I bought a put, it's up 80%, expires in 4 months...sell it or hold longer?

An option newcomer asked the question in the above title.  My answer:

In my strategy, I sellputsthencalls - I sell to open cash secured puts (occasionally naked puts) & then covered calls.  Recently, I uncharacteristically did buy a call to open.  And it did force me to consider your above question after you bought a put that quickly made you 80%.  I bought a call versus XLE, the energy ETF.  In my sellputsthencalls strategy versus XLE, I made 2 critical errors in which I lost money.  So I bought a long term XLE call to catch up, & importantly, to protect my sellputsthencalls strategy against strong XLE appreciation.  I was bullish on oil & the energy stocks.  The XLE call became profitable, but not enough to cover my earlier loss.  But time until expiration was running out.  So I sold the XLE call well before expiration to capture the available profit, even though I was bullish on XLE.  (You're never wrong to take a profit.)  Continuing with my bullishness, I then bought another XLE call with an expiration date that was 1 year longer.  About 10 months before that call's expiration, all of my loss from the 2 critical errors was covered, plus I was able to grab a few more dollars beyond my loss.  So I sold my call & put it behind me.  

covered call, in the money, ex-dividend?

I often sell monthly covered calls against DIA, the ETF that holds the 30 Dow stocks.  DIA pays a monthly dividend.  Its current yield is around 2%.  The ex-dividend date is always option expiration Friday, which is tomorrow, September 20, 2019.  My current DIA September 20, 2019, covered call has a strike price of $267.  Today, DIA's at $271.42, & my call's $4.42 in the money.  With dividend paying equities like DIA, in the money calls are often assigned against the call seller on the day prior to ex-dividend date, which is today, September 19.  If this happens, I'll be assigned to sell my DIA today, at $267, & because ex-dividend is not until tomorrow, I'll lose my monthly dividend.  As part of my monthly routine when my covered call is in the money, today (one day before ex-dividend date) I considered a one month repair strategy to avoid the premature assignment of my covered call & loss of my dividend:  buying back the September $267 call at the $4.60 ASK & selling the October 18, 2019, $269 call at the $4.90 BID, pocketing the 30 cent credit.  In my evaluation of this repair strategy, I calculate my potential annualized return.  I don't know which way DIA will move over the next 29 days, so I presume that DIA stays at $271.42 for this calculation.  If DIA stays flat, I'll be assigned to sell at $269 on October 18.  $2 strike price appreciation + $0.30 premium credit = $2.30 return.  $2.30/$267 = 0.86% which annualizes to 10.8%.  Add DIA's CY of 2% = 12.8% potential for the repair strategy.  My new October $269 call would still be in the money with today's repair, and premature call assignments generally do occur on the day before ex-dividend which is today, but it's reasonable to dismiss this concern until the next ex-div date which is October 18.  (It is unlikely to see my new October $269 call assigned today because then I'd receive the extra $2.30 repair return almost instantly!)  In comparison to the repair strategy, I considered allowing my September $267 call to be assigned today, obliging me to sell my DIA at $267.  If so, tomorrow I'd sell a DIA, October 18, 2019, cash secured put.  At today's pricing, I'd sell the $271 put, at a $3.60 BID.  $3.60/$271 (the cash secured put's reserve requirement) = 1.33% which annualizes to 16.7%.  Today, because I presume a flat market - I must do so since I don't know it's direction - I chose the put strategy at 16.7% over the covered call repair strategy at 12.8%.

Repair strategy for a covered call that's way in the money.

Click onto the very good BCI blog for a video/review of a $75 (strike price) covered call with the underlying stock over $100 at the expiration date!  Blue Collar Investor - FIVE's repair (roll) strategy