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.

Sold FXI Feb$36.5 Put and its return on capital

After closing a profitable naked put on FXI last Fridday, I started waiting for a possible rebound of FXI near the low up-trending line. Today the stock price did jump with a bullish MACD divergence. So I sold the Feb$36.5p for $0.65 with a Delta of 0.32 and a covered return around 11%. I plan to get assigned to the stock if it falls below the strike. I'll also set a GTC order to nail down profits earlier than expiration as discussed before.

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FXI Annualized Return on Secured Capital

To examine the ROC for the cash secured naked put, I created a ThinkScript to chart the curves relevant to Return on Capital. There are two ROC curves shown in the image below: One for Annualized ROC and another for approximated annualized ROC for a trading period of 30 calendar days (about 20 trading days assumed).

In the chart, the life long annualized ROC of this specific put option changes along with FXI price and time. At the price around 37.9, the following table showed annualized ROC values have not changed that much before.

• Date:   ROC
• 12-24: 11%
• 11-15: 11%
• 11-01: 12%
• 09:30: 11%

The lowest sub-graph showed annualized ROC if the trade lasted 30 calendar days. Note this number is usually higher than the life-long aROC if the stock price stays above the short strike. For example, if we buy back the option sold on 11-13 (20 trading days ago and ITM put selling) with a credit of $1.83, the return would be 41%.

The ThinkScript is given before as a reference.

#---------------------------------------------------------------------
#This script calculates Annual Return On Secured Cash for selling puts
#AROSC = [Profit/(Strike - Credit)] * (365/Days)
#---------------------------------------------------------------------

# 1. AROSC at entry for option life span
#def SoldCredit = OptionPrice();
# OptionPrice does not give current option price
def SoldCredit = Close();
def Days = GetDaysToExpiration();

def AROSC_Life0 = (SoldCredit / (GetStrike() - SoldCredit)) * (365/Days) * 100;

# Limit AROSC to 100% so that it displays curve better
plot AROSC_Life = if(AROSC_Life0 > 100, 100, AROSC_Life0);

Time decay chart and analysis of individual put options

As planned analysis of my closed naked put selling of FXI & TBT, I updated my ThinkScript to chart the delta-adjusted time value decay of Out-of-The-Money (OTM) put options. The updated script uses an average moving line to show the actual time decay of the option under analysis. Additionally, it shows the Bollinger bands of the time value in order to illustrate the overall time decay effect. BB showed a big contraction in the last 2 weeks in both cases. Some people may say the Bollinger band of the time decay is a wavy cone as a result.

To me, it suggests the option can be bought back 2 weeks prior to expiration. The charts provides supportive evidence to the conceptual drawing of OTM time decay after the inflection point in my previous post.

For the FXI put option trade, it demonstrated a more volatile time decay curve as the price of FXI fluctuated around the sold option strike. It can be found that time value was relatively high when the option is ATM.

For the TBT put trade, the price of TBT stayed OTM all the time. So the the time value at the last 4 weeks was quite small. When did time value start quick decline? It was difficult to tell from the chart. In June to July time frame, the option time value had big decline as a result of the rapid price ascend, even though we are using Delta-adjusted time value on the chart. In August to October time frame, the stock price dropped but the option price also fell as a result of time decay.

In the next posts, I'll examine the option time decay from a return of capital perspective.

Closed FXI Naked Put on Expiration Date

I finally closed the short Dec$37.50 puts on FXI today by buying them back at a cost of $0.13. I decided to take a good amount of profit on the expiration date, rather than getting assigned to FXI as the stock price was a few cents below strike.The intention is to sell another put when FXI rebounds.

As a winner management strategy, I could have set an good till cancel order to buy back the short put at a price of $0.10 to reduce risk of getting assigned when FXI fell. This option price was reached recently intraday, but not at the AM time period when I was trading.

I'll post the complete time decay chart of this option later with further analysis of the put selling strategy in the next few days.

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The time decay chart of a put option adjusted by Delta

Time decay is a fascinating part of option premium selling strategy. In my quest searching for suitable time decay, I'd like to get clear picture in areas such as what are good entry and exit points that capture rapid option time decay in a option's life span. I had posted a conceptual OTM option time decay chart  and an actual OTM time decay chart before. This time, I further studied the time decay of my naked FXI put option sold 3 weeks ago with the help of ThinkScript.

Since option price changes with underlying stock due to the impact of Delta, I decided to observe the option premium decay after taking out the Delta-induced option price changes. The option time value in my study was restricted to changes due to volatility (Vega) and Theta mainly in this way:
Option time value = extrinsic value  =
previous price + Delta-induced change + sum of Vega and Theta induced changes.

Using a simple approximation of Delta-induced option price changes, I was able to chart the Delta-adjusted time decay curve of the naked put which took out the Delta-induced change in the above equation. The directional price change from Delta is calculated as shown below using ThinkScript:
plot TmValExclDelta = extrVal - ((absValue(Delta()) + gamma() * opChange)/2) * (opChange);

The entire script is downloadable for anyone who is interested. It can be used as a base for other option premium analysis. The resulted chart is downloadable in a PDF file if anyone needs to see a clearer picture.

As shown in the above chart, I found a few key points below. I think a picture is worthless a thousand words. There are other points that can be observed from it as well. Note the left vertical axis is FXI ETF price and right vertical axis is FXI Dec$37.5 put option price.

• The FXI option price was high while its time value was low as FXI dropped below the strike price.
• The FXI option time decay acceleration started at about 2.5 months before expiration.
• The naked put sold at Delta around 0.3 and its time decay stayed close to the bottom downtrending line as FXI price consolidated for 3 weeks.

