How many premiums are fair for short options?

As an option seller, I've been interested to know if the premiums I received for selling options are fair or not. However, there are so many factors that impact the premiums of sold options. To obtain a reasonable feeling of the fairness, I studied the TLT option spreads that I dealt with in the last few months. I used TLT short options of similar probability of success, same amount of capital requirement with the same width ($5) for the vertical spreads, and day to expiration around 56+/-7 days. In this way, I was able to reduce the number of variables for this comparison.

My goal is to receive 10% to 13% return on capital (premium$/width$5) for all ETF's that I trade. For the TLT options that meet my criteria, it means the premium should be above $0.50. Based on the above table, it looks to me the following conclusions are true for the options of similar probability and risks.

• Put premiums are higher than call premiums under similar conditions
• Premiums are higher when the short option bid and ask prices are narrower
• Premiums are higher when open interests are larger
• Premiums are higher when Delta differences between short and long strikes are larger
• Premiums are higher when the IV differences (Skew) between short and long strikes are smaller
• Premiums may not be higher with longer DTE in the analyzed range
• Higher IV of the option does not guarantee higher premium

My biggest surprise is that the higher IV's do not always provide higher premium or ROC. In October  turbulent trading, I could obtain higher ROC as IV was much higher in those days. But now, the IV of TLT is still high and yet its option premiums offer less ROC. I found other more liquid options (i.e. IWM) offer reasonable ROC (>10%) at the same time. The only reason I could find so far was the lack of open interests in the options. So I would conclude the lack of option liquidity means lower ROC for option sellers and the middle option price of bid and ask may not be fair.

In general, I believe this is one way for option sellers to estimate the fairness of option premiums as they use options of similar parameters for the comparison.

A study of Bollinger bands and actual probability in stock market

Many traders use Bollinger bands as one of the trading tools. I also use this tool in my current high probability option selling strategy. I've studied standard deviations, in-the-money probability, Bollinger bands in my previous posts:

• Does 3 standard deviation move of an ETF match reality?
• Surviving a test of 3 SD event on TLT bear call spread trades
• Estimating In-The-Money Probability using IV and Standard Deviation

After further analysis of my recent post on the 3 SD events, I think there are something more for me to understand the relationship between Bollinger bands and actual probabilities. Considering the 3 days on a roll for the 3SD events of TLT on 8/2/2011, the actual days of 3 SD occurrences were 10. It was not the 8 days that I had posted. It means the actual number of events were much higher than the theoretical value of  7.

Therefore, I searched other related studies available from Internet and found a good post: Standard-Deviation Technicals by Adam Hamilton. The article demonstrated that there were 60% more occurrences of 3 SD events than what the theory suggested for S&P 500 in the long period of its study. The "fat tails" compared with normal distribution were sited as one of the major reasons for the discrepancy.

Another good source for my study is Bolling bands on Wiki. It indicated for 2 SD events, the theory states a 95% of probability of stock prices to stay within the bands while the actual data showed about 88% of probability only.

The following table is obtained from theoretical calculations, and is an extension of my previous study. I added a column "Days/Event" to indicate the number of days required on average for the corresponding event to take place. For example, if we use 2 standard deviations, one event in which the price breaks the bands is likely to happen in about 22 trading days, which corresponds to 1 calendar month.

Table of SD Multiple, Probability, Occurrences

SD Multiple	Statistical Prob	ITM Probability	Days/Event	Comments
0.5	40.0%	30.00%	2	Karen's Adjustment point
1	68.3%	15.87%	3
1.3	80.0%	10.00%	5	Karen's short call
1.6	90.0%	5.00%	10	Karen's short put
2	95.4%	2.30%	22	My short options
3	99.7%	0.13%	333

Note the days for each event is the number of trading days. ITM probability is the single side probability.

However, there are known issues in actual stock price distributions and the standard deviation theory. The SD requires a normal distribution as shown in the chart here. But financial products have fat tails due to greed and fear. Secondly, the SD model requires sufficient data sample points. If one uses 20 DMA for Bollinger bands as many traders use as default, it may miss the 2 SD events which require 22 days on average. This results inaccuracy in my opinion which may worth only 2 cents.

To the best of my current knowledge, it would require, at least, 2 times of the days/event of the sample data for the calculation to be valid. In another word, it needs 44 day MA, at least, for a 2SD probability to be close to reality in theory. For the 3SD event, it needs 666 day MA. Lastly, I'm doubtful that stock prices are evenly distributed around any moving prices at all. Even looking at a long term period like 700 days, market may be in a bullish up trend where prices continues to touch or break the upper Bollinger band while making a much smaller number of touches and breaks on the lower band.

In summary, I still like to use Bollinger bands and they should corresponds to some level of probability. However, if one use the associated probability in their trading formula, be careful about the differences between reality and theory. I think there are smart traders that are exploiting these discrepancies.

Worthless puts saved overall positions during the fast sell-off in October

As I have been testing water with my new option selling strategy inspired by the Super trader Karen, I started with TBT as described in my September post. Since then, mistakes had been made and some quick profits were earned as shown in the chart below. More importantly, lessons were learnt during the live trades.

