high‐POP, have moderate P/L standard deviation, and have well‐diversified underlyings, and the allocation amounts are below the 7% per‐trade buying power maximum. The total portfolio buying power allocated to short premium amounts to 30%, which is close enough to the minimum 25% to suffice for this backtest. With the port


P/L standard deviation, and have well‐diversified underlyings, and the allocation amounts are below the 7% per‐trade buying power maximum. The total portfolio buying power allocated to short premium amounts to 30%, which is close enough to the minimum 25% to suffice for this backtest. With the portfolio initialized using data from 2011 to early 2018, it can now be backtested on new data from early 2018 to late 2019, bearing in mind that this test does not take dynamic management or implied volatility into account. The results of backtesting this sample portfolio are shown in
Figure 8.3
and
Table 8.5
.
3
Interestingly,
Table 8.5
shows that the equity portfolio was the most volatile of the three and experienced the largest worst‐case drawdown despite having less tail exposure than the options portfolios. The POP‐weighted portfolio performed more consistently and had significantly less per‐trade standard deviation than either of the other two, with per‐trade POP matching the equal‐weight portfolio and average P/L comparable to the equity portfolio. Despite consisting of undefined risk strategies, the POP‐weighted portfolio had nearly half the P/L variability and worst‐case loss as the equity portfolio throughout the backtest period. The equal‐weight strangle portfolio also underperformed compared to the POP‐weighted portfolio although not experiencing any more P/L variance or severe drawdowns compared to a comparable portfolio of equities. To reiterate, the performance of both strangle portfolios can be further optimized by increasing the allocation percentage according to market volatility (which can be done with the addition of uncorrelated short premium positions) or by incorporating more complex management strategies. Still, this simplified backtest illustrates the impact of incorporating the risk management techniques of capital allocation, diversification, and POP‐weighted allocation.
Table 8.4
Core position statistics for 45 DTE 16
strangles from 2011–2018. The allocation ratio is the allocation percentages normalized such that the largest bet size is set to 1.0. The portfolio weights are determined by multiplying the allocation ratio by 7% (the maximum per‐trade allocation percentage). The adjusted portfolio weights show how portfolio capital is split across assets that are highly correlated.
Core Position Statistics (2011–2018)
POP
Allocation Percentages
SPY Strangle
79%
1.4%
QQQ Strangle
73%
1.0%
GLD Strangle
84%
1.9%
TLT Strangle
78%
1.3%
FXE Strangle
83%
1.8%
XLU Strangle
81%
1.6%
Allocation Ratio
SPY/QQQ:GLD:TLT:FXE:XLU
0.74:1.0:0.68:0.95:0.84
Portfolio Weights
SPY/QQQ:GLD:TLT:FXE:XLU
5.2%:7.0%:4.8%:6.7%:5.9%
Adjusted Portfolio Weights
SPY:QQQ:GLD:TLT:FXE:XLU
3.0%:2.2%:7.0%:4.8%:6.7%:5.9%
Figure 8.3
Portfolio performance of three different portfolios from early 2018 until September of 2019. Each portfolio has $200,000 in initial capital with 30% of the portfolio capital allocated. This initial amount of $200,000 allows at least one trade for each type of position, as $100,000 in initial capital does not. The 30% SPY equity portfolio (a) has 30% allocated to shares of SPY. The 30% equally‐weighted strangle portfolio (b) has 5% allocated to each of the six types of strangles, and the 30% POP‐weighted portfolio (c) has the 30% weighted according to the percentages in
Table 8.4
. All contracts have the same delta (16
), identical durations (roughly 45 DTE), and the same open and close dates. For the sake of comparison, the trades in the equity portfolio are opened on the first of each month and closed at the end of each month.
Table 8.5
Portfolio backtest performance statistics for the three portfolios described in
Figure 8.3
from 2018–2019.
Portfolio Performance Comparison (2018–2019)
Portfolio Type
POP
Average P/L
Standard Deviation of P/L
Worst Loss
SPY Equity
60%
$285
$2,879
−$6,319
Equal‐Weight
67%
$26
$2,440
−$6,117
POP‐Weighted
67%
$268
$1,610
−$3,561
The
heuristic derived from the Kelly Criterion provides a good guide for how much capital should be allocated to a trade when initializing a portfolio, indicating that more capital should be allocated to higher POP trades and less capital should be allocated to less reliable trades. However, this method does not provide a thorough structure for dynamic portfolio management. At different points in time, trades often reach profit or loss targets, require strike re‐centering, or present new opportunities. Traders can simplify the complex management process by, for example, choosing the same contract duration or management strategy for all trades in a portfolio. However, a framework for navigating these dynamic circumstances is still necessary, and this is where the portfolio Greeks and the re‐balancing protocol outlined in
Chapter 7
are particularly useful.