One of the interesting point to me is that this option started rapid decay around 2.5 months. If one sells the option on 2.5 months before expiration and exit it at around 1 month before expiration, he would capture a good amount of premium values with relatively smooth time decay as well. 

OTM Option Time Decay and its Exit Time

TastyTrade posted a video on Theta Based Exits for Sold Options on Youtube. It was quite educational. I’d like to share with everyone some of my review and thoughts on this topic.

On the time decay part, we sell options of delta of 0.30 to 0.35, which implies the ITM probability around 30% to 35% by expiration date. A credit is received after the option selling, which is similar to selling insurance premium. The OTM option time decay manner is somewhat different from that of ATM options which is show-cased in a lot of option text books. Based on the video introduction, the OTM option with Delta around 0.33 has a time decay chart as shown below. [Note I believe the hosts made a minor error in describing the units of the axes. The horizontal axis represent the passing time of the option in weeks (not days as they said) for an option that expires in 10 weeks. The vertical axis is the   option price x 100 in Dollars (not option price as they mentioned).]

For OTM options, the option’s price is the same as its extrinsic value. Time decay functions similar to insurance premium. This chart suggests OTM option (Delta = 0.33) price decay is relatively faster at around the first 7 weeks (49 days), which is the inflection point. After that, the time decay slows down as the price of the option has already dropped significantly and there is not much value left. The big assumption is that the OTM option stays OTM, although it was not elaborated how much price movement of the underlying could have to maintain such as time decay pattern. The discussion seemed to suggest that this 0.30 ~ 0.35 Delta OTM time decay chart is the merge of a 0.4 ~ 0.6 Delta ATM option at the 1^st few weeks and a 0.1 ~ 0.2 Delta OTM option at the last few weeks.

In reality, it may be difficult to come up with the above curve for any specific options, as prices always fluctuate. Demonstrating the daily rate of return on capital (ROC) in a chart is also interesting and it can give very good clues on when to exit this type of trades. Thus, this is one area that I intend to investigate in the future with the help of ThinkScript.

On the management of winners using Theta decay for exits, I believe it’s a great rule and Tom has been telling many of his students for a long time. Once most of the premium is decayed through time, the remaining value is quite small and the rate of decay becomes very slow. From risk to reward perspective, it will not look good if we try to gain a small reward that remains in the last couple of weeks before expiration. Therefore, it makes sense to buy back the sold option in the last couple of weeks immediately after the inflection point, as the return of capital gets smaller.

TOS offers free trades for option buy-backs within a nickel. However, many options at the inflection points are likely to be worth above $0.05. Only very low priced options can meet the free commission trade criteria. It would be much helpful for retail traders if TOS could offer free buy back trades at the inflection points such as Delta <= 0.10 or price <=  $0.10 J

Where should be a good point of entry to sell the options? This is not discussed in this video. But from the chart, it appears to tell us that 8 to 7 weeks before expiration is a good entry point where the option starts to accelerate its time decay. This entry point coincides with the option selling days used by Supertrade Karen.

In summary, the video discussed option premium selling by exploring the relationship of statistical probability (success rate and occurrence rate), return on capital, and management of winners. It did not use the option Greeks that much. Even though Theta had been mentioned in the whole discussion, the value of Theta or the trend of Theta was not shown at all.

The so called “Theta based exit” should be more accurately named as “Time decay based exit” in my opinion as Theta is only one component of the time decay. The other components for time decay include implied volatility/Vega and Delta which also change with time. There is no guarantee that Theta provides the most time decay when compared to Vega and Delta.

Sold Dec$37.5p on FXI

FXI gapped up and broke up the 2 month down trending channel today with high volume. Since I'm bullish on China over long term, I looked for a way to play this ETF. My rules require me to see a 6 week retrace from overbought zone for the MS line in order to enter an uptrend trade. But FXI MS is dropping for about 4 weeks only. Thus I used the naked put strategy as it requires FXI to move sideways or up. FXI also has a high cor-relationship with SPX. So I felt it's saver with the naked put as US market has been running up without a rest for quite some time. I plan to keep FXI if the put has to be exercised later. My cost will be 37.5-0.68 = $36.82. TOS indicated a 18% annual return rate.

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TBT: Profit from higher interest rates

Interest rate sensitive ETF's reacted on Government job numbers strongly today. TBT jumped above the recent 2 month long down trending channel with strong volume. My naked put Dec$70p sold about 10 days ago reached most of its profit with current Delta 0.09 in a surprising period of short time. So I bought them back for $0.25 each to nail down the profits and initiated some June$73c contracts for a longer term trade at the cost of $8.5 each. My stop loss will be around the recent low of $71. If TBT pulls back without heavy volume, I'll look for an opportunity to double my contracts. I'm impressed by the large pullback yesterday and the huge breakout today. The trade is consistent with my long term view of the interest rate rise. I'll change it to diagonal call spread later when I see TBT become far extended in price.

Another major beneficiary of the rising interest rate is the regional banks ETF KRE which also made an impressive breakout with huge volume today. I'll continue to investigate the possibility of playing with this ETF in the future. The real estate ETF's IYR got hammered again as a result.

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Sold TBT Dec$70p after its pullback for 2 months

TBT had risen for 4 months then started falling. Its price is around the support of an uptrending 200 DMA at $70. Since I expect an rising interest rate environment over the longer term, I sold Dec$70 put for $1.23 to get a cost of $68.77 in case I get assigned.

The average implied volatility shown in the chart appears to follow the price performance of TBT, due to its inverse relationship with market. This is different from other regular stocks. TOS option chain window indicated the covered return rate of 11.5% for this trade.

Similar to USO, TBT has a relative loose correlation with stock market. This gives me an opportunity to play the overheated market in the short team.

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