@ddljohn-- The analysis depends on the kind of investment and various factors of that market.
For the most part, the market risk analyst will look at the type of circumstances that may come about and then will make assumptions on how much these may cost the investor.
This gives the investor an idea of whether he or she would hold up in a crisis or if they will lose more than they can bear.
Analysts use mathematical calculations to make these assumptions. The value at risk analysis, for example, is a purely mathematical calculation.
Of course, like it was mentioned in the other comment, these are all hypothetical. A market analyst basically lays out the worst scenario. But if an investor is prepared for the worst scenario, they will do well. So the fact that the analysis is hypothetical doesn't take away from its benefits.