Measuring the capacity of China property-liability. insurance industry to respond to catastrophic events

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1 Measuring the capacity of China property-liability insurance industry to respond to catastrophic events Wang, Haiyan Wang, Bo Abstract: China is a natural disaster-prone country. Catastrophic event would cause such serious damage that may exceed the underwriting capacity of a country s property-liability insurance industry on which occasion the consequences would be disastrous. Therefore, a reasonable assessment of the underwriting capacity of the China property-liability insurance industry against catastrophic events is essential. Then we could find other ways to spread the risk that the insurance companies cannot afford. In this paper, we try to use the model of Cummins etc. (00) to measure the capacity of China property-liability insurance industry to cover catastrophe losses. We need financial statement data containing annual losses and equity of China property-liability insurance companies in our designated period ( ) to estimate the parameters of the model, and then figure out the expected payout of the whole industry by the end of 007 for different sizes of given catastrophe losses as well as the industry efficiency (defined in the article of Cummins etc.). Finally, we point out some recommendations and improvements in line with the status quo of China property-liability insurance industry. Key words: catastrophe losses, response function, expected payment, industry efficiency. Introduction In May 008, a devastating earthquake with a magnitude of 7.9 struck Sichuan province, China. Approximately people died and disappeared, whilst another were injured. Although the direct economic damage has been reported at USD 4bn, the Chinese National Development and Reform Commission (NDRC), announced reconstruction investment needs of USD 50bn. [] Catastrophe risk refers to a special kind of risks with small probability of occurrence, but may result in extensive property damage and serious casualties. There is no uniform international definition for catastrophe risk. Every country usually gives the definition and division of catastrophe risk in accordance with their particular situation in different historical periods. PCS (Property Claim Services) now defines catastrophes as events that cause $5 million or more in direct insured losses to property and that affect a significant number of policyholders and insurers. [] Swiss Re divides catastrophe risk into natural and man-made disasters, and has adjusted the catastrophe losses across the world according to the inflation rate of United States and published the results since 970. China is the one of the world's most affected countries by catastrophic events. At present, China basically uses government financial compensation and civil relief to cover catastrophe losses. But Chinese government keeps expenditures within the limits of fiscal revenue, which conflicts with the randomness of catastrophe risk. What s more, China cannot resort to taxation to WANG, Haiyan. Ph.D., Associate Professor, Economics & Finance Dept., School of Economics & Management, Tongji University, Shanghai, China. wanghaiyan@tongji.edu.cn WANG, Bo. Graduate student, majored in Finance, School of Economics & Management, Tongji University, Shanghai, China. lovetwinsbo@yahoo.com.cn

2 meet the catastrophe compensation. At the same time non-governmental relief features more participants but less amounts as well as no fixed pattern. Hence it is not a stable way of compensation. It is urgent to establish an effective mechanism for catastrophe risk protection system. Taking earthquake insurance system for example, the U.S. property insurance companies provide catastrophe products to the insured, at the same time they transfer the risk through the purchase of reinsurance or insurance derivative securities. Japanese property insurance companies bear part of the earthquake risk respectively, and all the companies co-fund to establish a "Japanese Earthquake Reinsurance Company" to bear some other part of the risks. And the remaining risks are borne by the Government. [3] Currently the responsibility of earthquake insurance in China is excluded from the basic provisions of property insurance, and the examination and approval of earthquake insurance is very strict. So there is no adequate coverage of earthquake risk. This is because the earthquakes and other catastrophe risks have lower loss probability but more serious consequences, and the losses in a certain region correlated with each other strongly, which is inconsistent with the law of large numbers. So the occurrence of catastrophic events would endanger the operation of insurance companies, or even threaten the stability of the insurance industry. Therefore, it s crucial to do relevant researches on catastrophe risk. At present, there are two main catastrophe risk model: the actuarial model and the simulation model. As mentioned above, the law of large numbers is not suitable for catastrophe risk, so the traditional actuarial model fails. There has been an actuarial model, which belongs to the mathematical statistics model, specific for the study of catastrophe loss. Catastrophe simulation model is starting from the causes of disasters, using systemic and integrated approach for the analysis of the disaster-related physical, social and economic factors, and making a forecast of losses caused by their interaction. [4] At present, there are many companies devoting to the analysis of disaster model, such as Applied Insurance Research, Risk Management Solutions, etc. J.D. Cummins puts forward a more general model which results in an option-like response function for the insurance companies against catastrophe losses. Now we use the model to measure the capacity of China property-liability insurance companies to response to catastrophe losses, analyze results and put forward appropriate recommendations. The full text is structured as follows: section is for model introduction, section 3 for the data selection and related explanation, section 4 for the calculation process and the results and results analysis, and the last part gives some strategies for China insurance industry.. Model By studying the distribution characters of catastrophe losses of a country, J. D. Cummins etc. derived an option-like response function of property-liability insurance company. The data they used included the company payment, the industry losses, their correlation and the company equity value. Given the size of industry losses, the response function describes the maximum payment to the catastrophe losses that an insurance company can afford and thus the maximum payment of the whole industry. This model contains two major factors: the size of the industry equity and the degree of diversification - how effectively the insured risk is spread though the whole market. Cummins etc. defines the industry efficiency which refers to the proportion of payment after

