  We propose a random walk model of asset returns where the parameters depend
on market stress. Stress is measured by, e.g., the value of an implied
volatility index. We show that model parameters including standard deviations
and correlations can be estimated robustly and that all distributions are
approximately normal. Fat tails in observed distributions occur because time
series sample different stress levels and therefore different normal
distributions. This provides a quantitative description of the observed
distribution including the fat tails. We discuss simple applications in risk
management and portfolio construction.

General Finance