In my October post, the TBT trade was going on according to plan. I did not realize that I had the best opportunity to close all the trades to achieve the maximum profit around 9-18 as shown in the chart above. I thought the far OTM puts were expire worthless as TBT was turning into a up trend. However, it did the opposite, and broke down my support level of $54. On 10-7, I settled to take a 50% profit by buying back Oct$53 put. There were no bids for Oct$49p at the time so I had to leave it on (I was not able to close the position as a spread trade) with only 2 weeks to expiration. It was the far OTM, worthless straight put that saved the overall position several days later when TBT crashed around 10-15 along with the stock market. As mentioned in the previous post, that was a test of 3 SD event. The other bull put position Oct$51/46p got crushed as price tumbled from $51.2 to $48 just 2 days before expiration. I decided to close the straight put which become ITM by selling it and the short bull put spread by buying it back, for a small profit on the crash day.

I think it was this small profit that gave me a little bit of psychological boost to follow my trading rule to hold on to the TLT position which was suffering a temporary loss that was over 3 times of potential MAX profit at the time. I did not look at the intraday loss and felt OK since I had a good amount of capital available in the account for possible rolling adjustments.

As happened many times in strong bull market before, the market sell-off was short lived. The market rallied back quickly. I strongly believe that bulls would not die without a big fight. For 5 weeks after the sell-off, market kept advancing. My TBT bear call spread Nov$57/62c (C5S/C5B in chart) was expired worthless last Friday. Now, I'm out of all TBT positions and transitioned fully into TLT trades as planned.

So what are the lessons to be learned from the market and the trades? This is the tough part of the trade review. With the help of the chart that recorded the trades, I think the following points are important for me.

1. After entering a trade for 1 month and with 1 month left for expiration, the trade may be exited for minor profit or loss if the stock prices goes against the position in general.
• I could have exited positions around 8-14 to open new positions.
2. Need to make sure adjustment sizes to be correct so that the potential profits remain the same.
• Made a mistake around 8-15
3. Should take deep profits as the stock starts to change direction around major support/resistance levels
• Around 9-19, TBT pulled back from 4 month resistance which was identified in an earlier post. That was the best exit point.
4. In a weak market, it may be worth to long really cheap ($0.05) OTM puts when key support level is broken. The contract sizes should depend on the long term bullishness of the market.
• Trades on 10-7 was perfect as market broke down the support level.
5. It's OK to follow the rules to adjust around Delta of 0.65.

Surviving a test of 3 SD event on TLT bear call spread trades

When I started to test my new premium selling strategy using TLT in middle to late September as described in my previous post on my positions on TLT & TBT, I had no idea that a 3 Standard Deviation test would soon appear. In fact, the 1st trades near middle of September were easy: 50% profit in 4 days as shown in the diagram below. At that time, FED announced end of QE. I thought TLT would start going down which was totally wrong as TLT continued to rise and shot up far beyond a 3 SD point at an intraday period.

Apparently, my short position of Nov$121/126c was in trouble as soon as it was opened. By Oct. 13, I began to realize that the uptrend of TLT was still intact as it firmly stayed above the $119 resistance level that I had in mind. So I began my adjustments and sold a larger number of bear calls of Nov$125/130c to make up possible deficits of existing losing position. The Delta of the short call strike Nov$121c reached my adjustment level of 0.65. So I rolled up and out the trade. On Oct 14 which was one day before the big 3 SD test, TLT broke up even further away from its upper Bollinger band. I had an opportunity to close the Original Nov$121/125c position and my sell order for Dec$127/132c was filled. I thought the price of TLT was pretty extended on that day. Then the big surprise came as market had a mini-crash and TLT sky-rocketed to test the 3 SD price. As usually, I watched market for less then one hour that day around Wall Street's lunch time. The Delta of my short strike Nov$125c were below 0.65, my adjustment level. Although shocked, I did not make any adjustments for TLT on that day. Well, the price started to move down which was what my positions favor since then. I think I was lucky to exit all the positions with 50% profits about 2 weeks later.

In retrospect, I think there are a few lessons learned from the adverse test for the high probability option selling strategies:

• Don't panic in the market extreme events and use trading rules to guide the reaction
• Trade a strategy only if you feel confident about it
• Keep sufficient capital to fight the adverse events (I'm still working on it)
• The high probability strategy can have large temporary losses (3 x potential profit this time)
• Profits can be earned even if price projections are wrong at times
• Refrain from over-adjustments

I had the thought of making adjustments if TLT reached and stayed above resistance level of $119. Had I done it, I would have sold TLT calls with lower strikes which would gave me larger temporary losses. It would be a bit more difficult to reach the 50% profit with the lower short call strikes. After reviewing my trades here, I think I should stick to the adjustment rule based on the Delta of short strikes, rather than support/resistance levels obtained from technical analysis.

Does 3 standard deviation move of an ETF match reality?

It was a fantastical test in the last couple of weeks for the premium selling strategy that I'm working on in both real and paper trades, as the market went extremely turbulent. It will take a while for me to digest the trades to firm up my trading rules.

In preparation to analyze my TLT trades as it ventured above the 3 Standard Deviation (SD) line intraday on 10-15, I studied the historical data. I think 3 SD corresponds to 99.7% probability approximately as I outlined in a post before. If I understand it correctly, there will be a 3 SD event every 1 year 7.5 months which corresponds to 333 (1/0.3%) trading days on average (assuming there are 200 trading days per year).

