The underlying problem with both notions is that you need to have a model for how markets behave in order to assess the risk associated with a position. The most popular risk measure is value at risk, which is based on a model that makes some questionable assumptions. During normal times, it's a reasonable approximate measure, but in times like last year, when risk measures are very important, it tends to go badly wrong.
When judging the risk of a portfolio of loans, for example, a highly simplified way of measuring 'Value at Risk' is
VAR = Probability of something bad happening * $$ Lost when Bad Thing happens
summed over all of the loans.
A lot of VAR models use a one-tailed 2-sigma event or 3-sigma event for the first term above, and historical averages of recovery for the second.
Problems, of course, can arise when things happen such as what ultrafilter stated above.
Many models sort-of assumed the Probability of Something Bad Happening was largely independent from asset to asset. In other words, the models
assumed a default on a loan in Stockton had nothing to do with a default on a loan in Las Vegas. They built that into their models because that's what the historical data showed. And for 2002-2007, that probably wasn't a bad assumption.
But recent events highlight how Bad Things Happening can become highly correlated, so that when one thing goes wrong, many things go wrong simultaneously.
To make things worse, the $$ Lost when Bad Thing Happens also rises dramatically - much more than what was expected in the models - in illiquid markets such as today's markets, which in themselves are correlated to Lots of Bad Things Going Wrong Simultaneously. Yoiks.
In short, the models assumed that every once in while somebody would get up from the movie theater because they didn't like the movie and go home. And then you would lose $2 in potential popcorn sales.
But when there's a fire, everybody stampedes for the exits and stomps on each other. Then you lose all of your popcorn sales, your Coke sales, and people demand refunds. Plus your movie theater burns down and you're out of business. And then the people who got stomped on decide to sue you, to boot.