If we invest all of our money in a set of financial instruments that move in the same direction and with the same relative speed, that is a riskier portfolio than if we invest in a portfolio of financial instruments that move in different directions at different speeds. If the instruments in the former portfolio all move down, we will lose money on each of these instruments whereas we would expect to make money on some instruments and lose money on the remaining instruments in the latter portfolio. Hopefully, in the case of the latter portfolio, we make more money than we lose, on average. Earlier, we stated that volatility was both dynamic and persistent. That is to say, volatility changes over time but it moves in a trending fashion.
Correlation is dynamic, too.
Correlations move with less persistence than volatilities. It is easy to see how complex the management of financial price risk can be with a portfolio containing more than two or three instruments. Once optionality is involved, it becomes computationally difficult to calculate the VaR, in some cases requiring statistical simulation of the portfolio. The reason for this is because of the convexity of option products. In describing VaR, I have emphasized the fact that VaR is only good for calculating an expected maximum loss under normal market conditions.