Takeaways
Options can be diversified with respect to a number of variables, but diversifying the equity underlyings of an options portfolio remains the most essential for portfolio risk managemen


where the portfolio Greeks and the re‐balancing protocol outlined in
Chapter 7
are particularly useful.
Takeaways
Options can be diversified with respect to a number of variables, but diversifying the equity underlyings of an options portfolio remains the most essential for portfolio risk management. Traders who can accommodate more involvement and are interested in further diversification can also diversify positions with respect to time and strategy.
Diversification with respect to time tends to reduce the correlations between portfolio positions because contracts respond differently to changes in time, volatility, and underlying price depending on their duration. The most effective way to diversify with respect to time without compromising occurrences is by trading contracts with consistent durations but a variety of expiration dates. This strategy is difficult to maintain consistently, however, particularly when multiple management strategies are used.
Diversifying portfolio capital across defined and undefined risk strategies allows traders to capitalize on the directional tendencies of an underlying asset while protecting a fraction of capital from unlikely outlier events. If implementing this diversification technique, note that defined and undefined risk strategies typically reach P/L targets at different rates and often require different management strategies.
The percentage of capital allocated to a single position can be calculated from the POP of the strategy and the correlation between existing portfolio positions. The percentage of portfolio capital allocated to a single position can be estimated using
Equation (8.1)
; however, this percentage can also be scaled up because the risk‐free rate yields a very conservative estimate.
Notes
1
For an introduction to the Kelly Criterion, refer to the appendix.
2
The POPs used throughout this chapter are calculated from historic options data. Options data are ideal for statistical analyses but inaccessible to most people. Trading platforms often provide the theoretical POP of a strategy, which can substitute measured POP for these calculations.
3
This backtest demonstrates one specific outcome out of many possible when trading short premium. The goal of this backtest is to demonstrate how one sample portfolio performs relative to other portfolios with similar characteristics under these specific circumstances.


Chapter 9
Binary Events
To this point, this book has highlighted unpredictable implied volatility (IV) expansions and their impact on short premium portfolios. However, traders can expect a certain class of IV expansions and contractions with near certainty. These expected volatility dynamics are the result of
binary events
. A binary event is a
known
upcoming event affecting a specific asset (or group of assets) that is
anticipated
to create a large price move. Though price variance is
expected
to increase, it may or may not actually do so depending on the outcome of the binary event.
1
Some examples of binary events include company earnings reports (motivating earnings trades), new product announcements, oil market reports, elections, and Federal Reserve announcements pertaining to the broader market.
Because the date of the anticipated price swing is known, there is typically significant demand for contracts expiring on or after the binary event for that underlying asset. This increased demand results in an increase in the asset's IV, which usually contracts back to nonevent levels immediately after the outcome is known. This trend is shown in
Figure 9.1
.
The impact from a binary event volatility expansion differs from that of unexpected periods of market volatility because the options approaching binary events are priced to reflect the expectation of large moves in the underlying. However, the high credits and immediate volatility contractions that often result from binary events do not necessarily translate into higher (or even likely) profits for short premium positions. This is because the
magnitude
of the price move following the outcome of the binary event is unpredictable, and it may meet or diverge from expectations. On average, the market response to a binary event tends to be quite large, causing the short options strategies that capitalize on these conditions to be
highly
volatile and not necessarily profitable in the long run. This phenomenon also follows from the efficient market hypothesis (EMH), as the well‐understood nature of binary events challenges any consistent edge for these types of strategies.
There is no strong evidence that buying or selling premium around binary events provides a consistent edge with respect to probability of profit (POP) or average profit and loss (P/L) because a lot of the IV overstatement edge is lost in the large moves following a binary event. However, binary event trades are a very time‐efficient use of capital because volatility contractions happen more rapidly and predictably than in more regular market conditions. Binary event trades may also be attractive to risk‐tolerant traders as a source of market engagement. During earnings season, a single week may present up to 20 high‐risk/high‐reward opportunities for earnings trades. Binary event trades can also be educational for new traders wanting to learn how to adjust positions in rapidly changing, high volatility conditions outside of sell‐offs. These types of trades, as they take place under unique circumstances, are structured and managed differently than typical core or supplemental positions.