3 relocate the insured losses between the insurance companies (through arrangements like reinsurance, guarantee fund, etc.) within given resources. In their view there are sufficient and necessary conditions in order to seek the minimum number of insolvency thus the maximum payment to the policyholders under any loss condition. The sufficient condition for capacity maximization is for all insurers to hold a net of reinsurance underwriting portfolio which is perfectly correlated with aggregate industry losses. [5] They divided the risks L i : faced by each property insurance company, into two parts: d i and c i L u (where c i is the proportion of the total pool of catastrophe losses written by insurer i, L u is the catastrophic risk faced by the whole industry), the former risk d i is special risk that can be diversified for the special risks of each company are not relevant with one another; the latter is catastrophe risk, because catastrophe losses have a strong correlation, the risk can not be fully diversified. In addition, they assumed that the two risks are not relevant and industry losses L are subject to normal distribution. Therefore the necessary conditions for capacity maximization is that all firms hold a net of the following portfolio: α i L = c i L u + k i D, where α i, c i, k i is a constant, L is the total industry losses, L u is catastrophe losses; and D is the losses that can be diversified. They believe that after the risk borne by insurance companies is fully diversified through reinsurance and company payment and industry losses are entirely relevant and the industry capacity will be enhanced. Ideally, all insurance companies act as a single company; it will pay for the 00% insured losses to the policy holders until all industry resources are exhausted. That means once losses exceed the premium plus the equity value of the whole industry, all these insurance companies would go bankrupt with no more solvency. The following is their model, and in section 4 we will use it to calculate the expected payment of each company R i L conditional on industry losses of L. Ri L = E( Li) + Qi E( Ti Qi, L) Where C = ( E( Li) + Qi) N( C i) +µ Li LN( Ci) σ Li i E( Li) + Qi µ = σli L Li L ρσ i i µ Li L = µ i + ( L µ L) σl σ = σi ( ρ ), Li L i n( C ) L i N( )= the standard normal distribution function,n( )= the standard normal density function. As can be seen from the above function, R i L is a function of the industry and company expected losses, standard deviations of losses, company net worth, and the correlation between industry and company losses. 3. Data Selection and Description We select financial statement data containing annual losses and equity of China propertyliability insurance companies from 999 to 007 from China Insurance Yearbook [6] Similar to the approach of Cummins etc., we divide all these companies into two major categories, namely, FTS (full-time series) and NFTS (non-full time series) companies, according to whether the data are complete or not. There are FTS companies and 8 NFTS companies. By the end of 007, there were a total of 4 property-liability insurance companies in China. China Insurance

4 Group, Tianping Auto Insurance Company and Generali China Insurance Company were excluded from our research because their financial data in 007 was incomplete; China Insurance Group lacked the equity value, and the other two lacked payment value. However, it does not affect our results. According to our estimation, the 39 selected companies accounted for more than 95% of the industry market both in the equity value and the payment value; they can represent China property-liability insurance industry. 4. Calculation Process, Results and Results Analysis In accordance with the articles of J.D. Cummins etc., there are two kinds of parameters: the raw (original) parameter and the detrended (to eliminate the time trend) parameter. Raw parameter is obtained directly based on the original FTS data, while detrended parameter on the residual from time trend regression, because they believe that there is a strong positive time trend of insurance company losses, and insurance companies can change its year-on-year premium in accordance with the predictable time trend, in order to eliminate its influence. Firstly, we formulate the FTS company parameter as follows: T σ i = ( Lit Li), σ = T t= ( ) ρ = T i T t= ( L it σ iσ Li)( L t T T t= L) ( Lt L) In order to obtain the estimate of detrended parameter we need to do the following regression: Lit = α 0i + αit + εit Lt = α 0 + αt + εt We use the estimated values of the residualsεit andεt to replace the corresponding parameters. Secondly, we use the estimated parameters as dependent variables and company financial data as independent variables, together with the FTS company data to estimate regression models. Then by inputting the 007 payment of the insurance company (FTS and NFTS) into the regression models, we get the fitted value as the basis of the third step. As for the FTS companies such procedure can smooth the fluctuations caused by abnormal years, and as long as we input the 007 payment value of NFTS companies we can get the corresponding parameter, allowing us to include more companies, other than limited to FTS companies. Finally, we can start to calculate the expected payment to catastrophe losses of each company by the end of 007--R i L. We set the range of L to be 0-70 billion yuan (that is, [E (L), E (L) + ΣQ i ]). The results are presented in Table. As can be seen from Table, the expected payments to catastrophe losses of each company calculated from raw parameter are increasing in L, until they reach the sum of the company losses and the equity value. After reaching the maximum point if the losses go on to increase, some insurance companies will go bankrupt because of insolvency. As catastrophe losses increase, the number of insolvent companies is growing. To the loss of 70 billion yuan, only Huatai, Pingan, BOC Insurance and China Export & Credit Insurance Corporation will not go bankrupt, which

