Umm, I'm guessing you aren't in the industry as most of what you wrote here doesn't really make sense.
> Also, unless a stock has crazy liquidity, instruments like shorts and options are generally not available to individuals for a while after an IPO. A hedge fund may be willing to issue them, but they're set up for low volume/high value trading so they only deal with other large institutional funds.
How can a hedge fund issue options until options are legally able to trade? Short answer, they can't.
> Your average bank that would back options or shorts for an individual isn't willing to take on that kind of risk for a recently-IPOed stock.
Banks dont' "back" options, what ever that is supposed to mean. They are created when someone writes one, This is almost predominately, market makers and buy side funds, though the sell side will write some options.
And the bank takes on almost zero risk when they lend securities to short sellers. The sellers post collateral at the end of each day that is usually around 100% of the current short. What risk do you think banks are taking on when lending?
> I would expect to see Square drop precipitously over the next week/month as the professional investors can make money by pushing the valuation down, then it'll stabilize somewhere near the IPO price in 6-12 months.
Based on what? probably not history as I just went through all the IPO's over the past 3 years, guess how many are trading within 5% of their IPO price? About 5% of them
> Company fundamentals have very little to do with share price in the first year or two of an IPO; it's almost entirely psychological.
Again, based on what? I don't think you get to state this without some basic research. Why after 2 years do people start looking at fundamentals?