Ursina Meier and Francois Outreville examine what causes the insurance cycle across Europe.

The insurance cycle in the property-liability insurance business is a recurring pattern of increases and decreases in insurance prices and profits. A number of theoretical and empirical studies of this cycle have appeared in the literature over the past 20 years. Many of these studies have shown that the underwriting cycle does exist in many countries, but there are still numerous debates on the causes of this cycle.

Cummins and Outreville (1987) suggested that the cycle, as observed in the US and in other developed countries, will also be present in other parts of the world through the proliferation of international reinsurance services. Reinsurance allows a primary insurer to increase its premium volume by more than would otherwise be possible with a given amount of capital. More recent research has demonstrated the presence and causes of the underwriting cycle in European and Asian countries. However, there has been no study to determine the impact of reinsurance on insurance prices and profits, although the fluctuations in the price of reinsurance during the past ten years have been documented recently in the business literature.

The underlying causes of volatility in insurance prices have apparently diminished in importance during the 1980s and this has caused some observers to suggest that the underwriting cycles have become obsolete. The fluctuations in the price of reinsurance during the past 20 years seem to contradict these opinions. If the price of reinsurance decreases, reinsurance becomes more affordable for insurance companies and this will be reflected in more capacity, price competition and, at the end, an increase in the loss and combined ratio. We have examined the existence of an underwriting cycle in property-liability insurance for France, Germany and Switzerland over the recent period 1982-2001 in connection with the price of reinsurance in Europe during the same period.

In a perfect market with rational expectations, insurers set pure premiums equal to the present value of expected future losses using all relevant information available to them. The price of insurance - the premiums - is therefore the best predictor of future losses in the sense that it incorporates all information and measures expected losses with an error term uncorrelated with this information when the price is set.

Over the last decade or more, a substantial body of insurance literature has developed attempting to explain a cyclical pattern of increases and decreases in insurance prices and profits in property-liability insurance.

We studied the underwriting results from three countries, Germany, France and Switzerland. These markets are organised in a similar way, are close to each other and are probably affected by the same economic environment.

Figure 1 shows the loss ratios of the three countries from 1962-2001.

We can see that the cyclical patterns are very similar over the period, although fluctuations have been exacerbated in the French market since 1990. Since 1972, Germany and Switzerland have exhibited very similar cyclical patterns. However, the German loss ratio is about 8 to 10 percentage points higher than that of Switzerland. Leng and Meier (2002) found that a structural change happened in Germany and Switzerland in the early 1970s and culminated in 1975. The loss ratio in Germany and Switzerland was consistently higher after 1975. Outreville (2002) found a similar pattern for France. Contrary to what was expected, the correlation coefficients are higher between France and Switzerland than between these countries and Germany (table 1).

We use the second-order autoregressive model proposed first by Venezian (1985) and developed by Cummins and Outreville (1987) to obtain the required parameters for testing the presence of a cycle under conditions of competitive markets and rational expectations. If all information were available concurrently, cycles would not exist under the rational expectations hypothesis.

The model is as follows:

LRt = a0 + a1 LRt-1 + a2 LRt-2 + wt

Where LRt is the loss ratio variable in period t and wt is a random error term.

A cycle will be present if a1 is greater than 0, a2 less than 0 and a12+ 4a2 less than 0.

The length of the cycle period can be expressed as follows:

Period (PI)= 2pi/cos-1(a1/2sq root -a2)

The coefficients of the simple AR(2) process have been estimated over several sub-periods with and without a trend variable. The results for the periods 1965-2001 and 1982-2001 are summarised in table 2. In France, the cycle period is shorter and could only be calculated with the existence of a significant trend variable. In Switzerland and Germany, the length of the cycle is very similar but the trend variable is necessary for Switzerland and never significant in the case of Germany.

One of the main arguments for extending the Cummins-Outreville-type model is the assumption that all relevant information is included in the past loss experience. The analysis of the residuals from regressions analogous to the model of Cummins-Outreville shows that the residuals are not uncorrelated and still include cyclical oscillations (Meier, 2001). This supports the hypothesis of missing variables and from an insurance pricing theory perspective, the interest rate and the loss ratio should be cointegrated. However, the money market rate variable was included in the model for the most recent period 1982-2001 and was never found significant for France and Switzerland. This variable is only significant in the case of Germany.

Cycle and index

Another argument to extend the Cummins-Outreville-type model is the approach used in capacity-constraint models' where the internal capital of the insurance firm is an essential variable. A negative relationship between capacity and insurance result is expected. Real frictions (adjustment costs) which prevent a fast adjustment to the long-run equilibrium, as well as market imperfections, lead to temporary capacity constraints and therefore to insurance cycles.