I'm interested how these numbers matching the reality. So I went through the TLT history using Prophet Chart available from TOS. I created the Bollinger bands with 30 day MA & 3 SD on TLT chart, scrolled through the entire price chart whose data started at 2002-7-26 for over 12 years. I found the follow 3 SD occurrences where prices closed outside the Bollinger bands by visual inspections only.

Number	Date	Days	Up/Low	Days outside 3 SD
1	7/2/2004	0	Up	Just 1 day
2	2/27/2007	970	Up	Just 1 day
3	11/20/2008	632	Up	Just 1 day, but continued to rise
4	5/6/2010	532	Up	Just 1 day
5	8/16/2010	102	Up	Just 1 day
6	8/2/2011	351	Up	3 days
7	3/14/2012	225	Low	Just 1 day
8	4/5/2013	387	Up	Just 1 day

From 2004-7-2 to 2014-10-31, there are 4480 calendar days. That is a period of 12 years and 3 month. I equated it to 2460 trading days roughly. With the 0.3% probability, we should have 7.3 (2460 x 0.3%) occurrences outside 3 SD in the period. In reality, we've had 8 occurrences as shown in the above table. I think this is very surprisingly close to the theory.

I have a couple of other findings that should be recorded here.

• 6 out of 8 times the price came back to Bollinger bands in the next day
• 1 out of 8 times the prices fell below the lower Bollinger band
• I guess there will be more events that the prices fall below the Bollinger band in the next 10 to 20 years.

I'm running out of time today. So I have to present my trade analysis (Lessons from surviving the test of 3 SD events) next time.

Review of current (November) TBT & TLT positions

In the last month, I basically followed the ideas in the last post and tried to let the TBT options expiring worthless. Well, the short call Oct$62 did expire on 9-20 with a mild level of risk of breaking above the short strike a few days before expiration. But I decided to hold on and it worked this time. However, I may be facing another challenge on the Nov$53p (P2S in the chart below), as TBT pulled back significantly to my surprise. If TBT drops below $54, I will consider closing the sold put spread.

As part of my plan, I started using TLT for my future trades as it's more liquid than TBT. I thought TBT & TLT would change their long term trends after the recent FED meeting. I will consider the thought invalidated if the ETF's take over their previous support/resistance.

For the TLT, I sold Nov$109/104 put spreads on 9-17 as it was approaching the lower Bollinger band with a high IV about one hour before FED meeting announcement. 4 days later, the TLT rose to give me a quick 50% profit and I exited the trade (P1 & P2). To my surprise, TLT continued to rise. I waited for a few days and finally sold Nov$121/126 call spread. All the short options were of 0.20 Deltas and credits were above or equal to $0.50 for a 10%+ ROM.

If TLT breaks above $119 firmly, I may start taking some adjustment actions. But the short call options may not be rolled until a 0.65 Delta is reached.

A review of my rolling adjustments on TBT

I sold option premiums on TBT in the last couple of months as TBT fell fast. Initially, I sold naked puts (P1S) of Delta 30 as TBT broke down its support line around $60. I planned to get assigned if TBT would drop below the sold strike as I had the view that interest rate would not continue to fall for too long. On the 2nd day after the opening short, I watched TBT failing to rebound and decided to sell bear call spreads to collect some premium on the down side. For about 4 weeks after that, TBT maintained a slightly downward trend and got a relative large increase of its implied volatility. Thus, there was not many premiums that could be materialized as shown in the chart below.

In the meantime, I developed a new general trading plan for selling premiums using some principles from Karen and some paper trades. It had enough rules for me to test it with the real money using TBT. So I started to trade it for the following occurrences. I also realized that rates may take 10 to 15 years to bottom historically. This puts the rising date to 2020 since we had a record low rate period.

Around 8-15, TBT broke down another level of support and fell hard. On that day, my short put had its Delta reached over 0.65 (which was my adjustment Delta). So I decided to roll it down to the next 30 Delta in the next cycle (October). I bought back the original short put and sold more bull put spread with 20 to 30 short Delta to cover the deficit. In this process, I made an mistake in selling less contracts, because I failed to consider my profit target was 50% of max potential. The proper formula for the new contract size should be the following:

Adjustment size = original size + 2 x (Deficit / new credit).

TBT started to bounce back immediately after my adjustment. After the 3rd and 4th day of the re-bounce, it became apparent to me that TBT was resuming its fall. So I sold more bear call spreads on the 5th day which TBT tried a weak pull-up. Luckily, the 50% profit target of the bear call spreads were reached in about 4 days. Thus, I closed it according to my rule. On the next day, I felt TBT dropping too low and too fast. I was able to find a lower put strike which was beyond my projected downward target. So, I sold some other bull put spreads (P3S & P3B). Since then, TBT started to pull up again. I followed it up closely and was trying to close the new bull put spread around 50% profit target. But I found this time, the re-bounce was more powerful especially the pull down on the 2nd day of the re-bounce was overcame on the 3rd day. Thus, I decided to let the profit accumulate. I may let it expire worthless if the market does not create a big ripple to shake me out. I plan to let the 1st bear call spread (C1Short/Bought) to expire as its short strike at $62 appears to be safe for me.

In retrospect, if I did not adjust around 8-15, my profit today would have been double that of the actual profit as shown in the bottom sub-graph. It also showed the P&L would have lager swing had I not adjust. This is a typical example of adjustment at the worse time. But I believe it's an uncertainty that we have to take. There are a couple of actions I could take that would make it better for the adjustment. First, I could have exited the P1S trade after 3 weeks when TBT kept testing lower side and did not show any sign of rises as the overall down trend was prevalent and persistent. Second, I should have sold more contracts when calculating the adjustment size. Overall, these trades were experimental and thus not consistent. I should be able to firm up my rules and apply them consistently in the coming weeks.

