Abstract
This chapter reviews the literature on underwriting cycles and volatility in property-casualty insurance prices and profits. It provides a conceptual framework for assessing unexplained and possibly cyclical variation. It summarizes time series evidence of whether underwriting results follow a second-order autoregressive process and illustrates these findings using US property-casualty insurance market data during 1955–2009. The chapter then considers (1) evidence of whether underwriting results are stationary or cointegrated with macroeconomic factors, (2) theoretical and empirical work on the effects of shocks to capital on insurance supply, and (3) research on the extent and causes of price reductions during soft markets.
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Notes
- 1.
The combined ratio is the sum of the loss ratio (ratio of claim costs to premiums) and expense ratio (ratio of administrative and sales costs to premiums). One minus the combined ratio gives the underwriting profit (exclusive of investment income) margin in premiums.
- 2.
- 3.
See Cummins and Phillips (2012) and references cited therein, including discussion of systematic risk of insurance.
- 4.
Capital shock models (discussed in Sect. 23.4) suggest that capital costs per unit might vary inversely with the total level of capital. Also, models incorporating default risk suggest that, all else equal, premiums will vary directly with the total level of insurer capital. Sommer (1996; also see Phillips et al. 1998) presents evidence that prices vary across insurers in relation to insolvency risk, which depends on the amount of capital held. Choi and Thistle (2000), however, find no long-run relationship between aggregate underwriting profit margins and the ratio of capital to assets. Weiss and Chung (2004) show that non-proportional reinsurance prices during the early 1990s were positively related to capital (policyholder surplus). Epermanis and Harrington (2006) present evidence that premium revenue varies directly with A.M. Best insurer financial strength ratings, especially for insurers specializing in commercial insurance.
- 5.
It is also well known that differences in predicted claim costs across regions and risk classes explain much of the cross-sectional variability of premium rates within a given time period.
- 6.
Evidence indicates that a material proportion of the growth in premiums and availability problems in the 1980s was caused by growth in claim cost forecasts and uncertainty of future liability claim costs rather than by cyclical influences (e.g., Harrington 1988; Harrington and Litan 1988). Basic theory and numerous studies argue that increased uncertainty would be expected to lead to increases in prices needed to cover expected future costs including the cost of capital (Doherty and Garven 1986; Winter 1988).
- 7.
Evidence also suggests that underwriting results vary in relation to changes in the estimated market price of risk, as is predicted if claim costs load on priced risk factors in the economy (see Cagle 1993). Mei and Saunders (1994) provide evidence of predictable variation in risk premia for insurance stocks.
- 8.
Engle and Granger (1987) show that linear regressions on time series data that are nonstationary (e.g., having unit roots) can lead to spurious correlation. If this occurs, cointegration analysis can be used to test for a relationship between the variables.
- 9.
The focus of time series studies on levels or differences in underwriting profit measures, ignoring possible conditional heteroskedasticity, can be explained at least in part by these problems. The estimation of ARCH and GARCH models with annual data over several decades would be unlikely to provide material insight.
- 10.
- 11.
- 12.
Cagle (1993) presents some evidence of cyclical variation in underwriting results after controlling for variation in the estimated market price of risk.
- 13.
The authors note, however, that regulatory lag and financial reporting procedures are unlikely to explain large price fluctuations in the commercial liability insurance market in the mid-1980s.
- 14.
That is, there is evidence that expense ratios follow a second-order autoregressive process.
- 15.
The causes of lags in adjustment are not explored in this work. Also see Tennyson (1993).
- 16.
The combined ratios are not adjusted for policyholder dividends. Following Harrington and Niehaus (2000), similar results were obtained using dividend-adjusted combined ratios and annual average rather than year-end Treasury yields. Qualitatively similar results were obtained using yields on 1-year Treasuries. Augmented Dickey–Fuller tests (see Enders 1995) including intercept and trend generally reject the null hypothesis of a unit root for both the combined ratio and interest rate series (as well as the gross margin and the ratio of net premiums written to GDP; see below), suggesting that the series were trend stationary during these periods. Box-Pierce and Box-Ljung statistics generally indicate that the residuals in the models reported in Tables 23.1 and 23.2 are white noise (two lags were included). We emphasize that our purpose is illustrative. Apart from these and a few other robustness checks, we have not investigated the sensitivity of the results of alternative specifications, such as alternative lag structures and the use of first differences. Also see our discussion below of studies that fail to reject the null hypothesis of a unit root (sometimes without including a trend variable in the testing equation) and then consider whether underwriting margins are cointegrated with other variables.
- 17.
- 18.
When TIME trend is omitted, the coefficient on YIELD becomes significant in the earlier subperiods. However, the evidence that the series are trend stationary makes interpretation of the models without a trend problematic.
- 19.
When the time trend is omitted, the coefficients are negative but with absolute t-ratios less than 1.4.
- 20.
Winter’s (1994) model (see below), for example, implies first-order autoregression, although he suggests that overlapping policy periods might explain second-order autoregression within the context of his model.
- 21.
