Review of Jan and Feb Trades and max drawdowns

In January, I started trading my option selling strategy "Selling verticals at the edges". I paper tested this strategy and traded it with real money with 1 to 2 positions last year. They were posted in the blog. This year, I decided to increase the position to 3 which means my monthly open margin is close to 25% of my capital.

I posted the individual trades, as well as the trading plan, in our study group in the last couple of months. Now, I'd like to review and share the overall trades that were closed in Jan/Feb. January was a seriously challenged month for my trades, as all 3 opening positions were tested as shown in the chart below. 

The prices of TLT and GLD moved in sync upward, pressuring my bear call spreads. The short strike $134 of the Feb$134/139c had a Delta of 0.67 when TLT rose to $137 area. So I had to adjust the position by rolling out and up on Jan 29. The next day, TLT continued to rise with a big gap up. It did give me a bit of psychological stress. I was evaluating the possibility to buy call options as insurance.

However, TLT started to turn down on the following day and had never gained strength to test the peak level so far. Interesting enough, the same behavior happened for my last October TLT adjustment (See surviving a 3 SD test on TLT). On the 1^st day of adjustment, TLT shot up and my portfolio was showing the largest drawdown of the cycle. On the 2^nd day of the adjustment, TLT started to pulls down.

With my TOS script, I was able to see the daily P&L for the portfolio and the largest drawdown based on closing prices. If I had not made the adjustment, the largest daily drawdown would be about $2.8K (2800/9000=31% of initially used margin). With the adjustment for which more capital was put in use, the largest daily drawdown increased to $3.5K (39%) roughly.  This is a major characteristic of the strategy, because more capital risks are added due to adjustments. But the probability of profits also gets increased after the adjustment.

Option early assignments due to stock dividends

Recently, I received a broker’s email regarding possible early assignments for my option positions on TLT which was approaching Ex-dividend date in two days. So I studied option early assignments for option sellers due to dividends.

First, here are the major dividend dates and events.

1. Declaration Date - date at which company approves dividend payment and designates the Payment Date and Record Date.

2. Ex-Dividend Date - the date on or after which the stock will be traded without the right to receive the dividend. The Ex-Dividend Date is two business days before the Record Date.

Call option early assignment dates are usually one or a few days before this Ex-dividend date. Put option early assignments usually happen on the Ex-dividend date.

3. Record Date - the date which determines which stockholders are entitled to receive the dividend payment. They have to own the (settled) shares as of the close of this date in order to receive the dividend. Because most stock trades in the US settle three business days after the trade, a trader must purchase the stock three business days before the Record Date to qualify for the dividend.

4. Payment Date - the date on which the declared dividend is paid to all stockholders owning shares on the record date.

Next, let’s take a look what kind of and when options are susceptible for early assignments.

The owner of the call often exercises certain type of call options at the strike price of the call, one the day before the stock goes ex-dividend, to receive the dividend, if the call option is in the money and the amount of the dividend exceeds the remaining time value of the call. As an option seller, the trader may get early assignment as a result of exercises of the call buyer.

For short puts, early assignment usually occurs exactly on the ex-dividend date, when those puts go in the money and expiration is a few days out or less (not much time value left). This happens when the long protective put holders who also own the stock can remain as the shareholder of record to receive the dividend on payment since they own the stock before the Ex-dividend date, and possibly benefit from the stock price drop at the opening of the ex-dividend date caused by the dividend. On the morning of the ex-dividend date, the opening price of the stock is reduced by the amount of the dividend. After the put exercise, the trader can receive cash and earn interests as well. Note exercising a put option on the day before an ex-dividend date means the put owner will have to pay the dividend.

Early assignment occurs when an option holder exercises his option by notifying his broker, who then notifies the Options Clearing Corporation (OCC). The OCC fulfills the contract, then selects, randomly, a member firm who was short the same option contract. The OCC then notifies the firm. The firm then carries out its obligation, and then selects a customer, either randomly, first-in, first-out, or some other equitable method who was short the option, for assignment. That customer is assigned the exercise requiring him to fulfill the obligation that he agreed to when he wrote the option.

Early assignment’s impact for covered call positions

For a covered call seller, it means the seller will not only unexpectedly lose the stock position, but also the next dividend payment. The early assignment forces the call seller to sell the stock in order to fulfill the obligation of the short call.

How does stock option impact stock prices?

How does stock option trading impact the stock prices? This is an interesting topic that many professional researchers trying to figure out. I had always thought options had minimal effects on the prices of the underlying other than the pinning to heavily traded option strikes at the expiration (pin risk) dates. This was in-line with the posted view expressed by Thomsett, the author of an option book:


However, after a recent study of a couple of academic papers and an investment company report, I found there are some evidences of the option trading that impacts the stock prices. The academic papers also provide theoretical models along with the empirical data (which I don't fully understand).

N. Pearson, et. al. of University of Illinois at Urbana-Champaign published a paper titled "Does Option Trading Have a Pervasive Impact on Underlying Stock Prices?" on Feb. 23, 2007. The paper introduces the following areas of research on how options impact underlying stock prices and mentioned that there were no conclusions before their publishing date except for the pinning:

• Whether option generation has a one-time price impact
• Whether option activities cause systematic price change at expiration dates (pinning)
• whether options produce pervasive changes in stock prices

They reported that there are about 12% of optioned stock daily absolute return that can be accounted for by option trader's hedging of their option positions. This constituted the first evidence that the option markets have a pervasive influence on underlying stock prices.

More recently, D. Yang, et. al. of Harvard published another paper titled "Does the Tail Wag the Dog? How Options Affect Stock Price Dynamics" on Dec. 13, 2014.  They demonstrated that institution call option sellers would buy stocks to hedge their short calls. It would create an upward trend. If the dynamic hedging is larger, the upward trend curve increases the auto-correlation of stock return in a higher degree. The opposite is true for institutional put selling.

Finally, a recent report from a Shanghai investment company studied the underlying stock price rising magnitude as a result of the very first introduction of options for the stock in a large number of countries. It claims that it's a worldwide phenomena that underlying stock prices would increase in the first month of the initial option introduction for the stock. The report thus asserts that Chinese stock market will rise this month since stock options are introduced for the first time in Chinese stock market.

The US stock market is included in this study. It finds that US stock prices increased, on average, an annualized rate of 50.4% in the very first month of option introduction. Comparing to S&P 500, the initially-optioned stock prices outperformed S&P500 by 45% in that month. The report states it would be a high probability event for the fundamentally sound stocks to rise during their 1st month of option introduction. Since there is no detailed information about the number of stocks used in the study and the years of the stock trades used in the study, I was not very sure about this result.

Therefore, I spent some time to verify this study a little bit. I reviewed the stock and option trading history for two of my positions on China: HAO & FXI. To my surprise, the first month price rise were 5.4% for them during the 1st month of option introduction. This is close to the average annualized rate provided by the report. Accidental or not, it gives me a little bit feeling of credibility of this report.

FXI	StockAvail	10/12/2004
	OptionAval	10/15/2004
	StockPrice	17.21
	1CycleLater	18.14
	Percentange	5.40%
	ATMExpireOI	904
HAO	StockAvail	1/30/2008
	OptionAval	5/27/2009
	StockPrice	20.25
	1CycleLater	21.34
	Percentange	5.38%
	ATMExpireOI	11

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.