Figure 9.1
IV indexes for different stocks from 2017–2020. Assets include (a) AMZN (Amazon stock) and (b) AAPL (Apple stock).
Option Strategies for Binary Events
Because binary event trades are highly volatile and have no strong evidence of a long‐term statistical edge, they should only occupy spare portfolio capital and their position size should be kept
exceptionally
small. For example, if a trader's usual position size for an AAPL strangle is a five‐lot (five calls and five puts, each written for 100 shares of stock), then an AAPL earnings strangle may comprise a one‐ or two‐lot. Additionally, underlyings for binary event trades are typically stocks, with quarterly earnings reports being the most common type of binary event. Binary event trades take place over much shorter timescales than more typical trades and must be carefully monitored. Earnings trades, for example, are typically opened the day before earnings and closed the day following earnings. This strategy limits downside risk and capitalizes on the majority of the volatility contraction, which tends to occur immediately after the binary event.
The long‐term success of binary event trades is difficult to verify because there are relatively few occurrences, resulting in high statistical uncertainty. AAPL, for example, has only reported earnings roughly 100 times since the mid 1990s. The Federal Reserve holds press conferences just eight times per year, and large‐scale elections take place once every two or four years. For trading strategies not built around earnings, there are thousands of data points and the statistics are more representative of long‐term expectations (the central limit theorem at work). Therefore, working with this small number of data points can yield an
idea
of how binary events trades have performed in the past, but they shou

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ound earnings, there are thousands of data points and the statistics are more representative of long‐term expectations (the central limit theorem at work). Therefore, working with this small number of data points can yield an
idea
of how binary events trades have performed in the past, but they should be taken with a large grain of salt.
Tables 9.1
–
9.3
demonstrate how earnings trades for three different tech companies have performed over 15 years.
There is clearly significant variability in strategy performance for these three different underlyings. To reiterate, high statistical uncertainty makes it difficult to make definitive conclusions about the success of earnings trades, but some consistent trends are observable. Earnings trades are highly sensitive to changes in time. This is evidenced by the significant differences in the per‐trade statistics further from the earnings announcement and demonstrates why binary event trades must be closely monitored. The
majority
of earnings trades are usually profitable, but do not necessarily average a profit in the long term because of the high per‐trade standard deviation. Per‐trade variance and tail exposure also tend to increase the longer the trade is held, indicating why these types of trades should be relatively short term. This is why generally, binary event trades, such as earning trades, are closed the day following the binary event.
Table 9.1
Statistics for 45 days to expiration (DTE) 16
AAPL strangles from 2005–2020. Trades are opened the day before an earnings report and closed either one, five, 10, or 20 days after earnings.
AAPL Strangle Statistics (2005–2020)
Day Position Is Closed Relative to Earnings
POP
Average P/L
Standard Deviation of P/L
Conditional Value at Risk (CVaR) (5%)
Day After
72%
$85
$203
–$405
5 Days After
70%
$43
$400
–$1,027
10 Days After
61%
$60
$408
–$1,025
20 Days After
56%
−$34
$660
–$1,976
Table 9.2
Statistics for 45 DTE 16
AMZN strangles from 2005–2020. Trades are opened the day before an earnings report and closed either one, five, 10, or 20 days after earnings.
AMZN Strangle Statistics (2005–2020)
Day Position Is Closed Relative to Earnings
POP
Average P/L
Standard Deviation of P/L
CVaR (5%)
Day After
65%
$99
$803
–$1,927
5 Days After
65%
$85
$842
–$2,154
10 Days After
72%
$1
$1,446
–$4,416
20 Days After
76%
$78
$1,540
–$4,477
Table 9.3
Statistics for 45 DTE 16
GOOGL strangles from 2005–2020. Trades are opened the day before an earnings report and closed either one, five, 10, or 20 days after earnings.
GOOGL Strangle Statistics (2005–2020)
Day Position Is Closed Relative to Earnings
POP
Average P/L
Standard Deviation of P/L
CVaR (5%)
Day After
75%
–$60
$1,320
–$4,639
5 Days After
67%
–$113
$1,358
–$4,724
10 Days After
65%
–$122
$1,275
–$3,675
20 Days After
71%
–$2
$1,584
–$4,909
Takeaways
A binary event is a known upcoming event affecting a specific asset (or group of assets) that is anticipated to create a large price move. This anticipation creates demand for options contracts expiring on or after the binary event and an increase in the IV of the asset. IV typically contracts back to nonevent levels immediately after the outcome is known.
