According to Darren O’Connell, Australian institutes of higher learning weren’t teaching probability and risk in a manner that reflected the technological advancements of the 21st century. The methods employed by educators tended to be relatively inexpensive, easy to use, have a wide range of statistical functions, could analyze large data sets and didn’t require significant staff training costs. But O’Connell believed those advantages were often outweighed by frequent inaccuracies and the absence of many commonly-used statistics and methods.

To prove the point, he explored these deficiencies in his doctoral research at Curtin University of Technology (Australia), using Palisade solutions. Having utilized tools such as @RISK in an occupational setting, O’Connell was convinced that the technology offered more efficient and accurate means of teaching risk.

### O’Connell’s Methods

Darren O’Connell’s research sought to highlight the importance of probing beyond standard textbook theory, which assumes that an asset’s return should follow a normal distribution. To illustrate his point, O’Connell presented methods of modeling the stochastic price process of two illiquid securities under uncertainty by application of probabilistic techniques, in order to manage price risk within a Value-at-Risk (VaR) framework. To do this, he utilized multiple Palisade solutions.

Weekly price data for both securities from November 2002 to January 2011 were gathered and converted into weekly “rates-of-change,” or returns. Using StatTools, the summary statistics of each security was examined before constructing a histogram to examine to the tails of the empirical distribution. Then, the @RISK distribution fitting tool was used to select a theoretical distribution that closely matched the historical data using the Anderson-Darling best-fit criteria. In the case of both securities, the best fitting theoretical distribution appeared to be logistic, and that the normal distribution was a very poor fit to the historical data.

The next step of the evaluation compared how each distribution performed within the VaR framework, in terms of generating the expected number, and independence of violations. He found that the logistic distribution was better suited to capturing the stylized facts concerning volatility - mainly its reaction and persistence. It also better accounted for the heavier tails present in both securities.

Then, a Kupiec /Christoffersen back testing procedure was performed to compare the number and independence of VaR violations—forecasted returns that exceed the VaR estimate, for example—under the logistic and normal distributions. Both distributions generated similar results in terms of the number and independence of VaR violations. The logistic distribution resulted in tighter rejection zones above and below the expected number of violations and less clustered violations.

*"The benefits gained from using Palisade software were the ability to select probability distributions from a large universe, which opened up greater statistical modeling possibilities that develop more realistic solutions to problems encountered by industry practitioners."*

*Dr. Darren O’Connell*

**Curtin University of Technology**### The Findings

O’Connell discovered that relying on the classic textbook assumption of normality—when the true distribution can be better represented by a non-normal distribution—leads to an increase in both the number of violations and the instances of clustering, which multiply the level of potential losses sustained. As a result, the resulting VaR models were suboptimal and lead to a greater amount of capital tied up for regulatory purposes. Selecting a probability density function that is closer to the real, but unknown distribution of the underlying portfolio will show that the number and independence of violations occurring are more strongly aligned to the theoretical expectation, than would be achieved by simply relying on the normal distribution to model price risk.

“The benefits gained from using Palisade software were the ability to select probability distributions from a large universe, which opened up greater statistical modeling possibilities that develop more realistic solutions to problems encountered by industry practitioners,” said Darren O’Connell. “The seamless integration of Palisade products into the Excel development environment is a huge advantage, and allows practitioners to learn to use DecisionTools as if it’s a natural extension of learning Excel. This in turn reduces training and system development costs, because risk departments are not investing in expensive / extensive proprietary system solutions.”