5 shows that the catastrophic great impact on insurance industry in China. Table. Expected payment to catastrophe losses of each company by the end of 007 Table. China property-liability insurance industry efficiency to respond to catastrophe losses in 007 (efficiency=expected payment/losses)

6 As can be seen from Table, the industry efficiency calculated from detrended parameter is lower than that from raw parameters, because the elimination of the time trend leads to a larger reduction in the correlation coefficient than in the standard deviation. And the response function values are positively related to the former and negatively related to the latter. The corresponding capacity curves and efficiency curves are as follows: Capacity Efficiency raw detrended raw detrended loss(billion yuan) loss(bil. yuan) Fig.. Capacity curves Fig.. Efficiency curves Capacity calculated by raw parameter against the losses of 0 billion, 30 billion, 40 billion yuan is estimated to reach 00%, which means the losses of these three levels can get fully compensation. That is because the resources of PICC have not been exhausted, and its annually payment has a very strong correlation with the total industry losses (reaching 0.999). If the industry losses grow by 0 billion yuan, while the payment of PICC maintains a high growth rate, and so do other insurance companies, the total industry losses can be compensated by the increased payment. However, when the industry losses increases to 50 billion yuan and the expected payment of PICC reaches the ultimate resources, the increased payments of all the companies cannot make up for the increased industry losses and the efficiency of payment will be less than.the increase of industry losses leads to the larger number of insolvency with the efficiency of payment beginning to decrease. The efficiency of payment of China insurance industry in 004 against catastrophe losses (ranging from 60 billion yuan to 95 billion yuan) decreased from 97.4% to 64.7% (by detrended parameters) [7]. At the same time, from Table we can see that the industry efficiency in 007 against catastrophe losses (ranging from 0 billion yuan to 70 billion yuan) decreased from 9% to 69.5%. It shows that in 007 China industry could pay at least 69.5% of the 70-billion yuan losses, and in 004 could pay at least only 64.7% of the 95-billion yuan losses. It can be seen that in this 3-year period the capacity of China insurance industry respond to catastrophe losses has been improved to some extent. On the one hand, during this period the equity capital of China insurance industry has expanded from about 35 billion yuan to nearly 60 billion yuan. On the other hand, the number of companies increasing from 8 in 004 to 4 in 007, which to some extent diversifies the catastrophe risk the industry faces.

7 5. Conclusion Using the model of Cummins etc. we have measured the capacity of China property-liability insurance industry to respond to catastrophic events. We believe that the affordability of China property-liability insurance industry for catastrophic events still has room for improvement. In this case we propose the following three recommendations: () Establish a comprehensive catastrophe insurance system and seek a variety of ways to diversify catastrophe risk in order to pay for catastrophe losses without bad effect on the operation of Chinese insurance industry. For example, establishing the catastrophe security system that calls in government's participation can spread the catastrophe risk throughout the country; the implementation of catastrophe risk securitization (the most common way is the issuance of catastrophe bonds) can raise venture capital from the capital market. () Accelerate the development of China property-liability insurance companies. It is necessary to increase the size of its premium income and increase the size of its equity capital, aiming at improving the capacity of China insurance industry to respond to catastrophe events as well as gradually opening up the underwriting business against catastrophe risk such as earthquake risk. (3) Improve China reinsurance market. The maturity of reinsurance market decides the risk tolerance ability of China insurance market. The more perfect is the insurance market, the more efficient it can spread risks throughout the whole industry, and the capacity of China insurance industry against catastrophe losses will be enhanced. References [] Sigma. Natural catastrophes and man-made disasters in 008: North America and Asia suffer heavy losses, Swiss Reinsurance Company Ltd, 009. [] Numbers.html. [3] Li, Jun. On the establishment and improvement of catastrophe insurance system in China, Southwest University of Finance and Economics, 006, p.37-38,. [4] Wang, Bo. Study on Risk Management Model of Property Insurance Company in China - Based on Enterprise Risk Management Theory, Hehai University, 007, p.98. [5] Cummins, J. David. Doherty, Neil. Lo, Anita. Can insurers pay for the ''big one''? Measuring the capacity of the insurance market to respond to catastrophic losses, Journal of Banking & Finance, 6 (), 00, p [6] China Insurance Regulatory Commission. Yearbook of China s Insurance, , China Insurance Yearbook. [7] YAO, Qinghai. Research on compensation mechanism for catastrophe loss with discussion on the role of government and market in catastrophe risk management. Beijing: China Financial & Economic Publishing House, 007, p