A comparison chart of selling naked puts and spreads

I have been studying ways to sell options using a modified super trader Karen style for non-PM (portfolio margin) accounts (including IRA). To reduce risks, we have to sell spreads instead of naked options. Thus, it's very interesting for me to understand the differences of selling spreads or naked options. Today, I finally got some time to analyze the differences from the P&L behavior perspective. Other aspects (ROM, Bid/Ask slippages under high volatilities, easiness of execution, commissions, etc) of the differences will be studied later.

I selected a recent period that involved some market fluctuations as shown in the picture below. A 20% ITM probability put on SPY (2014May$175p) was used as the basis. The profit and loss of the following 3 option selling strategies were charted by a ThinkScript that I developed:

• Short Naked put
• Short put spread of $7 wide
• Short put spread of $3 wide

As the width of the spread got narrower, the overall contract sizes were increased to maintain a similar level of maximum potential profit. The overall Delta of each strategical position was kept to a similar value around 200. As can be seen in the chart, all of the positions behaved similarly for these trades. They reached 50% profit target in a couple of weeks before dropping to negative territory, then bouncing back.

Due to the different contract sizes, the overall Greeks of the option positions were in similar ranges. Therefore, it's understandable that the P&L of these positions behaved similarly. If the number of contracts were kept the same for each position, then the spreads would have smaller Greeks values than those of the naked puts. In this case, I would expect the P&L curve of the spreads become less volatile than the naked put position, and it takes longer time for spreads to reach profit target. The narrower the spread, the slower its P&L moves. Additionally, the study focused on the 2nd month before expiration. If we chose a period that was closer to the expiration, I would expect larger behavior differences due to increased Gamma risk of the positions.

Issues in the TOS ThinkScript

I found there were many missing data points for extremely far OTM options, even though the ThinkBack showed valid data. I tried to analyze a put spread $159/$149 which had a 5% ITM probability for the short strike. But the corresponding P&L curve appeared to be erratic. After some investigation of the script, I realized that for far OTM options which traded less often (OI < 1,500) there were too many data holes to receive a proper chart. For this reason, I had to increase the ITM probability of the strikes used for this study. I plan to share the script with the Karen Study Group later.

A study of Super trader Karen's trading process

I've been interested in studying the trading process and mindset of successful traders. Today, I reviewed what I learned from Karen's interviews from the trading process perspective.

Karen treats trading as a process and manages the process all the time. As far as I can see, her trading process involves the following elements as discussed in her interviews:

o   A suitable set of strategic trading rules,

o   An advanced trading software platform,

o   A successful trading mindset and psychology,

o   A daily trading routine,

o   A trading number game management,

o   An experienced trading team,

o   A Sufficient amount of time and money for trading and learning, and

o   Others.

Karen’s daily trading routine starts from market open hour till the end. The constant watch on the market by her trading team allows them to react to market changes promptly. Karen’s trading rules help them staying away from over-trading or over-adjusting. Her high degree of confidence on the high probability trades enables her of proper trade actions in the face of market uncertainty.

Karen treats trading as a number’s game so that she can play it objectively. She enjoys playing the big game all the time and taking the market challenges as well. There are no feelings wrapped around her trades or positions, as they are just numbers to her. The ability to turn emotions and perceived risks into a set of trading numbers and to focus on the numbers helps traders to decouple themselves from emotions and irrational trading actions. The emotion and fear are the biggest obstacles in trading and they take down most traders. The focus on trading numbers takes away the feeling of heart-ripping during adverse market conditions. As a result of the application of high probability trades by going far out of the money, a heavy percentage of Karen’s positions are winners.

Karen had discussed her learning and trading improvement process. She had more failures than successes in initial years. She was willing to invest in learning knowledge with a large amount of money and time that many other people may not be comfortable with. Her education fee at Investools alone cost over 20K USD. Small traders may have this limited amount in their trading accounts.

Karen established a tremendous trading team of about 6 members. 5 of them are experienced retail traders and 1 is an accountant. She encourages different ideas from team members. They usually will listen to each other, discuss the ideas and agree as a group. From time to time, they will test water with new ideas using a small amount of capital. If the new idea is proven to be working, then they don’t hesitate to apply it in full scale. The selling of weekly option was a good example of this process of adopting new ideas.

Some traders may get extremely disturbed if the temporary position loss becomes very big. Karen does not get emotional about any of her positions. When positions are in danger, she will do whatever it takes to fix them and make them back to the original profit at the expiration date as described in Section 6 Trade Adjustment Rules. She is not bound by the future direction of market moves, but always reacts to it if the ITM probability and profit percentage of her positions indicate to her for adjustments.

