From April 1995 to August 1998, the pair rose just over 85 percent. In brief, in the mid-90s, the US were raising interest rates (who does that anymore? Psh), which made the dollar stronger following the recession of 1990.
The Japanese yen was devalued, too, as their asset bubble grew bigger. The Japanese saw this as the cause of the "lost decade," while it could also have been blow back from the Plaza Accord in 1985.
Nevertheless, the pair ultimately crashed 31 percent from it's 40-month cycle high. Following the Asian Financial Crisis in 1997, the began lowering rates in 1998, briefly increased the Fed funds rate before rapidly lowering rates into the 2000 bubble bust and recession. (Which I believe will happen next).
Fast forward to the current 40-month cycle, spanning February 2012 and June 2015. The pair has been able to gain a respectable 65 percent, and there is no reason why one would not BFTD; but, is the pair's fate remain the same as it were in the mid-1990s?
Analysts take of a policy devergence, but really it's come to a rhetoric divergence. The Fed has yet to tighten , and even if it does, Fed officials have opined that it would still be "accommodating" and largely based on market reaction.
We very well could see a 25-50 bps increase in the Fed funds rate over the course of several months or a year, but that is when the true economic rot will fester to the surface; and the Fed will undoubtedly reverse course.
The BoJ has admitted, no matter how many times Kuroda tries to revert course, that there are diminishing returns in regards to a weak yen.
Quasi-monetary policy can only take economic growth to a certain point before fiscal policy takes the reigns, and we have not seen that from either country.
Both central banks have embarked on massive programs; yet nobody wonders why in the same period the US is undergoing its slowest recovery from a recession, while Japan has had three recessions since the financial crisis. During the 40-month expansion, Japan has had three quarters of GDP growth matched with three of economic contraction.
Central banks don't see to want to believe they are responsible for asset bubble, yet they are always the root cause.