JPMorgan's disclosure of (ongoing and on-growing) $2 billion trading loss provides excellent illustration of just how loosely the word "hedge" is used in the financial industry. Strategies that experienced the loss were described as a hedge for JPM's credit exposure. If they really were a true hedge then presumably this $2+ billion loss would have been offset by a $2+ billion gain elsewhere in JPM's portfolio. Obviously this was not the case. The so-called "hedge" was little more than a directional bet that backfired.
While the $2 billion scale of the loss is certainly rare, the misguided notion that a short investment almost necessarily "hedges" a long one is omnipresent in finance. It is nonsense in majority of cases. Only when the two investments have both historical and logical near-1.0 correlation should they be considered potential hedges for one another. Virtually zero pairs of investments meet this criteria.
Seemingly high 0.8 or 0.9 correlations are nowhere close to enough to be true hedges. Historical correlation of EAFE and S&P 500 equities has been on the order of 0.85 which at first glance seem quite high and is logically plausible (after all, it really is a global economy). But if you decided to "hedge" long EAFE exposure with short S&P500 exposure starting a year ago you'd be looking at a 20% loss right now! Examples like this abound and most alleged "hedges" are far more ridiculous, such as "hedging" long Apple with short Microsoft.
The word "hedge", whether in "hedge fund" or "investment hedge", has very little meaning in the world of investing. It is true that a positively correlated hedge ought to reduce the potential loss (and potential gain) somewhat, but I doubt that a 20% absolute loss in one year is within expected range of outcomes for a "fully hedged" portfolio. In reality most investors don't even bother to analyze correlations. They simply concoct stories why one investment is bound to go down while the other is bound to go up, enter the corresponding short and long positions, and call the two a "hedge".
Long story short (get it?), you should view hedging strategies as (smaller-scale) directional bets and not as any kind of portfolio insurance.