# The limits of quantitative

models for insurance

investments

##### Chapter 1

### Regulatory solvency regimes determine the amount of capital that insurance companies must hold to support the risks within their asset portfolios. In recent years, these regulations have become increasingly sophisticated, detailed and risk-sensitive.

#### The evolution of solvency regimes

A purely quantitative approach cannot be relied on to deliver a genuinely optimal investment solution for insurers.

- 2006: The Swiss Solvency Test
- 2013: Australia’s LAGIC solvency capital approach
- 2016: Solvency II in the European Union (EU)
- 2016: Bermudan Solvency Capital Requirement; enhanced in 2019

Today, a number of Asian countries are developing risk-sensitive, probabilistic approaches to solvency risk capital. A similar process is underway in Canada.

The International Association of Insurance Supervisors is consulting on an International Capital Standard in a bid to establish common ground. This would aim to deliver a detailed, risk-sensitive capital assessment method for all insurers.

All of these assessments – as prescribed by regulators – are formulaic, using calculations typically based on historical data.

Insurance investors can incorporate these assessments into algorithmic optimisation methods. These methods calculate the efficient frontier from a risk capital perspective – the highest achievable expected return for each level of a portfolio’s incurred capital charge.

This is particularly effective for fixed-income portfolio construction, where measures of risk, expected return and capital requirements of individual securities are straightforward to calculate.

#### Quantitative models: positives and pitfalls

These quantitative approaches appeal to both asset owners and asset managers. For insurance companies, they offer the ability to optimise portfolios to meet their specific needs. For asset managers, these models allow them to demonstrate the value of their proposed investment solution.

However, this regulatory capital-optimisation approach may not deliver a genuinely optimal investment solution for insurers. Its focus on maximising or minimising capital-driven metrics places a heavy reliance on regulatory capital calculations.

While the capital formula may be more sophisticated than before, it cannot provide a perfect, or even a reasonable, representation of all forms of risk. It seeks out solutions that work, for now, according to the capital formula. However, these solutions are not necessarily attractive from an investment perspective.

In addition, this quantitative approach does not provide scope for the asset manager to add value using fundamental analysis.

Active managers construct portfolios that reflect their active investment views, as agreed with clients in investment mandates. They use forward-looking judgements alongside analysis of historical data. Yet how can they add value when the investment process is an algorithmic function of the regulatory capital formula?

In this paper, we seek to answer this question. We illustrate how capital-sensitive insurance companies can apply active asset management — even ones that operate under a regulatory solvency capital regime that is sophisticated, detailed and risk-sensitive.

A purely quantitative approach cannot be relied on to deliver a genuinely optimal investment solution for insurers.