The high credits and immediate volatility contractions resulting from binary events do not necessarily translate to large or consistent short premium profits because the magnitude of the market response is unpredictable. Binary events trades are generally highly volatile and undependable sources of profit but can be used for market engagement or an educational experience for new traders.
Binary event trades should only occupy spare portfolio capital and their position size should be kept
exceptionally
small. Binary event trades should also take place over much shorter timescales than more typical trades, and they must be carefully monitored.
Note
1
The term binary is used to describe systems that can exist in one of two possible states (on/off, yes/no). In this context, a binary event is a type of event where price changes either remain within expectations or exceed expectations.


Chapter 10
Conclusion and Key Takeaways
Successful traders do not rely on luck. Rather, the long‐term success of traders depends on their ability to obtain a consistent, statistical edge from the tools, strategies, and information available. This book introduces the core concepts of options trading and teaches new traders how to capitalize on the versatility and capital efficiency of options in a personalized and responsible way. Options are fairly complicated instruments, but this book aims to lessen the learning curve by focusing on the most essential aspects of applied options trading. The detailed framework laid out in this book can be summarized succinctly in the following key takeaways:
Implied volatility (IV) is a proxy for the sentiment of market risk derived from supply and demand for financial insurance. When options prices increase, IV increases; when options prices decrease, IV decreases. IV gives the perceived magnitude of future movements and is not directional. It can also be used to approximate the one
standard deviation expected price range of an asset (although this does not take strike skew into account). The CBOE Volatility Index (VIX) is meant to track the IV for the S&P 500 and is used as a proxy for the perceived risk of the broader market. The VIX, like all volatility signals, is assumed to revert down following significant expansions, which indicates some statistical validity in making downward directional assumptions about volatility once it is inflated.
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 two most important goals of a short premium trader are to profit consistently enough to cover moderate, more likely losses and to construct a portfolio that can survive unlikely extreme losses.
The profitability of short options strategies depends on having a large number of occurrences to reach positive statistical averages, a consequence of the law of large numbers and the central limit theorem. At minimum, approximately 200 occurrences are needed for the average profit and loss (P/L) of a strategy to converge to long‐term profit targets and more is better.
Extreme losses for short premium positions are highly unlikely but typically happen when price swings in the underlying are large while the expected move range is tight (low IV). Because large price movements in low IV are rare and difficult to reliably model, the most effective way to reduce this exposure is to trade short premium once IV is elevated.
Although high volatility environments are ideal for short premium positions, short premium positions have high probability of profits (POPs) and some statistical edge in all volatility environments. Additionally, because volatility is low the majority of the time, trading short options strategies in
all
IV environments allows traders to profit more consistently and increases the number of occurrences. To manage exposure to outlier risk when adopting this strategy, it is essential to maintain small position sizes and limit the amount of capital allocated to short premium positions, especially when IV is
low. This strategy can be further improved by scaling the amount of capital allocated to short premium according to the current market conditions.
VIX Range
Maximum Portfolio Allocation
0–15
25%
15–20
30%
20–30
35%
30–40
40%
40+
50%
Buying power reduction (BPR) is the amount of portfolio capital required to place and maintain an option trade. The BPR for long options is merely the cost of the contract, and the BPR for short options is meant to encompass at least 95% of the potential losses for exchange‐traded fund (ETF) underlyings and 90% of the potential losses for stock underlyings. BPR is used to evaluate short premium risk on a trade‐by‐trade basis in two ways: BPR is a fairly reliable metric for the worst‐case loss of an undefined risk position, and BPR is used to determine if a position is appropriate for a portfolio based on its buying power. A defined risk trade should not occupy more than 5% of portfolio buying power and an undefined risk trade should not occupy more than 7%, with exceptions allowed for small accounts. The formulae for BPR are complicated and specific to the type of strategy, but the BPR for short strangles is approximately 20% of the price of the underlying. BPR can be used to compare the risk for variations of the same strategy (e.g., strangle on underlying A versus strangle on underlying B), but it cannot be used to compare risk for strategies with different risk profiles (e.g., strangle on underlying A versus iron condor on underlying A).
Traders trade according to their personal profit goals, risk tolerances, and market beliefs, but it is generally good practice to be aware of the following:
Only trade underlyings with liquid options markets to mini

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