Karen suggested traders to look at the profit and loss numbers of the portfolio but not to focus on the P&L. This is reflected on her trading team structure as well as there is only one accountant (vs 5 to 6 traders). With this team, the traders should be able to focus more on the other important trading numbers. Personally, I think the key numbers Karen discussed in the interviews can be summarized as the following:

·         ITM probability

o   First factor used to determine if opening, closing or adjustment is required

·         Prices and trend of the underlying

o   Second factor used to determine if adjustment is required

·         Stress-tested market crash losses vs net liquidation value

o   Critical number that indicate how many contracts to sell

·         Option premium changes and time to expiration

o   Available options for adjustments

Karen stated she is willing to take losses when necessary and she will keep existing profit in her positions also. However, there were no examples discussing when to give up positions for losses (probably after the portfolio margin runs out). It’s worthwhile noting that Karen did not indicate any rules based on position losses. She did not mention any direct trade reaction to the amount of loss of a position. Her trade adjustment rules are based on ITM probability and the current market trends.

Which index option provides better premium return per volatility?

Major indices have their own volatilities over the last 5 years as shown in the chart below. The volatility $RVX of RUT is consistently higher than those ($VXN and $VIX) of NDX and SPX. For example, RUT had a 59% higher volatility than SPX on June 6 of 2014. This difference was on the high side. On March 1 of 2010, RUT volatility was 17% ((20.43-17.42)/17.42) higher than that of SPX which was a normal difference. The volatility of NDX is only slightly higher than that of the SPX most of times.

Karen stated she prefer to trade SPX over NDX and RUT. She had a good year (probably 2009) trading RUT with relatively higher return. But she likes the lower risks trading SPX. She does not want to trade NDX which has higher risk with similar return rate.

How do we know we are getting a good return for the risk of a trade using each vehicle of different volatility? I made a simple attempt to investigate the covered return per implied volatility of each trade and showed the results in the top right corner of the above chart. Basically, the covered return for each call and put option on 6-7-2014 were obtained from the TOS analyzer. The options had 41 days to their July expiration date. The calls had around 10% ITM probability and the puts had around 5% ITM probability. The implied volatility of each individual option was obtained from the TOS analyzer as well. I assume the ratio of covered return over IV would give us a fair measurement of return for the IV of each trade.

As can be seen in the table embedded in the above chart, selling puts of SPY, IWM, and QQQ would have similar returns (about 6%) on this date. Given SPY is less volatile, SPY put would be a good choice. For the short calls with 41 DTE, SPY does have lower returns (12.8%) than IWM (14.5%) and QQQ (14.6%). Please be advised that this study includes one set of data from one day only. It may not be generalized for other days. Further study is required to understand it more deeply.

Investigating stress tested portfolio margin for Karen style positions

Thanks to the help from Tom of the Karen Study Group, I was able to set up my TOS paper account to portfolio margin and came up with the following initial understanding.

Karen uses a unique method to manage the allocated trading capital. She pretends the market dropping over 12% in her margin crash tests while TOS portfolio policy stated a minimal 10% drop for portfolio margin using broad index based vehicles. Using the TOS analyzer, she watches potential crash loss in the portfolio against the net liquidation value of her account as shown in the following picture. On the Analyzer tab, the daily P&L numbers at 10% up and 12% down must not exceed net liquidation value. 

In the above chart, the +6% and the -10% slices are broker SPX stress test prices. All the other slices beyond them are Karen’s stress test points. In order to maintain sufficient adjustment capital during market sell-offs, Karen lowers her stress test point below the 10% down point by another 100 to 200 offset points, depending on the long term market volatility condition.

• · 2013 Crash price (cushion) = (Current price – 100) x 88% due to lower volatility.
• · 2011 crash price = (current price – 200) x 88% due to higher volatility.

According to Figure 2: SPY and Its Implied Volatility Since 2008 shown before, there are 2 levels of IV in the past few years. Starting at January of 2013, the volatility made a lower low and stayed within a much narrow and lower channel ever since. Thus, it makes sense to use the smaller and pretended drop of 100 points of SPX in the crash price calculation starting at the beginning of 2013.

In my personal opinion, it will be a good time to switch to the larger drop of 200 points of SPX when the IV makes a higher low and forms a newly elevated channel in the future. If the volatility VIX is generally lower to a level of 11 and 12 at its bottom (this is a long bull market condition), the 100-point offset is used. If the volatility is higher to a level of 13 at the bottom of the VIX, the 200-point offset is used.

Additionally, it is easier in the TOS analyzer and more conservative if a Karen style trader uses the following formula to determine the crash price. Karen does not offer complete details of her trading system but encourages traders to come up with the system that they are comfortable with.

• ·         crash price = current price x 88% - 100 or 200

According to the statements in the interview, the 12% crash down price has a probability of ITM of 5% approximately. Let’s investigate it using today’s data as a specific example. The SPX price is 1900 on May 25, 2014. The 12% down SPX price based on Karen’s stress test formula is 1584. There is a 53 DTE July 1585 put option of ITM probability of 2%. Although the probability to expire ITM on July expiration date is quite low, the probability to touch the strike of 1585 is a bit higher, probably twice the amount of expiration probability to 4 to 10%.

Now, we can study the margin requirement and its changes for the hypothetical position shown in the above chart. It’s clear that the opening or initial margin requirement is $6,291. The “Explain Margin” section embedded in the chart indicates the margin requirement changes from -10% to +6% of SPX price changes.

However, if SPX drops to 1565, a level looked by Karen style trader, the loss would be $19,968. Karen would make sure the loss number is less than the net liquidation value of the account on the opening day with the proper size of contracts. This amount of the loss would be higher than the initial margin requirement of $6,291. As of today, I’m not sure what would the new margin requirement be in this scenario. Would it become 4.9 times of the initial margin requirement to $30,869? How margin requirement changes in market crash conditions still needs investigation in the future.

