A Statistical Distribution for the Solvency Ratio of Indian Non-life Insurers
Authors: Sinha R. K. , Nizamuddin M. M. , Hassan Ameer 
Published: June 2017

The Indian Insurance Industry, which was privatized in the year 1999, has witnessed steep growth in terms of its business statistics, such as number of insurance companies, number of policies issued, aggregate premium underwritten, etc. However, many of the insurers are still struggling to break even after a decade of their business operations. The insurance companies are different from other companies, which take longer time to stabilize. The progress of stabilization of the new companies can be measured in many ways. One way is to analyze the level of volatility in the various financial ratios, in addition to their average levels. It may be generally expected that an older company will have lower volatility in its financial ratios than the new ones. This is because of better understating of business and knowledge gained over years of business. This is one of the indicators for judging the stabilization status of the company. The solvency ratio is one of the most important financial ratios for an insurer, which signals the overall health of the company. Accordingly, it is an important figure, which any stakeholder in the industry would like to watch closely. It is generally monitored either on a quarterly or an annual basis depending on the regulatory requirements of the specific country. Insurance companies which may be in a good financial position at a given point of time may fall short of the solvency margin requirement in the next period because of uncertainties and unforeseen factors. Although it is difficult to assess when such a situation for an insurance company could happens, it remains an important task to get best estimates possible with the available data and other factors. The paper attempts to study and analyze the solvency ratio of the non-life insurance companies in India and model it through a statistical distribution. It examines the differentials in its trend and movement in the public and private insurance companies (as public sector companies are very old companies, as compared to the private ones), amongst the private insurers and across the time. It does not find significant difference in the public and private insurers, as the public sector companies too appears to struggle with high level of volatility in their solvency ratios despite their long years of business experience. It is found that the 3- parameter Burr distribution explains our quarterly time-series dataset of solvency ratio appropriately. Given the observations are independently and identically distributed and the Burr distribution explains the dataset appropriately, the paper reveals that the default cases are expected to be more than the actual cases, as observed so far. In the last, the paper suggests further studies on this, which may be taken up. For example, it suggests that a multiple linear regression analysis could be carried out to explain the variation in the solvency ratios through few independent variables and identifies them, which are likely to impact the solvency ratio of non-life insurance companies.