Statistical analysis of rainfall insurance payouts in southern India.

Evidence on the distribution of payouts is presented in figure 2. The x-axis for the graph is "payout rank," which ranks payouts in increasing order of size, expressed on a scale from 0 to 1. Figure 2 plots payout amount against payout rank. The payout is zero up to the 89th percentile, indicating that an indemnity is paid in only 11% of phases. The 95th percentile of payouts is around Rs 200, double the average premium. In a small fraction of cases (around 1%), the insurance pays the maximum indemnity of Rs 1,000, yielding an average return on the premium paid of 900%.

Figure 2 suggests that the ICICI Lombard policies we study primarily insure farmers against extreme tail events of the rainfall distribution. Confirming this graphical evidence, we calculate that around one-half of the value of indemnities is generated by the highest-paying 2% of phases. Without further evidence on the sensitivity of household consumption to rainfall shocks of different types, it is difficult to say whether this structure approximates the optimal insurance design. For example, Paxson (1992) and Jacoby and Skoufias (1998) are generally unable to reject that consumption of rural households in Thailand and India, respectively, is fully insured against rainfall fluctuations. However, these two papers do not consider whether the degree of consumption insurance is lower for extreme shocks, such as a severe drought, which could for example exhaust the household's stock of precautionary savings.

From the perspective of ICICI Lombard, the skewed distribution of payouts suggests a significant reserve of liquid funds may need to be held against policies whose risk is not transferred to reinsurers. This in turn could be costly due to informational frictions in raising external finance or tax disadvantages in holding capital (Zanjani 2002; Froot 1999; Froot and Stein 1998). Among other factors, the insurer's exposure to risk will depend on the value of policies originated, the extent to which reinsurance is used, and correlation of insurance payouts across contracts and through time. We present some evidence on these correlations in the next section.

Dependence in Insurance Payouts

To calculate the degree of cross-sectional dependence in payouts, we calculate the standard deviation of phase payouts for each weather station, restricting analysis to the 11 contracts for which we have the most historical rainfall data. The average of these 11 estimated contract standard deviations is Rs 112.3. We then calculate the standard deviation of the mean insurance payout averaged across the 11 stations at each point in time. This standard deviation will in general be smaller than 112.3, reflecting the diversification benefits from pooling a portfolio of contracts whose returns are not perfectly correlated. If insurance payouts are independent, the standard deviation of the mean payout will asymptotically be 1/[square root of 11] times as large as the standard deviation of individual contract payouts (i.e.,1/[square root of 11] x 112.3 = Rs.33.9, a reduction in the standard deviation of 70%). In contrast, if payouts are perfectly correlated across contracts, there would be no difference between the standard deviation of the mean payout and those of the individual contracts.

Empirically, we calculate that the standard deviation of the mean payout is Rs 60.7, 46% smaller than the average standard deviation of individual contract payouts. This reduction in the standard deviation is smaller than 70%, indicating that insurance payouts are positively correlated cross-sectionally. However, there are still surprisingly large diversification benefits from holding a portfolio of insurance contracts, even though all insurance payouts are driven by rainfall in the same Indian state. Diversification would be larger still if contracts are pooled over a wider geographic area.

An alternative approach to estimating the insurer's exposure to rainfall risk is to compute extreme quantiles of portfolio exposures, such as the 95th or 99th percentile of losses. This methodology, known as value at risk (VaR), is widely used by financial risk managers. See Saunders and Cornett (2006) for a textbook introduction to VaR. For our sample, the 99th percentile of the distribution of mean insurance payouts is Rs 412. This is 13.6 times larger than the mean insurance indemnity, and 4.1 times larger than the mean insurance premium. In contrast, the 95th percentile of mean insurance payouts is Rs. 130, while the 75th percentile is only Rs 30. These results indicate that the distribution of mean insurance payouts is highly skewed, in keeping with the distribution of individual contract payouts presented in figure 2, and that extreme rainfall events produce losses several times in excess of phase insurance premia collected.

ICICI Lombard could employ a variety of strategies to ensure sufficient funds are available to pay claims in case of extreme rainfall events, such as holding a precautionary buffer of liquid assets, securing a bank line of credit, or selling part of their risk exposure to a reinsurer. In practice, even though only a modest number of policies have been written to date, ICICI Lombard has indicated to us that they do use reinsurers to limit their exposure to rainfall risk. Costs associated with these risk-mitigation strategies may be one explanation for why insurance is priced at a premium to actuarial value.

Next, we estimate a simple autoregressive model to examine the time-series correlation in insurance payouts. These estimates are of interest because persistent rainfall shocks may be more difficult for households to smooth. (For example, under a permanent income model, the sensitivity of consumption to current income shocks is increasing in the persistence of the shock.) In addition, temporal dependence in rainfall and payouts may allow insurance purchasers to take advantage of a kind of "stale pricing" opportunity. If weather patterns are persistent, rainfall shocks after insurance premia are fixed by ICICI Lombard would shift the actuarial value of the contract relative to the premium. A household could take advantage of this lack of price updating by delaying its purchase decision until just before the start of the phase, and adjusting their insurance demand in light of updated weather information. Zitzewitz (2006) provides empirical evidence of a related kind of "late trading" behavior among U.S. mutual fund investors.

We estimate two simple autoregressive models. The dependent variable in both models is the phase insurance payout. In the first model this variable is simply regressed on lagged phase payouts. In the second model we include two additional rainfall variables that may be useful predictors of insurance payouts: a dummy variable indicating whether lagged payouts are greater than zero, and cumulative rainfall in the previous phase. (Since we regress phase payouts on variables lagged one phase, we estimate these two regressions for payouts on the second and third phases of the monsoon only.)

Results are presented in table 2. In both regressions, the degree of persistence in payouts is economically small and not statistically significant. Furthermore, neither of the additional lagged variables included in the second model are significantly correlated with insurance payouts. For our sample, the fact that variables based on current rainfall have little predictive power for future insurance payouts perhaps suggests that the "stale pricing" issue discussed above is not a significant concern in practice.

Correlation with Aggregate Variables

Finally, we estimate correlations between insurance indemnity payouts and several aggregate variables, including GDP growth, inflation and stock returns. Such correlations could plausibly be nonzero, because rainfall shocks are spatially correlated within India, and the agricultural sector represents a significant fraction of Indian output and employment. Therefore, extreme rainfall events may represent a nontrivial productivity shock for the overall Indian economy.

Our estimates of these correlations are presented in table 3. The first part of the table estimates bivariate and multivariate correlations between insurance payouts and several Indian macroeconomic variables measured at an annual frequency: growth in Indian GDP per capita, the inflation rate, and the change in the short-term and long-term Indian Treasury yield. Depending on the variable, either 30 or 38 years of data is available for this exercise. Regression standard errors are clustered by year.

Insurance payouts are found to be negatively correlated with growth in Indian GDP per capita, significant at the 10% level in the bivariate regression and the 5% level in the multivariate model. Economically, a 1 percentage point fall in GDP growth is associated with an increase in payouts of Rs 4-5, around 15% of expected insurance payouts. Insurance payouts reflect only the tail of rainfall realizations; in unreported regressions we also find that GDP growth is negatively correlated with phase rainfall, significant at the 1% level. None of the other macroeconomic variables are significantly correlated with rainfall insurance payouts, however.