Analytics Title Headline Matter When Pricing Title Subheadline Catastrophe Reinsurance By Author Names A Case Study of Towers Watson s Catastrophe Pricing Analytics Ut lacitis unt, sam ut volupta doluptaqui ut haruntoresti vendae consedipsae By Joseph Qiu and Ming Li volorit optaspi ciatum serovit, am, te ant ommolup tatene nis velitam, Cedants occum que face voluptassi a challenge res to reperci control isitis risk modit transfer erum costs rentist, in a volatile nihilliam, saeceri catastrophe buscimus, erioratur reinsurance militatendit market but volore can labo. use solid pricing analytics and exposure management as powerful tools for price negotiation. Catastrophe risk has always been a key element of insurance companies risk management, especially for the property sector. The conservative investment and reserving strategy used by most property insurers makes catastrophe the de facto risk that can potentially jeopardize their solvency. Historically, reinsurance is the major source of protection from catastrophes, but its pricing has not been transparent or formulized by actuarial method. Modeling and analytics are increasingly important in today s reinsurance market, and pricing analytics can assist cedants. This article uses a case study to illustrate how catastrophe-pricing analytics, such as a series developed by Towers Watson, can help a hypothetical cedant manage its reinsurance programs. Robust pricing analytics for catastrophe reinsurance should have the following properties: Pricing consistency Ability to factor in both modeled and non-modeled losses Flexibility to work with multiple models Capability to model complex reinsurance terms First, pricing consistency is important because it builds credibility in the market, and lets cedants foresee prices and use exposure management to influence reinsurance cost. Second, catastrophe reinsurance pricing is complex because many Pricing consistency is important because it builds credibility in the market, and lets cedants foresee prices and use exposure management to influence reinsurance cost. modeling and non-modeling factors can impact the final prices. Solid pricing analytics must consider both for price formation. Third, a multi-model approach has been widely used to reduce model risk, particularly since Risk Management Solutions (RMS), a catastrophe risk modeling firm, released its v11.0 U.S. hurricane model, which significantly increased RMS-modeled loss estimates. This market trend requires the pricing analytics to be able to work with results of different models. Finally, a reinsurance contract may have complex terms, such as a territory exclusion and a trigger specification. A proper pricing method must have the capability to model these terms accurately. A Hypothetical Cedant Suppose a U.S. property insurance company is reviewing its catastrophe reinsurance strategy for the upcoming renewal. Recently, this insurer expanded the operation by acquiring a regional carrier and is now concerned that the acquisition may drive up the reinsurance cost. The catastrophe reinsurance market has also hardened by 5% since the previous renewal due to the recent heavy catastrophe losses experienced by the industry, another factor that will lift the price. To simplify this example, we will rely on the loss output from one model in the current exercise, but the same techniques can be applied to other models as well. To assist the cedant in analyzing all options, we aim to answer a few key questions: What price does the cedant expect to pay for the original structure in the next renewal? How much of the price change comes from an exposure increase, and how much is due to the hardening market? How do you price and evaluate catastrophe reinsurance structures? 8 towerswatson.com
Figure 1. Hypothetical cedant s gross loss before catastrophe reinsurance Occurrence exceedance probability (RMS v11.0) All perils including near-term hurricane with storm surge Layer Simulation The first step is to run the cedant s exposure data, from both the previous year and the current year, through a catastrophe model. Figure 1 illustrates the probable maximum losses (PMLs) for various return periods. As we can see, the cedant s PMLs would have declined slightly if the acquired book was not taken. However, the acquisition led to a significant PML increase. For example, one-in-100-year PML grew to $372 million from $301 million, a 24% increase, due to the acquisition. Although PML is a very important metric for insurers to manage catastrophe risk, one cannot infer reinsurance cost change solely from such information. Our approach looks at a catastrophe reinsurance transaction from the perspective of a reinsurer s risk-adjusted return. A reinsurer s return is used as a hinge to connect different transactions. Fundamentally, reinsurers write business to earn a return for their shareholders. Underwriters need to not only maintain a profitable portfolio but also strive to achieve target margin