Princeton Team Develops TIRM Risk Methodology

METHODS & REGULATIONS

Princeton University professor John Mulvey is working with financial market practitioners to design a long-term asset/liability and risk management system that uses parallel processing to analyse companies' strategic plans and risk/reward profiles.

Mulvey, who specialises in statistics and operations research, has developed his theories into a what he has named the Total Integrated Risk Management (TIRM) methodology.

TIRM is based on research into asset/liability management methods and optimisation techniques conducted by Mulvey along with his Princeton graduate students.

He has also worked as an independent industry consultant with companies such as Towers Perrin, the international benefits and pension consultancy.

TIRM at Unilever

One indirect TIRM adopter is Unilever, the $55 billion manufacturing and consumer products multinational. Unilever is using Towers Perrin's TIRM-based software for long-term financial planning and analysis of its European pension funds.

TIRM can also quantify and dynamically manage the overall make-up and structure of an organisation's assets and liabilities, via interfaces to lower level deal pricing and risk management systems, says Mulvey.

The Towers Perrin system links econometric variables to an organisation's assets and liabilities.

This is accomplished by models that describe the behaviour of component asset and liability portfolios over a range of simulated economic paths and historical market scenarios.

The Towers Perrin system thus links econometric modelling of variables such as interest rates, inflation and currency exchange rates to theories on the behaviour of an organisation's portfolios of assets and liabilities.

Alternative asset/liability strategies are evaluated by simulating them over the various scenarios, says Mulvey.

Monte Carlo method

TIRM employs a Monte Carlo simulation-based process to generate its economic and asset/liability scenarios.

These are used in building a probability-weighted distribution for these variables, yielding dynamic risk/return profiles and information such as value-at-risk, or the likelihood of a specified amount of income over a period.

The system then attempts to match these patterns with actual historical distributions. "Each scenario is a realisation of a set of stochastic differential equations," says Mulvey.

"We sample from a hierarchical structure of interrelated differential equations, and apply them to datasets of fundamental macroeconomic variables to generate a set of possible scenarios. These are then calibrated against actual historical outcomes," he adds.

Each country has its own economic history for the key macroeconomic variables used in TIRM, such as the term structure of spot and forward interest rates, currency exchange rates, dividend returns and real estate prices.

Thus each set of simulated outcomes has to be calibrated separately for each country where the organisation concerned invests its assets or sources its liabilities, says Mulvey.

"The structure of the equations is the same [across countries], but their coefficients depend on each countries' historical experience," he explains.

A company's strategic objectives can then be incorporated within the system by including a set of heuristics, or decision rules, wealth optimisation models, or some combination of the two.

These are then used as inputs in defining the objective functions and constraints of non-linear optimisation models that result in the identification of optimal combinations of assets and liabilities.

"Given the scenarios and a decision process for investments and borrowings, you can get a view of the future for each of the scenarios. These can the be used to develop best case, worst case and average performance benchmarks for each particular instance," explains Mulvey.

Incorporating the large number of time periods and variables involved in such long-term, strategic asset/liability allocation decision models results in scenario tree lattices that reach massive proportions, warns Mulvey.

But adding heuristic decision rules into the system's scenario tree analysis streamlines the optimisation process and speeds up calculation times, he says.

Non-convex effects

There are side effects to adding such decision rules to the system, however. "By adding decision rules you obtain a smaller problem - but you also end up with optimisation problems that are non-convex, meaning their distributions have multiple peaks," Mulvey adds.

Since many optimisation programs stop after identifying the first peak in the distribution they come across, specialised optimisation algorithms are necessary to ensure that such a peak is a global and not a local optimal point, he adds.

The optimisation algorithm included in Microsoft's Excel spreadsheet, for instance, is not able to optimise non-convex distributions, says Mulvey.

Convex optimisation solvers such as IBM's OSL and Cplex from Nevada-based Cplex Optimisation may be adapted for use in tackling such problems.

They address large scale, non-convex distributions by starting their search at various points within the distribution space, eventually converging on global optimal points.

Searching out starting points within the distribution space is a thorny problem in itself, according to Mulvey.

The professor and his students have developed "specialised algebraic structures within an optimisation context" into TIRM that enable such previously unmanageable problems to be solved using currently available parallel processing technology.

Working with software engineers at Silicon Graphics' California headquarters, the researchers have implemented TIRM on Unix-based symmetric multiprocessing technology.

The research team used Silicon Graphics' top-of-the-line Power Challenge parallel processing machines to test and validate TIRM's functionality, according to Mulvey.

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