Although the PM requirement changes according to market conditions for existing portfolio and the changes may be different for various brokerage firms, the net liquidation value of an short option account is more deterministic. Therefore, the net liquidation value is used as the basis for comparing the daily P&L number in Karen style trading.

It should be noted that the initial margin $6,291 of the position is dictated by the short call option at an upside movement of +6% of SPX price as the down side movement of -10% requires a less amount of margin of $6,266 only. It implies more puts can be sold in trade adjustments if market tanks, because short put options require significant less margins. This is naturally helpful to obtain more credits to cover the deficit of put option rolling down or out when market crashes.

Continued analysis of Karen style short put trades during flash crash

After the last post on flash crash study, I tried to create a couple of simulated trades for the flash crash option cycle using Super trader Karen's style and to test possible adjustments on the big down days (May 6 & 7 of 2010). The results were a bit surprising as the simulated positions did not pass the 30% ITM probability too much according to end-of-day data from TOS. The following is the details of my analysis of the simulated trades.

Karen discussed the flash crash day as a great day of option trading for her style. She mentioned she had to give up profits for a few months to get into a safe territory. Before the crash date, a portfolio of Karen style would have naked options of the May (14 DTE) and June (42 DTE) cycles most likely. The May options might be started more than 40 days ago in the last two weeks of March following the 56 day rule to open trades. The June options might be started over 14 days ago in the last 2 weeks of April. 

Let’s take a look at the life of the May put options first. As marked in the above chart, March 25 was the 56 DTE. On the next market down day on March 26, we could sell SPX May $960 put which had ITM probability of 4.90% for $2.13. However it was a bit surprising that the actual trading volume for the strike was minimal. It looked like Karen did not trade on that day. The option reached 50% profit zone in one week or two. If we took profit following the rules in Section 5 Exit Rules and Winner Management, then everything else would be simple for this position. Otherwise, it would be a rough ride. On May 7 with 14 days to expiration, the put option price was $7.4 with ITM probability of 13.2%, about 3.5 times of the originally sold price. With Karen’s winner management rules, the option would be let expire worthless for a maximum profit since it might not reached the adjustment point. Overall, the May put options did not appear to be in real danger when compared against June put options at the flash crash according to this analysis.

Now, let’s study the life of the June put options. There were 56 days to expiration for June options on April 22, 2010. This day and the next day were up days for market as shown in Figure 11: SPX Daily Chart of Flash Crash of May 6, 2010. So we could sell calls in these two days.

On April 27, 2010 the market dropped significantly and it was a good time to sell puts. We could sell 100 contracts of June $935 put with a 4.88% ITM probability (Delta = 4) following Karen’s entry rules described in Section 3 Option Selection and Section 4.1 Entry (Legged in) Rules. The bid/ask prices were $2.00/$2.90 (middle price = $2.45) and the volume was over 500. 

Additionally, if the some puts were sold some time before the close of market, the trade could have seen June $950 strike having ITM probability at 5% (5.68% EOD) and sold these contracts for a premium around $2.45. The end-of-day price became $2.90 for the strike which indicated a $0.45 loss on the day. By the way, the actual volume of this specific put strike on the day was about 1.7K, the 2^nd largest quantity for OTM strikes of the day.

According to Figure 12: The Life of a 5% ITM Probability Put Option Survived the Flash Crash, the June $950 put option’s ITM probability would have approached 30% at the lowest point of the flash crash day.  But it was unlikely that it exceeded the 30% ITM probability too much, even if the position losses could be 7 times of the original premium received. If the Karen trader stayed calm, did not get scared by the big account loss at the moment and followed the adjustment rules, there would be no need to adjust this position.

However, most retail traders are likely to get close to panic in the market crash environment, because they would find a huge loss number at the profit and loss field of the portfolio and figure out that the loss on paper would take many months to a year to recover. They may start to forget about rules and disciplines and execute special trades that would ruin the portfolio later on. Karen gave some help on how to deal with such psychological issues as discussed in Section 8 Psychology and Mindset.

A review of May 6, 2010 flash crash and the far OTM put options

As part of my project of the study of Super Trader Karen, I worked on the analysis of surviving the flash crash using Karen's trade style in the last couple of week and would like to share the initial part of this analysis here. Any comments are welcome.

 On Thursday May 6 of 2010, the US stock market had a famous flash crash when Dow Jones Industrial Average crashed 1,000 points (9%) and S&P 500 Index crashed 100 points (9%). The VIX shot up 18 points (74%) on the day as market volatility exploded. However, the US stock market recovered most of the losses within a couple of days. The 5 minute chart is shown below as a reference to the flash crash market action.

Looking at the big picture, the US market was in a big and long bull market since the historical bear market bottom at March 2009. The flash crash occurred in the beginning of a market correction. The correction lasted for about 4 months ending in late August of 2010 and the fall from top to bottom was about 17%. Although the market crashed about 30 minutes only, the volatility remained extremely high for over one day, as the fear of continuing market crash stayed rampant in those two days.

