Using weekly data for the last 5 years for DAX (german equity index), S&P (US equity index) and EUR (value of "german" currency priced in US dollars) we have the following results:
EUR fluctuates with an annualized volatility of 8.8% a year, DAX with vol of 18% a year and S&P vol 12% a year. In my experience it is generally true that a currency is less volatile than a major stock index (as a rough guide about half as volatile). I am a little surprised by how low S&P vol has been, my guess would have been 14 or 15%; DAX typically a little more volatile than S&P and this is confirmed.
The correlations of the currency with the two stock indexes are as follows: EUR with DAX is -0.23. This is in agreement with a general observation I/many people made over the years: when American investors see a foreign stock market go up, they usually see the currency of that country go down and vice versa (not always true of course). Between EUR and S&P correlation is -0.05, perhaps a little surprising to me, I would have expected it slightly positive. But generally these correlations are between -0.25 and 0.25 in my experience, i.e. not very large.
[I left out the correlation between DAX and S&P: it is 0.725. Major world stock markets are always positively correlated].
Of course for a stock (as opposed to a stock index) the volatilities would be much higher (maybe double).