How to measure potential market risk

The difference between market risk and potential market risk is emphasized and a measure of the latter risk is proposed. Specifically, it is argued that the spectrum of smooth Lyapunov exponents can be utilized in what we call (l, s2)-analysis, which is a method to monitor the aforementioned risk measures. The reason is that these exponents focus on the stability properties (l) of the stochastic dynamic system generating asset returns, while more traditional risk measures such as value-at-risk are concerned with the distribution of returns (s2).
Introduction: Financial market risk reflects the chance that the actual return on an asset or a portfolio of assets may be very different than the expected return.
For this reason, a measure of market risk is necessary to carry through a successful risk management.Nowadays, financial investors often use value-at-risk to assess the market risk in their portfolio since they would like to ensure that the value of the portfolio does not fall below some minimum level that would expose the investor to insolvency. The value-at-risk is the level of loss on a portfolio that is expected to be equaled or exceeded with a given small probability.This risk measure can, therefore, be seen as a forecast of a given percentile, usually in the lower tail, of the probability distribution of returns.