From this experience of a 100 point crash of SPX, it should be easier for us to understand why Karen chooses a crash point of 100 or 200 SPX fall in her money management rules. In the following sub-sections, we’ll examine the available option chains first. It should help us to understand the possible trade adjustment options. Then, we’ll try to make up a hypothetical trade that is opened before the crash and required for trade adjustment.  It should help us to gain some insights on how our trade position reacts to market crashes and what kind of impacts the position will experience after the trade adjustments.

The Option Chains at the End of Flash Crash Day

As the market started to fall significantly on this day, the put contracts with the original 5% ITM probability would have its probability increased to over 30% rather quickly. A Karen style option trader would be likely to begin the normal trade adjustment strategy by rolling down or rolling out the part of the put options in the portfolio. Considering the trader would not know how deep the drop would be for the day when the probability reached 30% initially, it would be logical for the trader to roll down or roll out to the next month at first.

After reviewing the put option trading volumes and open interests of June, June Quarterly and July cycles, it looked like Karen’s team might have rolled down the June puts to a strike of $800. As shown in Figure 9 SPX June Option Chain on May 6, 2010, the strike had an ITM probability of 4.2% and trading volume of 53K on the day. The trading volume of put strikes of about 5% ITM probability for June Quarterly and July had so much less contracts that they did not appear to be traded by professional traders. For example, the June Quarterly puts at $800 with 4.79% ITM probability had 55 days to expiration which was close to the 56 day norm as Karen specified. But it had only 7 contracts traded for the day.

Note Karen stated she had rolled out to October time frame. But there were no October and November options available on the day of May 6, 2010 according to TOS. I assume Karen did not remember the exact months for her trade adjustments during the flash crash a couple of years ago before the interview.

As the market continued to fall deeper in the afternoon, the Karen style option trader would be likely to see more and more put option strikes in existing portfolio reaching the points of 30% ITM probability. At this time, it would be logic to assume that the trader would like to further roll out the rest of the put options in the portfolio. A review of the option chains of July (70 DTE), August (105 DTE), September (133 DTE), September Quarterly (147 DTE) could give us some clues as well. The September put options of around 5% ITM probability were heavily traded as shown in Figure 10: SPX September Option Chain on May 6, 2010. The September Quarterly puts were thinly traded with the open interests under 100. So it did not look like Karen used this option cycle on that day.

Therefore, let’s take a deeper look at the September option chain to understand what kinds of trade adjustments could be done in this type market crashes...

A study of market drop and volatility rise for the last 4 years

I've been curious about the market volatility changes in the last 4 years (2010 to 2014) since Super trader Karen started her naked option selling strategy around 2010. Today, I finally got a chance to chart the SPY and its implied volatility and performed a brief analysis. In particular, I'm interested to see if there is some kind of relationship between SPY fall percentage and its IV rise percentage.

So I picked a few times in the last 4 years that IV rose quickly as shown in the chart below and created a table to investigate the percentage changes of IV and SPY price. In 2010, the market had the steepest drop (about 17%) within one month time, causing SPY IV (VIX) to rise 220% (more than tripled) in the same period. We have not seen this type of change 3 years since that.

After 2010, we had seen SPY IV rising close to 100% in a couple of months occasionally except in the last Jan in which month the IV doubled within 1 month. But the absolute values of SPY IV ranged from 11 to 15 and 20 mostly since 2013. This is the challenging period for the Karen style option selling. She used a set of different rules in the period, including using Weekly call options of 14 days to expiration, etc.

Selling calls of small Delta in up-trending market

In analyzing my losing bear call spreads in the last couple of months, I updated my TOS option profit and loss charting script so that it can track daily P&L for 6 rounds of trades. Then I did a back-test to see if I could keep selling calls with increased size and fixed Delta around 0.32 to end up with profitable month in current low volatility environment (VIX around 13 to 17).

As shown in the picture above, I made the trades using a combination of technical analysis and high probability method. On the technical side, I thought SPY broke a major support level of $177.5 initially and faced a resistance level of $185 later. All of these were invalidated by market moves. On the high probability side, I used Delta around 0.3 for short call options which corresponded to 70% probability of success approximately. After one adjustment, I decided to close all positions on 2-28 for a loss.

In my back test today using the ThinkScript, I wanted to see if I could adjust losing trades by increasing position size while keep Delta around 0.3 for up trending  market since I believe market does not "crash-up". So I started the bear call spread at 1 contract on 2-5. In the 1st adjustment on 2-12, I increased the contract size to 2. In the 2nd adjustment on 2-28, I increased the contract size to 3. When looking for Delta around 0.3, I found the strike prices got a lot more closer to the current SPY price as we approached expiration day. With 28 DTE, the short call price could be just $2.00 above current SPY price.

Thus, this test leads me to believe that we would still face challenges if we continue selling of small Delta (or small ITM probability) call options of the same month as the adjustment strategy in our efforts to maintain profitability for the option cycle in high probability trades even if the contract sizes are increased to bring in more potential profits to offset trade loses of adjusted trades. The starting point of the trade is also very important. If the trade did not start at the bottom of the Bollinger Band, the adjustment should work much better.

Due to the lack of any option data on 2-28 and in that weekend in TOS software (both ThinkBack and ThinkOnDemand), I could not sell option on that day while SPY price was higher in this back test.

A summary of Karen, the super trader's option selling strategy in 2013

More than one year ago, I was intrigued by the Interviews on Karen, the supertrader and posted an outline of her strategy discussed in the video. Since then, there were many reader comments. So I studied the portfolio margin that she used to achieve high return on margin, and wrote a few other posts related to the strategy. Besides, I also started working on back-testing Karen's strategy and set up a Karen Study Group.

