Theta Decay in Selling Options

Welcome to Investment Planning Operational Research blog! In our first post we will be discussing the TastyTrade's lesson on selling Strangles and the effect of Theta decay.

The key component of this video involves the findings from the research team.

DTE	Profit
30	4.08
45	10.32
60	14.68

If you do a Log fit on this you will find the function to be y = 15.299ln(x) - 47.944 (R2 = 1). I am not sure if the team buy to close the strangle a few days prior to ending the strategy but I am assuming they did it around 7 days prior to expiry. If assuming 7 days then the new function based on the days committed for the ROC is 23, 38, 53 days respectively for the same profit. The new equation is y = 12.676ln(x) - 35.701 with R2 = 0.9998.

The equation for capital per day committed is the equations above divided by the number of days or "x." Doing some Calculus reveals that the optimal ROC occurs on day 62 for the original 30, 45, 60 scenario. [ln(x) = 63.243/15.299 = (47.944+15.299)/15.299]

In the second scenario looking at the 23, 38, 53 day the math works out to be 45 days. [ln(x) = (35.701+12.676)/12.676]

Two charts below show the annual payout of the repeated strategies. Notice the tapering that occurs at day 45 for 23, 38, 53 and day 60 for the 30, 45, 60 scenarios. The sweet spot would seem to be between the two values of 45 and 60.

The lesson here to always be curious and back test a few strategies to see the most optimal duration necessary for sufficient ROC. This holds true for most premium collecting strategies but always test them out yourself.