One way of expressing the return is the difference between the current price and the previous period's price, divided by the previous period's price. The success of RiskMetrics has been so great that Morgan has spun off the RiskMetrics group as a separate company. RiskMetrics forecasts the volatility of financial instruments and their various correlations. It is this calculation that enables us to calculate the VaR in a simple fashion. Volatility comes into play because if the underlying markets are volatile, investments of a given size are more likely to lose money than they would if markets were less volatile.
Volatility here refers to the distribution of the return around the mean.
A volatile market is one in which the returns can vary greatly around the mean while a calm market is one in which the returns vary little around the mean. Correlation is important, too. Modern portfolio theory is familiar to many people who intentionally diversify their investments. 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.