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.