Surplus cannot be adjusted in the short-run without incurring transactions and/or agency costs. The insurance market provides a simpler and more efficient method of capital allocation, namely reinsurance. Reinsurance provides a tool to rapidly expand the amount of insurance written. Reinsurance allows a primary insurer to increase its premium volume by more than would otherwise be possible with a given amount of capital. Reinsurance also enables insurers to circumvent the effect of tax considerations and international insurance trade barriers. If the price of reinsurance decreases, it becomes more affordable for insurance companies and this will be reflected in more capacity, price competition and, at the end, an increase in the loss and combined ratio. If reinsurance is a significant factor in the behaviour of primary insurance companies, the price of reinsurance should have an immediate and negative impact. The lagged values of the price index should not have an impact on the decisions of insurance companies.

It is very difficult to get any price data in reinsurance and there is no price index for the reinsurance business overall. Swiss Re (2002) has proposed to use the price index for 'proportional property insurance' as a dummy for the price of reinsurance. Because of data collection problems, US business is lacking in the data set and therefore the European business determines the index. Figure 2 replicated from Swiss Re (2002) shows this reinsurance price index over the period 1980-2002.

Property reinsurance business is typically subject to price cycles. Periods of several years with high premium levels are followed by phases with low reinsurance rates. From a business perspective, fluctuations in the reinsurance price can originate from the supply side as well as the demand side. In years with equity growth, low claims and high investment income, the supply of reinsurance capacity expands and prices fall. Inversely, low returns on investment and catastrophic losses cause prices to rise.

The price of reinsurance is considered as an additional variable in the model. Although a trend variable is not necessarily compatible with the idea of the model, it is estimated with and without a trend and with and without the money market rate. The estimations over the period 1982-2001 are done with concurrent and lagged variables and show the following results:

- the estimation for the reinsurance variable is negative and significant in all three countries, and the lagged value is never significant as expected;

- for France, the cycle is no more significant, nor the trend variable or the money market rate. Only the reinsurance price index is a significant variable explaining the fluctuations in the loss ratio over the period under study;

- for Switzerland, the length of the cycle remains significant and similar to previous estimations. The trend variable and the money market rate are not significant and the reinsurance price index is negative and significant as expected; and

- for Germany, there is no cycle and the reinsurance price index explains significantly the fluctuations of the loss ratio. There is no trend variable and the money market rate is a significant variable.

Summary

Through several model specifications we demonstrate empirical evidence for cycles in property-liability insurance business in the three countries.

However, the results do not seem very robust over time and among the countries.

The money market rate is a significant variable in the model for Germany but not for the two other countries.

When dealing with reinsurance, an important caveat must be emphasised.

Ideally, it would be best to conduct the tests using policy year loss data rather than calendar year data. Unfortunately, these data are not publicly available, and so calendar year loss data are used which probably creates a bias in the results.

REFERENCES

Cummins, J David and J Francois Outreville, 1987, An International Analysis of Underwriting Cycles, Journal of Risk and Insurance, vol 54, 246-262.

Leng, Chao-Chun and Ursina B Meier, 2002, Analysis of Multi-National Underwriting Cycles in Property-Liability Insurance, Paper presented at the Annual Meeting of the American Risk and Insurance Association in Montreal, Quebec, Canada.

Meier, Ursina B, 2001, Multi-National Underwriting Cycles in Property-Liability Insurance, Paper presented at the EGRIE Meeting in Strasbourg, France.

Outreville, J Francois, 2002, Cycles in Insurance, Paris International Conference on Risk and Insurance, Les Entretiens de l'Assurance, December.

Swiss Re, 2002, The Insurance Cycle as an Entrepreneurial Challenge, Zurich: Swiss Reinsurance Co.

Venezian, Emilio, 1985, Ratemaking Methods and Profit Cycles in Property and Liability Insurance, Journal of Risk and Insurance, vol 52, 477-500.

- The opinions expressed in this paper are those of the authors and do not necessarily reflect the views of the United Nations Office at Geneva.

This article is based on: Meier, Ursina B and J Francois Outreville (2003): The Reinsurance Price and the Insurance Cycle, paper presented at the Seminar of the European Group of Risk and Insurance Economists in Zurich.

The current version of the paper is available at

http://www.egrie.unizh.ch/wp/meier.pdf.

- Ursina Meier is a PhD student at the Universities of Cambridge (UK) and Bern (CH). J. Francois Outreville is Executive Secretary of the Staff Mutual Insurance Society at the UNO in Geneva (CH).