I agree, markets can stay irrational for a long time.
My two short positions (Uber and SNAP) are now about 1.2% of my net worth, and I would be comfortable with up to 8%, though not all in one sector.
Many people in San Diego are 200%+ invested in local real estate: e.g., they have a net worth of $400,000 and own a $800,000 house.
I don’t think that is a bad idea given the tax advantages and relatively low price of owning local real estate if you live here. However, in such situation it is also prudent to make your non-RE investments conservatively, or in areas that will benefit from a downturn.
Currently my only non-IRA stock position is in TUR, the Turkey ETF. I entered a couple weeks ago. The p/e of that market is about half that of the USA despite stronger growth. I think despite the instability there, the country is still committed to market capitalism and a recovery to even half of the 2015 price would be a huge return.