on every transaction. Pricing analytics, such as the one we developed, take advantage of this reinsurance underwriting philosophy. Return period (years) Previous year without acquired company Current year without acquired company 10 61.6 60.9 74.1 20 113.6 111.9 134.0 50 209.8 205.1 249.8 100 312.6 301.1 372.4 250 481.6 458.3 564.0 500 606.4 575.5 728.6 1,000 726.5 691.9 947.6 pricing. While expected layer loss, the most important factor affecting reinsurance price, is reflected by the expected underwriting profit, tail loss is a crucial consideration due to the nature of catastrophe, and it is explicitly considered in the capital requirement. The ability to calculate a reinsurer s risk-adjusted return equips us with a tool to price the renewal layers. Theoretically, the best information to use for inferring a renewal price is the previous renewal s data and price, assuming the market uses similar methods to price the layers in both years. If a reinsurer requires a level of return that is the same as the return achieved in the previous renewal, it means Current year with acquired company We use a ratio to define a reinsurer s risk-adjusted return: expected underwriting profit divided by risk-adjusted capital required to support the deal. The challenge of calculating expected underwriting profit is to model all the reinsurance terms explicitly, such as annual aggregate deductible, second-event trigger and non-claim bonus. For risk-adjusted capital, the modeled tail loss of a reinsurance layer is a reasonable proxy of the amount of capital that needs to be set aside for underwriting the layer. However, further adjustment must be made due to other elements such as reinstatement terms and the correlation with the overall catastrophe reinsurance market. A key concept in this process is that we consolidate the multidimensional modeling results into a reinsurer s return, a one-dimensional metric. This is a practical method for catastrophe reinsurance Emphasis 2012/3 9
Figure 2. Catastrophe reinsurance pricing Layer simulation tool based on RMS v11.0 modeling All layers have one-at-100% reinstatement Joseph Qiu Specializes in reinsurance analytics and catastrophe modeling. Towers Watson, Philadelphia Previous year Current year $30 x $20 $50 x $50 $100 x $100 $50 x $200 Expected layer loss 5.8 4.6 3.9 0.9 Standard deviation 12.2 14.1 18.2 6.7 Expected underwriting profit 4.2 3.9 4.9 1.8 Capital requirement 42.4 51.2 90.6 45.9 Price (rate on line) 28.3 % 15.7% 8.5% 5.4% Reinsurer s risk-adjusted return 9.8% 7.6% 5.4% 3.9% Expected layer loss 7.1 5.6 4.9 1.2 Standard deviation 13.4 15.6 20.2 7.5 Expected underwriting profit 4.1 4.4 4.9 1.8 Capital requirement 41.6 58.0 91.6 45.7 Price (rate on line) 30.6% 18.1% 9.4% 5.8% Reinsurer s risk-adjusted return 9.8% 7.6% 5.4% 3.9% Rate on line = reinsurance premium / layer limit Reinsurer s risk-adjusted return = expected underwriting profit / capital requirement Ming Li Specializes in reinsurance analytics and catastrophe modeling. Towers Watson, Philadelphia that we know the target return and can back-solve for the price that will realize this target return. Figure 2 summarizes this price formation process. In Figure 2, current renewal prices were adjusted so that the reinsurer s returns become the same as the returns from the previous year. Using a $50 million excess $50 million layer as an example, the expected layer loss changed from $4.6 million to $5.6 million, a 21% increase, but the rate on line changed from 15.7% to 18.1%, only a 16% increase. In this instance, other factors are influencing the reinsurance price, especially the layer s tail loss. This analytical result can be used to support the argument that the reinsurance price should not increase as much as the expected layer loss. It is also worth noting that these are purely technical prices based solely on modeling results. The technical prices should be inflated by 5% to reflect a hardening market. This calculation also identifies Figure 3. Catastrophe reinsurance structure comparison Based on current renewal data including acquired book RMS v11.0 modeling Original structure First Second Third Reinsurance premium 30.5 31.9 32.4 33.7 Expected recovery 18.8 19.3 19.8 20.3 Net reinsurance expense 15.2 16.0 16.2 17.0 Tail-loss reduction 224.7 253.4 229.5 258.1 Cost of capital 6.8% 6.3% 7.1% 6.6% First : Add $30 million x $250 million to the top so that probability of program exhaustion is similar to that from the previous year. Second : Add $10 million x $10 million x $10 million to provide a buffer for small events and to smooth earnings (but its effect on tail-loss reduction is limited). Third : Combine the first and second s. the price change attributable to exposure and market condition. To assist the cedant in evaluating reinsurance options, we design structures and price them using the analytics described above. It should be noted that we cannot use the returns of the existing layers on these new layers because