The Challenge of Portfolio Optimization for Insurance Companies

Portfolio optimization is a vital practice to the business of insurance but the term itself can be used with slightly different nuances and emphases to describe varying processes used. In essence portfolio optimization can be simply defined as the use of tools that enable the selection of a set of policies to maximize the desirable metrics of performance for an insurer’s book of business, while simultaneously constraining undesirable metrics.

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The challenge of portfolio optimization

Insurers are constantly on the lookout for opportunities to grow their business, expand their revenues and improve their profitability. However, for every line of business, and for the enterprise as a whole, portfolio growth can lead to an increased exposure to risk. The challenge of portfolio optimization is to maximize profitability by delivering the optimal risk/reward relationship which balances loss exposure and potential profit margin.

Liability streams and solvency

The liability stream of insurance companies will often extend several years into the future because it represents future payouts on long-term products like life insurance. These future liability streams are usually termed stochastic, as it cannot be confidently determined exactly when they will need to be met. In terms of life insurance the variants will include a customer’s length of life and other factors such as cancellation rights.

The stochastic nature of these streams presents a very real challenge in determining aportfolio of bonds and assets whose cash flowscan replicate and mirror these liabilities. With an increasing demand from regulators that firms can robustly demonstrate their abilities to achieve this solvency, risk management firms like SunGard APT are bringing new sophisticated management and optimization solutions to meet the increasingly complex challenges faced by insurers.

At a simple level, one way to demonstrate solvency is to determine a fair market value of liabilities by building a replicating portfolio of default-free bonds. In mathematical terms this is the determination of the expected present value of liabilities using the zero-couponyield curve.

Stochastic modelling

The balancing of risk and return is increasingly complex forinsurers with unmanaged catastrophe accumulations who can experience rating pressure and resultant high reinsurance costs. This means that whilst the evaluation of individualrisks is undoubtedly important, getting the mix of risks right is absolutely critical.

The stochastic model is an approach that can be used to determine whether the addition of a newrisk is a good fit for the current portfolio. This method has been used fruitfully for handling manyeconomic and financial problems. It allows decisions to be taken based on an objectiveperformance criterion but in a situation of uncertainty.

A game of chess

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The range of possibilities and effects of the addition of new risks from actions offering new potential gains can become mathematically baffling. It is akin to the legend of the invention of chess. The king asked the inventor what he would like as a reward for such a wonderful game. The reply was ‘one grain of wheat for the first square of the chessboard, twice as much for the second, double again for the next, and so on.’ This seemingly trivial reward soon stacked up in reality and the king opted to chop off the inventor’s head instead.

Insurers do not have this luxury in determining how to handle the mathematically complex interrelationships of risks and returns. It is to mathematical science rather than brute violence that they must turn.

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