All of the capital shock models are built on the assumption that external capital is costlier than internal capital. This notion is often justified using the logic of Myers and Majluf (1984) where managers are better informed than investors and that transaction costs make raising new capital costly.
- 22.
While the optimal amount of capital per unit of coverage is likely to decline with the number of units of coverage over some range given the greater diversification of claim costs that can be achieved by writing additional coverage, it is common to assume that demand for coverage (at any price) greatly exceeds the point at which such economies of scale are material.
- 23.
As discussed below, the cost of new capital in Cummins and Danzon (1997) is that it bails out old claimants without increasing the premiums paid by these claimants.
- 24.
The costs of holding capital should be distinguished from the cost of adjusting capital, which are central to short-run analyses of prices and quantities.
- 25.
Some authors suggest that following negative shocks that cause a hard market capital is gradually restored and prices eventually fall to long-run equilibrium values until another negative capital shock occurs. Accordingly, the soft phase of the underwriting cycle is characterized by prices equal to rather than below long-run equilibrium values implied by the perfect markets model (see e.g., Gron 1994a, b).
- 26.
As noted, Winter’s model predicts a first-order process for prices, not a second-order process. He suggests, however, that a higher order process would result from the model if the assumption of single period contracts was replaced with the more realistic assumption of overlapping contracts. Winter (1991b) extends the basic capital shock story by examining the effect of regulation that restricts an insurer’s premium to surplus ratio to be below a certain level. This regulatory constraint can further exacerbate the reduction in short-run supply following a capital shock if demand is inelastic. Intuitively, as prices rise in response to the capital shock, inelastic demand implies that premium revenue will increase, which in combination with the reduction in capital causes more insurers to bump up against the regulatory constraint, which in turn causes supply to shift back even more.
- 27.
As noted earlier, Winter (1994) avoids this issue by imposing a zero probability of insolvency constraint, and Gron (1994a) assumes that there is regulatory constraint on the probability of insolvency. Cagle and Harrington (1995) consider demand responses to capital shocks and show that such responses diminish the ability of insurers to recoup losses from price increases following capital shocks.
- 28.
Froot and Stein (1998) present a model of banks and insurers in which capital structure, hedging policy, and investment decisions are jointly determined based on the assumption that financial institutions are concerned about risk because a realization of a random variable that depletes internal funds can cause the firm to pass up profitable investment opportunities due to the costs of raising external capital. The firm can manage the risk by (1) holding capital ex ante, which is costly due to tax and agency costs, (2) engaging in costly hedging transactions, and (3) adjusting their exposure to the random variable through their investment policies. Their model implies that financial intermediary pricing depends on intermediaries’ capital. To the extent that insurers operate across different lines of business, the result that insurer pricing depends on their capital implies that capital shocks should affect pricing across lines of business, regardless of the source of the shock.
- 29.
During the 1980s, however, the correlation between domestic insurer capital and the economic loss ratio was negative. Winter argues that the 1980s can be explained in part by the omission of reinsurance capacity in the capital variables, a factor which also may have influenced the results of Cummins and Danzon (1997, see below), and which remains an open area for further work.
- 30.
Similarly, popular explanations of “cash flow underwriting” usually imply that insurers are irrational in that they reduce rates too much in response to increases in interest rates. Winter’s model implies that hard markets that follow large shocks tend to be preceded by periods of excess capacity and soft prices. However, as suggested earlier, shocks should be unpredictable. Neither Winter’s model nor other shock stories can readily explain second-order autoregression in profits.
- 31.
- 32.
While insurers’ reported loss forecasts may be biased for tax and other reasons, loss forecast revisions should nonetheless reflect moral hazard induced low prices assuming that low price firms deliberately understate initial reported loss forecasts compared with other firms to hide inadequate prices from regulators and other interested parties, but that larger, positive forecast errors materialize compared with other firms as paid claims accumulate. In addition, if prices vary due to differences in true loss forecasts at the time of sale, less-informed firms should experience relatively greater upward forecast revisions over time compared with other firms as information accumulates.
- 33.
Another avenue of inquiry regarding regulatory policy has been whether delays in the rate approval process under prior approval rate regulation could influence or even cause cyclical fluctuations in underwriting results (Cummins and Outreville 1987). Many studies have analyzed whether rate regulation affects cyclical movements in statewide loss ratios (or inverse loss ratios; see, for example, Outreville (1990) and Tennyson (1993)). Such studies generally consider the hypothesis that regulatory lag amplifies cyclical movements in underwriting results by increasing loss ratios in hard markets by delaying rate increases and reduces loss ratios in soft markets by delaying rate reductions. An alternative view is that rate regulation may damp cycles by preventing excessive price-cutting in soft markets. As summarized by Harrington and Niehaus (2000), a number of authors have debated whether cooperative pricing activities in conjunction with the insurance industry’s limited exemption from federal antitrust law might aggravate hard markets.
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The authors thank the anonymous referee for helpful comments.
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Harrington, S.E., Niehaus, G., Yu, T. (2013). Insurance Price Volatility and Underwriting Cycles. In: Dionne, G. (eds) Handbook of Insurance. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0155-1_23
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