The yen's level until last year was abnormally weak. Now it's coming back to normal.

A relative opinion. I dare say there is no normal value of currency.

It is hard to find a nation that has a commodity backed money (not saying that it is the best form because I dont know enough on the topic). Since the money is tied to nothing (fiat currency) in this case, it is hard to tell where the currency "should be at".

Now with that said, the "non-elite" of the world put more of their money in to the American dollar to support their American funds (if the dollar collapsed, all they have invested becomes nothing). But the "elite" of the world put their money in Japan, because Japan had a similar situation to this in the early 90's or so. But instead of businesses buying land up and hoping the price would rise forever (Japan's case), the American's bought houses in hope that their price would keep going up. Other factors such as the lack of understanding on how savings works and solvency issues are there too of course.

So all in all, people put their money where they feel it is most safe. In this case it is Japan because they have had something similar happen before and have put regulations in place to prevent it from happening again.