Your thinking is correct about looking at your entire portfolio vs each individual fund. You can calculate the standard deviation, but it's not too easy. Here are three discussions on the subject where you can get more information. I've only included the third discussion because it contains some replies that point out the dangers of putting too much emphasis on back testing.

The problem is correlations change, so optimal portfolios change. You can't get perfect answers. The second link contains additional links to some example portfolios. They are all valid, but one may outperform in one time period and lag during another.

I should also point out that most of your sensitivity and potential downside losses will be due to your asset allocation to stocks vs bonds/cash.  Being well diversified in equity asset classes can lower risk for a given return or increase return for a given amount of risk.

http://www.bogleheads.org/forum/viewtopic.php?t=21756&sid=f4e6c4b8f23ad03096fed70e17be75ca 

http://www.bogleheads.org/forum/viewtopic.php?t=21769 

http://www.bogleheads.org/forum/viewtopic.php?t=21768 

Now that I've given you information on correlations and SD, maybe it's not the information you were looking for. If you only want beta, that's easier, but it's not as useful.

http://financial-dictionary.thefreedictionary.com/Portfolio+beta 

Paul