The question is more of a philosophical one, as you gotta define what you mean by hedging in the first place. As many of expressed, there is no such thing as a fully hedged risk-free portfolio. Every portfolio is hedged only with respect to specific components of risk, but exposed to other components of risk. Convergence or statistical arb has the risk of divergence and vice versa... options portfolio have a multitude of non-linear parameter risks ad yada yada.. People willingly or unknowingly take on a position to gain exposure to specifically those unhedged components in the first place, to make that extra return.
I used to say this all the time when I first started posting here. As it turned out the people who really needed to "get it" never did, and those who did "get it" didn't need to...lol So here it is (again) for whatever it is worth. "It is the risk that you are unaware of, that will kick your ass" Now I HOPE someone gets it, and makes use of it
Think about it this way. In the futures markets, a producer sells forward contracts to hedge against adverse price movements. Someone, usually a speculator, takes on the risk. So if a hedge fund is fully-hedged, then someone must be speculating. Thus, the $1 trillion hedge fund industry cannot be fully hedged(reply to some post before.)
PCA would help one understand the small and medium-sized risks by revealing the historically dominant sources of covariation among various tradables. But for bigger shocks, PCA suffers from two faults. First, it assumes a linear correlation and symmetric distributions among the various tradables. Thus it will fail to tell you how to hedge nonlinear effects and outlier events. Second, it assumes that the future will be like the past in terms of how things covary. Thus it's another example of driving by watching the rear-view mirror. Overall, PCA won't help hedge big shocks and major shifts in how markets interrelate. If you want to understand bigger shocks, I'd study the outlier events such as LTCM, 9/11, Oct 1987, 1929, the Arab oil embargo, the Asian currency crisis, Argentina's debt crisis, hyperinflationary countries, etc. PCA on the price streams just before the event might tell you how you might have hedged and then the event shock itself can tell you how thoses hedge would have performed.
Not to be glib, but from what I can tell about these scenarios historically, the best thing to do is to have capital ready to allocate to severely depressed assets after the panic. No such luck in political disasters except for leaving the country with whatever gold you could muster. Hence, the proposed asset classes I gave, which in proper allocation would probably give you a 3-5% return. Hardly impressive, but in a significant downturn, might leave you with 50% of your assets instead of 10% or worse. Everything in finance is relative, and if you have only lost half your wealth relative to everyone else who is wiped out, you are now the rich one who owns the bank. There is a matter/antimatter theory for the big bang which states that the particles were equally paired and each wiped each other out, until the sole remaining unit of matter remained, which gave birth to the whole universe. I like that as an analogy. I still would like anyone with good access to MPT portfolio tools and testing to consider what I had posted and run the #'s. If you can point me to a web based solution or an excel based solution, I'll do it myself and post the results.
This is probably the most insightful comment in terms of handling big shocks. Avoiding 100% commitment to a market that could experience a big shock ensures that one lives to trade another day. Always maintaining a reserve ensures that when the panic comes, one can buy the low as opposed to being wiped out by the decline. Too many hedges take the opposite strategy by being overcommitted. The big problem is the use of leverage to amplify the gains and counterbalancing hedges with a small amount of capital. It's too easy to think that one can use high leverage when one thinks the risks have been cancelled out with hedges. But the leverage means that if the markets move too far or too long out of balance, the hedge fails. I believe that LTCM is a good example of this. Their core bet was correct, but they couldn't handle the length of time it took the trade to go their way. As John Maynard Keynes says, "the market can stay irrational longer than you can stay solvent."