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By BEN BROOKES, director, RMS RiskMarkets

The catastrophe bond market has seen the development of multiple views of risk, with the three main catastrophe modeling companies--Risk Management Solutions Inc., AIR Worldwide Corp. and EQECAT Inc.--now providing an analysis of each catastrophe bond in the market.

Figure 1 shows the expected loss as published by the modeling agent on each catastrophe bond currently in the market, along with the RMS reanalysis of the deal based on the information contained in the offering circular.

Three things are apparent. First, as expected there is a clear trending for many deals along a 1:1 ratio: i.e., a significant number of points have similar expected loss as re-modeled by RMS as they do in the original risk analysis. Second, there is a spread around this, with an upward bias for RMS results--that is, RMS estimates are generally higher. Third, there are a number of cases for which the RMS estimate differs significantly from the original analysis, characterized by the outliers.

Let us then consider the reasons for these effects, as it gets to the heart of an important question in catastrophe modeling: What is the cause of such differences, and how can they be explained?

WHEN TWO PLUS TWO DOESN'T EQUAL FOUR

It is perhaps counterintuitive that there are a number of points in Figure 1 that appear to show strong agreement--but not perfect correlation. The ones with the closest agreements are the transactions for which RMS was the original modeling agent, providing an assessment of the expected loss associated with the deal.

The reason that the points do not exactly match often causes a healthy debate in the catastrophe bond market. The information contained in the offering circular for a CAT bond is not a complete statement of the information used by the modeling agent in order to conduct its analysis.

For example, during a risk analysis for a new indemnity CAT bond, RMS will receive the full detailed portfolio of the reinsurer--much like that provided as part of a reinsurance submission. RMS will then analyze this portfolio using detailed loss models to generate the most accurate view of the expected loss possible.

However, when it comes to reanalyzing the deal after close, RMS must rely only on the information contained in the offering circular, because the detailed underlying portfolio is not generally part of the disclosure for the deal. As a consequence, the data used to reanalyze the bond is coarser, and thereby results in slightly different results for the expected loss.

DIFFERENCES IN OPINION

The second category of modeling differences is driven by scientific opinion as to the nature of the underlying risk. This is seen as a "healthy" disagreement. Because clearly there are many unknowns in the catastrophe modeling process, it is expected that different models produce different estimates, with differences driven by many potential sources.

Take the case of a repeat of the Great San Francisco Earthquake of 1906. We would expect many reasons for different modeled industry losses for this event, such as:

-- Data. Different approaches will yield alternative views of the amount of exposure in the San Francisco region. A broad range of assumptions are required to estimate industry exposures, from total values, distributions by line of business, to insurance take-up rates.

-- Models. Clearly alternative approaches to model development will result in differing views of risk. The relationships between hazard experienced and loss caused are particular to an individual model and may be a significant driver of differences between models.

-- Science. Even the precise re-enactment of the event may be different between modeling firms. For example, in many parts of the world, there is no single authority on the ground motions resulting from past earthquakes, particularly those occurring over a century ago. So each modeling firm may use a different view of the historical record. As a result of differing views on ground-motion attenuation and original event parameters such as location, magnitude and depth, there will inevitably be variance in the views as to the hazard associated with any historical catastrophe.

These differences in opinion are further compounded by the effects discussed above relating to the coarseness of data available for analysis. Because reanalysis often depends on the aggregated data given in the offering circular, any data assumptions are usually made on a conservative basis--that is, the most helpful approach is to choose assumptions such that the modeled expected loss is higher. This leads to the additional upward bias in expected loss comparisons mentioned previously.

DIFFERENCES IN INTERPRETATION

The third category of modeling difference, which often leads to the greatest outliers, is a variation in structural interpretation.

A recent example of this revolves around the peril of European windstorm. In this case, there have historically been subtle differences in the way modeling firms have designed parametric triggers, which are based on specific characteristics of an event.

RMS transactions use an interpolation procedure that calculates wind speeds across the impacted area of Europe, taking into account the "roughness" of the surface of the terrain, which can moderate wind speeds. In contrast, non-RMS triggers work off wind speeds measured directly at wind stations.

An important effect of the RMS interpolation is to remove outlier data measurements from the wind field, which would remain in the station-based trigger. Interpolation reduces the volatility risk, calculating a wind speed for each required location on the basis of multiple readings in the surrounding area and producing wind measurements that are more representative of the hazard over the event footprint.

While this difference in structure appears to be small, it can have significant implications for the modeling of a CAT bond. By incorrectly assuming that the two trigger forms are comparable, one could end up with incorrect estimates of expected loss by as much as three or four times. (See Figure 2.)

This simple example demonstrates the importance of clean, uncomplicated catastrophe bond structures, with full disclosure where possible.

CLOSING THE DIVIDE

Because differences in modeling opinions are somewhat inevitable, what can be done to further elucidate them? Given there are a multitude of potential sources of modeling differences, the scientific approach would be to conduct controlled experiments for the industry asking the following questions:

-- Vulnerability curves: Taking standard exposure data and a standard hazard footprint, how do losses vary by model?

-- Exposure data: How do losses vary by model when we consider standard exposure versus actual views of industry exposure?

Such controlled experiments could even be performed in the public domain. Similar comparisons have been drawn in the reinsurance markets, in particular at the modeling symposium put on every year by the Reinsurance Association of America.

A final and important step will be greater disclosure in the offering materials for bond transactions, providing detailed exposure data and leveling the playing field between the reinsurance markets and the capital markets as the strong push for convergence continues.

BUT HOW MUCH HEADROOM IS THERE?

From the investment standpoint, and in the current reinsurance market and financial climate, there is significant comfort to be drawn from a simple analysis of required returns.

Let us imagine for a moment an investment portfolio with a maximum of 2 percent invested in CAT bonds of any one peril region--allowing a total catastrophe bond allocation of perhaps 10 percent, across all peril regions.

Now, let's assume the original portfolio has a risk premium (the expected rate of return above the risk free rate) of 6 percent, and a standard deviation (the variability of returns) of 3 percent

We can then calculate the required return on a new single-peril CAT bond investment, in order that the particular benchmark for the portfolio is maintained. The Sharpe ratio is a measure of risk-adjusted returns, or returns per unit of risk. In this example, let's assume the portfolio's Sharpe ratio of two must be maintained.

Figure 3 shows the results: For a 1 percent annual expected loss, the required return is just above 3.5 percent over LIBOR. This somewhat intriguing result is due to the inherent diversification benefit achieved through the small allocation to CAT risk. Also shown on Figure 3 is the spread paid (greater than 10 percent above LIBOR) on a recent single-peril catastrophe bond, with an expected loss of a little over 1 percent.

This difference between required return and actual return is vast and leads to an interesting observation: The modeling on this particular deal could be different by a factor of four, and it would still be a transaction worth investing in.

September 1, 2009

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