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There are several modem portfolio shortcomings that we should address in relevance to our framework, represented in these MPT assumptions:[1]

• Asset returns are (jointly) normally distributed random variables.

• Correlations between assets are fixed and constant forever.

• All investors have access to the same information at the same time.

• All securities can be divided into parcels of any size.

• Risk and volatility of an asset are known in advance and are constant.

To address the first point, we have already discussed our use of nonnormal distributions and feel the framework is robust enough to handle any variation of distributions that a modeler feels is appropriate. In postmodern portfolio management, the use of normal distributions has also been relaxed for similar reasons, so this is not as much of a concern as originally stated.

Correlations are clearly not constant or fixed, and once more, they are hard to measure without good historical data. The modeler will often make assumptions around correlations and use copulas to simulate different relationships between correlations at different points of a distribution. It is clear that, again, modern computing power has allowed us to use correlations in a much different way than in the past. Unfortunately, the flexibility is not always a good thing. As correlations are often a modeler's assumption, the use and selection of them should be highly scrutinized.

In insurance, the market is very far from what one would call efficient. On stock exchanges there are clearinghouses and information services to provide an up-to-date information exchange. And even then, the market is not truly efficient. In insurance, pricing different contracts is dealt serious information asymmetry and is fraught with poor information, as the data and pricing start with an actuary in a corporate insurance company, then are translated by an underwriter, and then are ignored by sales professionals (only slight exaggerations involved). This lack of an efficient market is what makes our risk framework so critical. Without it, the insurance buyer has little chance of getting the best deal.

Our framework does have an issue with the ability to fractionalize options and to get the insurance market to respond to all potential mathematical pricing options. This can happen for a variety of reasons: internal restrictions, lack of proper information, risk limits, reinsurance requirements, and so on. The framework can, however, lead insurance markets to more optimal insurance contracts. So even if an option is not technically available, the closest option available in the marketplace can be substituted in similar fashion.

In insurance, especially for large corporations, the party who controls the information can hold a competitive advantage. Both parties to a transaction (corporation and insurance company) have pieces of the puzzle in determining the true risk exposure for the corporation. The insurance company has a significantly larger database of similar risks, and the corporation has very specific data to its risk profile and a much better understanding of how its risk profile is changing. All of this means that the underlying risk is clearly not constant and is difficult to predict. Thankfully, to optimize a risk portfolio one does not require perfect information, only relative accuracy and reasonable assumptions on information that is not available.

In our framework, we are not fully constrained by the limitation of modern portfolio theory, as we are not developing a theory, but rather a practical modeling application. We also have use of greater computer power than ever before, which allows the relaxation of many of the constraints presented earlier in this chapter. We believe that we have addressed the major concerns of modern portfolio theory and its application to insurance, but we will leave that conclusion fully up to the reader.

  • [1] Miccolis and Goodman, "Next Generation Investment Risk Management," 2012.
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