Modelling Uncertain Returns in a Risky Market

When will you retire? How much money will you have to live on after retirement? And what income and savings will you need to invest to achieve your financial goals?

Important decisions are made in an uncertain market environment, particularly for younger adults who have a longer working future ahead. To help people meet retirement goals, a large financial management firm turned to Data Analysis Australia to assist in building a forecasting model. The model was to incorporate something that the financial industry in Western Australia previously found difficult to present to customers - the variability of future markets and how that would really affect their customers' financial future.

Understanding variability and risk is a natural problem for statisticians. The challenge was to combine an understanding of risk with a correct model of a person's finances, not an easy task when superannuation and tax rules must be considered. Data Analysis Australia recognised simulation as being the most appropriate method since it allowed the exact application of tax and accounting rules at the same time as considering a range of possible scenarios for financial markets.

A key component was the modelling of future returns. Obviously the only data available was from past returns, measured by standard indices that are closely linked to investment classes. The precise choice of indices was the first step, involving a detailed understanding of the business model. The eventual selection included a mix of indices covering the International, Australian and Emerging Markets.

A detailed statistical analysis followed, examining features such as average returns, variability, correlations and the precise distributions. The last feature involved the development of some proprietary methods for efficiently simulating the heavy tailed distributions encountered in finance - it is no longer good enough to assume that returns follow a normal distribution since financial markets are subject to shocks that can distort returns.

Many other features of financial returns, such as the most appropriate way of handling inflation were also considered. Even this requires some care since inflation tends to be correlated with nominal investment returns.

Data Analysis Australia also identified the most appropriate software environment for the simulations - the program Visual DSS developed by Perth company, Trueblue Systems. This is a sophisticated financial modelling system that has many advantages over spreadsheets such as Excel - it has a succinct language for clearly specifying complex models and it has simulation or risk analysis facilities built in. This meant that there were no compromises between incorporating all the accounting rules and carrying out the risk analysis.

Data Analysis Australia also assisted in the design of the Web based front-end, ensuring that the displays followed good statistical practice and were as informative as possible. The presentation of inflation effects was critical here since the models typically cover several decades.

The resulting simulations can answer questions such as "what is the probability that the client will meet their financial goals?" This goes far beyond traditional modelling that only considered the "most likely" outcome without saying how likely it really was. Clients can then see the result of changing investment portfolios so that they can choose the balance of return and risk that is right for them.

February 2004