return must reflect intrinsic risk. Our experience is that the higher the loss on line, the higher the reinsurer s return requirements, reflecting the reinsurer s relative reluctance to expose too much of its capital at more frequent return periods. Once the prices of those structures are derived, a consistent approach is needed to examine the trade-off between reinsurance expense and risk reduction. For this purpose, we use the cedant s tail losses before and after the reinsurance layers to calculate capital savings. We then calculate net reinsurance expense and divide that by capital savings. This ratio is considered cost of capital and is summarized in Figure 3. The first structure has an additional top layer that effectively reduces tail loss. Together with the relatively low price of this top layer, the first structure achieves the lowest cost of capital. The second structure adds a bottom layer and features a $10 million annual aggregate deductible to achieve a reasonable price. It does not reduce tail loss as effectively as the first structure and therefore has a higher cost of capital. However, it is a good option if the cedant s goal is to control profit volatility. The third structure combines the first two and has a midrange cost of capital. The optimal structure depends on the cedant s business goal and risk appetite. 10 towerswatson.com
Figure 4. Synthetic reinsurer PMLs Occurrence exceedance probability (RMS v11.0) Based on global exposures Synthetic Reinsurer So far, the catastrophe reinsurance transaction has been evaluated on a stand-alone basis, and the reinsurer s existing portfolio has not come into play. In practice, reinsurers usually price a transaction based on the marginal impact on their portfolios. Portfolio theory and diversification are the rationales behind this market practice. So reinsurers often quote differently on the same layer because their existing portfolios reflect different marginal impacts and different capital allocations. We captured this concept by developing a synthetic reinsurer tool to mimic the pricing process of reinsurers. It possesses a portfolio that is representative of average reinsurers. The PMLs of the two synthetic reinsurers we created are detailed in Figure 4. To quantify the marginal impact, we calculate a synthetic reinsurer s tail losses before and after the deal is added to its portfolio. The increase in tail loss is a proxy of the capital allocated to this deal. We divide the expected underwriting profit by the allocated capital to calculate the synthetic reinsurer s risk-adjusted return. Similar to the layer simulation analysis, we use the synthetic reinsurer s return from the previous year to infer the price for the current year. Figure 5 illustrates how the synthetic reinsurer analysis is conducted. The renewal prices were adjusted so that the synthetic reinsurer s returns would be equal to the previous year s returns. Because of diversification, the marginal capital requirement from the synthetic reinsurer approach is always lower than the standalone capital requirement from the layer simulation, Return period (years) and different synthetic reinsurers generate different capital charges. Initially, these discrepancies may seem problematic since we cannot identify the most appropriate capital charge. But since the year-to-year comparison underlies the pricing, an approach will be valid as long as it is applied to both years. Reinsurer s Return First synthetic reinsurer 10 58.1 79.0 20 85.6 118.7 50 125.7 175.0 100 151.6 228.5 250 191.4 314.4 500 226.2 407.6 1,000 264.6 549.1 The capital requirement and the reinsurer s return are two key elements to price catastrophe reinsurance. The capital requirement is primarily driven by the tail loss calculated through catastrophe models, but the reinsurer s return can be more complicated. Many factors beyond the loss distribution produced by probabilistic modeling can affect the required rate of return, and sometimes their impact can be significant. To thoroughly analyze pricing accuracy, our analytics further adjust the required rate of return according to a cedant s exposure profile, deterministic results, data quality, loss experience and other factors. It is not appropriate to build a mathematical model to determine the impact of these factors because their ability to change prices depends on subjective Second synthetic reinsurer The capital requirement and the reinsurer s return are two key elements to price catastrophe reinsurance. Figure 5. Catastrophe reinsurance pricing Synthetic reinsurer tool based on RMS v11.0 modeling All layers have one-at-100% reinstatement Previous year Current year $30 x $20 $50 x $50 $100 x $100 $50 x $200 Expected underwriting profit 4.2 3.9 4.9 1.8 Marginal capital requirement 29.6 38.8 70.8 31.9 Price (rate on line) 28.3% 15.7% 8.5% 5.4% Reinsurer s risk-adjusted return 14.1% 10.0% 6.9% 5.6% Expected underwriting profit 4.5 4.8 5.5 2.1 Marginal capital requirement 32.2 48.2 80.4 36.9 Price (rate on line) 31.9% 18.9% 10.0% 6.4% Reinsurer s risk-adjusted return 14.1% 10.0% 6.9% 5.6% Emphasis 2012/3 11
