# VARIANCE

There is much that statistics has given us in the century that followed. Randomized clinical trials, and the means to analyze them moved medicine fully into the modern, science-based era. Statistical process control, and the associated doctrine of continuous improvement gave us the era of modern mass precision manufacturing. Big data analytics put information (if not wisdom) in the hands of anyone with an internet connection.

One area of an application based almost wholly on the modeling of variance is financial risk management. Understanding the distribution of possible future outcomes requires fitting known data to theoretical probability distributions that can serve to “generate” many Monte Carlo simulations of the returns on investment portfolios, insurance products and the like. Najeeb Taleb wrote of the importance of the “long tails” of these assumed probability distributions, for that’s where the unlikely events with huge impact lie in his book The Black Swan – the Impact of the Highly Improbable.

He chose the term black swan because these birds were initially assumed to be non-existent because people had not seen one. But, though rare, they do exist. In the same way, cataclysmic financial events do happen, even though they may not be seen in the data on which your probability distribution is based.

Making the convenient assumption of a normal distribution may underestimate the probability of extreme events; a probability distribution with fat and long tails may be more appropriate. Overconfidence in statistical models and nice, symmetric bell curves was one factor in the financial crash of 2008.

Modeling financial data is all about modeling events over time, so it also involves time series analysis. Putting it all together are Huybert Groenendaal and Greg Nolder, experts with considerable industry expertise, in

Financial Risk Modeling

They will answer your questions and comments on a regular basis throughout the course on a private discussion forum.

The software used is Model Risk, which operates in Excel. You’ll learn how to

• Specify how a probability distribution is used in a financial model simulation
• Characterize the different components of a time series (trend, seasonality, autocorrelation, volatility, mean reversion)
• Fit various autoregressive models (ARCH, GARCH, more)
• Use Markov chains in simulations
• Work with multi-variate time series
• Determine the correlation structure in time series
• Fit appropriate probability distributions to historical data, and assess the fit (AIC, etc.)

The course takes place online at Statistics.com in a series of weekly lesson and assignments and requires about 15 hours/week. Participate at your own convenience; there are no set times when you are required to be online.