Research conducted on exchange rates found the same random walk phenomenon as found in the stock market. Exchange rates move unpredictably. Currency exposure tends to increase the volatility of a portfolio and this is especially true in the bond markets.
At the same time there is no reliable evidence to suggest that the expected return of exchange rates (assuming monies are invested in short-term currency deposits) is generally anything other than zero.
To test this, I created an equally weighted portfolio of 12 currencies compared to the US$ for the period Jan 1970 to March 2010 and compared the performance of this to US Treasury Bills and Long-Term Government Bonds.
The average annual return for the currency portfolio was around 1.45%pa compared to 5.66%pa for Treasury Bills and 8.63%%pa for Bonds.
Significantly the volatility of the currency portfolio was approaching that of long-term bonds (7.98% compared to 10.79% for Long bonds).
Investing in currencies involves risk but not positive expected return hardly suitable for "stability".