On Feb 11, 2014, Karen was interviewed by Tasty Trade again to provide an update of her trading in 2013 and some of her general trading guidelines. Here, I'd like to share my understanding from the interview on this naked option selling strategy. Please note Karen will adapt her strategy according to market conditions such as the volatility VIX. She highly recommended traders to come up with strategies that work for themselves.

Karen, the Super Trader 2013

2013 Fund Performances & Goal

• Two funds totaling 196 Million USD, yearly return after expense
• 27%, 24% (over 50M USD profits)
• No losing month on 2013 (13 straight months, incl. Jan 2014)
• Close out every month. No rolling out to the next month, closed current month positions.
• Goal
• At least to beat SPX gains yearly (but there were no specifics discussed on what rules were used to ensure beating SPX)

Strategy of Selling Naked Options

• A strategy to profit on Theta (time decay) and volatility
• Rules may be changed depending on market trend and volatility
• Sell calls or puts independently
• Never sell options as spreads (i.e. strangles)
• Sell more puts depending on market trends
• In 2013, maxed out on the put side to sell twice as many puts as calls
• Sell calls with greater risks as market does not crash up
• In 2013, stayed light on call side to sell calls with shorter period of time
• The variable ratio of put to call contract sizes allows the strategy to adapt to market trend
• In 2013, the 2 to 1 put to call ratio kept the portfolio Delta from negative
• Most premium selling option portfolio have negative Delta (but not Karen's)

Trading Vehicles

• Traded SPX options mainly, used options of SPX e-mini futures /ES sometimes
• Main reason not trading SPY is commission costs, plus tax advantage 1256.
• No problems with SPX option liquidity
• Can potentially go to RUT if need other positions to put on
• Disciplined to avoid trading individual stocks even though they have high volatility

Option Strike Price Selection

Sell far out-of-the-money, high probability options depending on market volatility

• In 2011 & 2012 when volatility was higher (VIX >= 15), sold puts with 2 SD (5% ITM Probability)
• In 2013 when volatility was low (VIX around 11 to 13), sold puts with 1 SD (15% ITM Probability) to 1.5 SD (7% ITM Probability)
• Sell calls with 10% ITM probability

Option Cycle Selection

• 14 days to expiration for calls in general for 2013
• 56 days to expiration for calls if price can be projected and good premium can be obtained from far above the projected price
• Use trend analysis including 2 SD Bollinger bands, resistance, and FIB retracements
• 56 days to expiration for puts

Trade Entry (Always legging in trades)

• Sell calls when market rises
• Sell puts when market falls
• In 2013, sold more puts when VIX jumped
• Trades are entered in multiple days around predetermined option expiration days

Trade Exits

• Actively take profits and risks off the table
• For options (puts) starting around 56 DTE
• Close positions if profits reach 50% within 1^st 16 days
• Leave positions on after the 40 DTE neighborhood if they are not closed yet so that they can expire worthless
• For options (calls) starting around 14 days
• Close positions if profits reach 20% to 30% or even better 50% in a few days
• If price continues to rise with 1 week left for call options, then take the calls away and move them to next week while keeping puts on
• After some point of time, may stop pulling back profits since a built-in profit is realized already.
• Leave remaining positions of current month alone and start working on next month.

Trade Adjustments

• When ITM probability is less than 30%, no adjustment is required.
• When price drops and ITM prob becomes 30% (an arbitrary number) or greater for puts with plenty of days left (> 30 day)
• Adjust the position by taking it off and sell other far OTM puts about 20% ITM prob cautiously
• Some puts may be sold 10 points lower in ITM proba and others sold 15 points lower in ITM prob
• It may be pushed out to another week for puts (Not another month)
• Try to fix it in current week if possible
• It may lose one or a few dollars
• Try to make up the loss either through selling more put or call contracts
• Will keep existing calls as their value decrease and let them expire worthless
• Do not use existing calls as adjustments to the losses on the puts
• It avoids risks due to sudden market direction reversals
• Don’t have any option ITM!

Money and Risk Management

• The most important part of the trading game
• Use portfolio margin and further stress test potential loses
• Unlimited risk in theory
• Use TOS Analyzer Tab for risk evaluations
• The daily portfolio P&L numbers derived at 10% up and 12% down of the market price must not exceed net liquidation value in normal cases
• Portfolio P&L losses at the crash price must not exceed net liq
• In 2013, crash price = (current price – 100) x 88%
• The extra cushion is added due to low volatility (11, 12 to 14)
• In 2011, crash price = (current price – 200) x 88%
• The less cushion due to higher volatility
• Managing risk at this crash point assuming the portfolio had a major loss already
• If net liq drops due to adverse market conditions, the unrealized positions are losing money but they are considered safe if they have not reached adjustment points
• In worst cases, may buy some low valued puts or calls to offset the push from market move
• But this is not very often
• Don’t care or fear as long as the positions are safe
• Do not over-manage positions

Psychology and Mindset

• Control the emotions of both fear and greed
• Trust statistics and high probability (Use 2 SD for 95% odds of success)
• Use structured method and manage positions well
• Require a high level of confidence and repeatable successes for a long time.

Team Members

• 7 members: 6 traders and 1 controller
• Encourage other traders to set up of trading team for additional ideas