Figure 6. Additional factors affecting required rate of return Based on year-to-year comparison Factors Correlation with industry exposures Exposure concentration (Herfindahl Index) Exposures in high-risk counties Lloyd s RDS Exposure data quality Treaty recovery experience Poor data quality reduces a reinsurer s confidence in modeling results and increases the possibility of unexpected losses. Year-to-year change Increased by 7% due to new exposures introduced by the acquired book Decreased by 6% due to exposures in new counties No significant increase U.S. Northeast windstorm loss increased from $0 to $86 million due to the new exposures in the Northeast introduced by the acquired book Unknown occupancy and number of stories increased by about 10% $30 million x $20 million layer triggered in the previous year Loading to reinsurer s return Not sufficient to move reinsurance price Not sufficient to move reinsurance price None +2.5% penalty on all layers +2% penalty on all layers +5% penalty only on the triggered layer judgment about the real market. So we use a penalty factor approach. Outliers from a year-to-year comparison are identified, and then, for each of the outliers, a penalty factor is applied to the required rate of return. The underlying assumption is that the factors impacting the prices in both years have already been accounted for in the previous year s prices and do not need to be factored in again. Only the outliers from the year-to-year comparison matter. For the exposure profile, we first look at the correlation between the cedant s exposures and industry exposures. A significant increase in correlation on a year-to-year basis means that the deal brings in less diversification and will be priced higher. Second, high exposure concentration increases the chance that a single event will affect a large portion of the portfolio. This will also increase the reinsurance price. There are various approaches available to evaluate exposure concentration, ranging from a simple side-by-side comparison of exposure by region to the more complex method of using the Herfindahl Index, a measure of size compared with peers. Additionally, an exposure increase in high-risk areas also raises a red flag for reinsurers because it not only means higher catastrophe risk but also reflects the cedant s underwriting trend. To reflect this, we have compiled a list of high-risk counties and apply a penalty factor when the cedant s exposures increase significantly in those counties. Compared with a probabilistic model that simulates tens of thousands of events, a deterministic approach focuses on losses from a few events and is often used to supplement probabilistic results. A deterministic approach is particularly meaningful for the prices quoted by Lloyd s syndicates because the syndicates risk management will be evaluated through Lloyd s Realistic Disaster Scenarios (RDS). So we apply a penalty factor when we observe a significant increase in RDS losses. Poor data quality reduces a reinsurer s confidence in modeling results and increases the possibility of unexpected losses. It also suggests a cedant s lack of effort in managing catastrophe risk. Data quality is a top concern for reinsurers and rating agencies, and is a meaningful pricing factor that is increasingly attracting attention. Additionally, the cedant s loss history in recent years will almost definitely affect renewal prices. So we apply penalty factors for poor data quality and treaty triggering. Figure 6 summarizes our penalty factor approach used on the hypothetical cedant. The penalty factors should be used to adjust a reinsurer s target returns. Renewal prices then need to be revised accordingly. The example here is for illustrative purposes. In practice, there are other factors that also influence catastrophe reinsurance prices that should be examined. Analytics Matter The volatility of the catastrophe reinsurance market makes it challenging for cedants to control risk transfer cost. Solid pricing analytics are a powerful tool for price negotiation. At the same time, knowing what makes a difference will empower cedants to influence reinsurance price through exposure management. Presently, catastrophe reinsurance pricing is increasingly driven by catastrophe modeling results. This is illustrated by the technical pricing benchmarks derived from our layer simulation and synthetic reinsurer tools. Even so, non-modeling factors still may have a significant impact on short-term prices. This is demonstrated in the reinsurer s return section. Cedants need thorough analytics to understand their positions in the market and to achieve the correct reinsurance prices. For comments or questions, call or e-mail Joseph Qiu at +1 215 246 1767, joseph.qiu@towerswatson.com; or Ming Li at +1 215 246 1743, ming.li@towerswatson.com. 12 towerswatson.com