8. One vendor of risk models, FinAnalytica, publishes daily risk measures. The following extracts are from the company’s website:22 As an industry standard, Value at Risk (VaR) measures the worst expected loss of a portfolio over a specific time interval at a given confidence level. Most commercial risk analytics products today measure VaR based on the thin-tailed and symmetric normal, “bell-shaped” distribution curve. As demonstrated by the current crisis, these normal distribution assumptions result in overly optimistic VaR estimates and they inadequately account for extreme events.

a. Explain what is meant by the above excerpt.

FinAnalytica’s Cognity risk management software platform uses fat-tailed, asymmetrical distributions throughout, and incorporates the most advanced statistical methods to model extreme events, volatility clustering, regime switching and correlation shifts in times of market crisis.

b. In the above excerpt, what is meant by “extreme events”?

c. What is meant by “volatility clustering”?

d. Why do you think it is important to model “correlation shifts in times of market crisis”?
Cognity risk analytics provide more accurate fat-tailed VaR estimates that do not suffer from the overoptimism of normal distributions.

e. In the above excerpt, what is meant by “the over-optimism of normal distributions”?
But Cognity goes beyond VaR and also provides the downside Expected Tail Loss (ETL) measure—
the average or expected loss beyond VaR. As compared with volatility and VaR, ETL, also known as Conditional Value at Risk (CVaR) and Expected Shortfall (ES), is a highly informative and intuitive measure of extreme downside losses.

f. In the above excerpt, explain what each of the concepts of risk means.