The Asset Market Model theory suggest that a currency will be in more demand and hence will likely appreciate in value if the flow of funds into other financial market of the country such as equities and bonds increases and vice versa.
This is specially true in developed nations like the U.S.A., Japan and Euro zone where both public, and institutional investors hold their funds in investment products such as stocks and bonds which dwarf the amount of funds that are exchanged as a result of import and export processes.
Many well known pundits suggested the likely fall of dollar as the world's reserve currency on the grounds of ever increasing U.S. current account deficit.
Its quite logical to conclude that a high debt level can affect inflation, interest rates, and economic growth in the U.S.A. So foreign investors would gradually withdraw their funds from the U.S. equities and bonds markets increasing the risk of dollar devaluation.
Between 2007-2009 the dollar plummeted against Euro primarily because of widening current account deficit and sub-prime mortgage crisis. However, by the late December of 2009 and early January 2010 dollar bounced back and continued it's winning streak that extended June 2010.
Possible sovereign debt default by Greek and other European nations like Spain and Portugal plagued the Euro zone around early 2010. This further fueled the rise of dollar against major currencies, contributed primarily due to the enormity of the U.S. equities and safe haven nature of the U.S. government issued bonds markets.
At times of global uncertainties, the classical move that investors make is to shift their funds to safe haven funds such as the U.S. government bonds. So the dollar rose against Euro and major other currencies despite the massive budget deficit.
The asset market model theory is fairly new and still needs test of time.
It's hard to establish a relationship over a long run between a country's equity market performance and currency performance.
Generally speaking, with rise in the country's equity market, it's currency should rise due to higher demands.
However, during global financial uncertainties like the sub-prime mortgage crisis, the crisis that we experienced between 2007-2009, the relationship can become very uncanny.
Also, when the equity market trades in sideways like the one that we experienced in the U.S. in 2002, this model of forecasting was out of the window.