When to close a short option position to maximize the return from premium decay?

Discussion in 'Options' started by dragonman, Dec 28, 2012.

  1. Hi, I have a question regarding option's premium decay when selling cash-secured puts (similar to covered calls): as I understand, the option's premium decay is non-linear, so that the percentage of the option premium that is decreased by each additional day is not equal. Thus I am trying to find the point that after which the additional decay in time value generates much lower return on capital-at-risk, so that it is preferable to close the position instead of waiting until expiration.

    I will use an example to better illustrate my question: if I currently sell May 2013 40 put on a stock (at-the-money option), and receives a premium of 2.6 per option, the maximum annualized return on capital-at-risk is 17.9% (considering 142 days to expiration). However, the 17.9% is only the total maximum possible return over the period, and it does not relate to differences within the period regarding the return on capital-at-risk. If the bulk of the premium decay occurs in the first 100 days, for instance, and if we break down the returns over this period, we will see that the actual return in the last 42 days is much lower than the return in the first 100 days. To illustrate, if after 100 days the option is worth only 0.3, then this amount represents the maximum profit over the remaining 42 days, and of course it translates into a much lower return on capital-at-risk than the return that was in the first 100 days. Therefore it may make sense to close the position after 100 days (in which about 88% of the original premium has decayed and the remaining return is only about 12% of the original premium) and open another position thereafter in order to have a higher level of return on capital-at-risk.

    So my question is if there is any rule of thumb which dictates that after a certain decay of the option's premium has occurred (such as 70% or 80% of the original premium received) it is better with respect to the return on capital-at-risk to close the option position than to keep it until expiration and let it expire worthless?

    My question relates generally to a cash-secured put strategy regarding options that expire within a few months. For simplicity let's assume that there is no change in the other parameters of the option over the period (such as stock price, implied volatility, etc.) and that trading costs are very minimal. Thanks.
  2. 2rosy


    maybe there is a diminishing marginal utility type formula for theta decay but for decay itself it kicks in the last month. for me, I dont want to risk much to get little. take profits :D
  3. gamma risk pays theta..
    theta costs gamma...

    for simplicity take out all real world assumptions....
  4. With no change in stock price or IV, the scenario you are looking for will never happen. In other words, after 100 days your $2.60 put will never be $0.30. It will be more like $1.30.

    Because the most decay occurs as we near expiration, your "return on capital" will always be highest right before expiration and will decrease the further out in time you move.

    On a side note, the non-linear decay theory is generally applicable only to ATM options. OTM options tend to decay much more linearly.
  5. well put.. adding to that.. closer to the money options and ATM experience the most theta decay near expiration at the direct increasing gamma risk.. the risk changes it doesn't decrease.. thats a common flaw in thinking..
  6. ktm


    I'll give it a go from another angle.

    I usually take profits around the 75% - 80% mark. In your case if you take $2.60 in premium...maybe 50 - 60 cents or so. Others use specific deltas to guide the closure...maybe in the .15 - .10 range, although that may coincide with the 50 - 60 cent mark in this example.

    You also have to consider the amount of time involved in the trade. If you have most of your premium very quickly, you may want to close early. If a trade is to last 30 days and you have half your profits in 5 days, lots of people like to close that. The way to approach that is the risk remaining of the position reversing vs. the premium remaining to be realized.
  7. I encountered cases in which the premium that was decayed as a percentage of the original premium was much higher than the days that have passed as a percentage of the total days until expiration. So even if it will not be exactly as the situation I described, the rationale is still the same and there is the question when to close the position to maximize return.

    For instance, you will agree that if 80% of the premium was decayed after only 50% of the time until expiration has passed, the incremental return from holding the position will be much lower than the return that was received so far. So the question is just what is that point -- 80% premium decay? 75%? 70%? or anything else.
  8. Of course the time issue is taken into account (see my previuos response in this regard). But I am trying to find a rough guidance regarding the premium decay, or any concrete formula that takes both the premium decay as % and time remaining as % and comes up with any accurate result as to when is best to close the position. Why did you choose specifically the 75%-80% range? How did you find that this range is favorable than, say, 65-70% or any other range? Could you please elaborate on this issue?

    Also, if you are aware of any such formulas (as the ones you mentioned regarding the deltas) please let me know, thanks.
  9. Although the most theta decay occurs near expiration, it may not be relevant to my question, as it relates to maximizing return on a position that was NOT opened near expiration. Therefore if 80% of the premium was decayed after 50% of the time has passed, then anyway I will not be able to earn more than 20% of the original premium by holding my position during a time which is equal to the time that it took me to earn 80% of the decay.

    And if so, the fact that near expiration the decay is higher will not help me, as anyway I will not be able to earn more than 20% of my original premium during that time.
  10. ktm


    For me, 80% applies to S&P FOP puts only, and in my case it's closing a spread that's typically ITM. If I have a 10 point spread, I'm closing it at 8. The 80% figure was the result of a lot of backtesting of the products that I trade and assessing higher and lower percentages, reversals, etc... For S&P FOP calls, the number is slightly different because the fat tails are generally absent. I should also add that I have offsetting positions and hedges and that my strategies typically involve capturing movements rather than avoiding them - as most net sellers are more apt to do.

    As far as specific formulas, you'll probably have to make your own based on your comfort level. Those variables (time to expiry and premium decay) are so subjective that it's really different for everyone. I think that gets overlooked here the most when traders talk about proper exit points. Some people have the mental ability to ride positions to 10 baggers. I discovered long ago that I am not capable of doing that. I can't mentally sit there and risk a reversal once I get serious profits on a position, so I've structured my strategies to fit my own psychological capabilities.
    #10     Dec 29, 2012