Statistical Analysis of Rainfall Insurance Payouts in Southern India

Transcription

1 Statistical Analysis of Rainfall Insurance Payouts in Southern India Xavier Giné (World Bank, DECRG) Robert Townsend (University of Chicago) James Vickery (Federal Reserve Bank of New York) This draft: May 28, 2007 Abstract: Using 40 years of historical rainfall data, we estimate a distribution for payouts on rainfall insurance policies offered to farmers in a semi-arid region of India in We find that the contracts primarily protect households against extreme tail events; half the expected value of indemnities paid by the insurance are generated by only 2 per cent of rainfall realizations. Insurance premiums appear high compared to expected payouts. Contract payouts are significantly correlated cross-sectionally, and also inversely associated with real GDP growth. We discuss implications of these findings for the potential benefits of insurance to households, the risks facing a financial institution underwriting rainfall insurance contracts, and pricing. We gratefully acknowledge the financial support of the Swiss State Secretariat for Economic Affairs, SECO, CRMG and the Global Association of Risk Professionals (GARP). We thank representatives from ICICI Lombard for their assistance, and Zhenyu Wang for helpful comments. Paola de Baldomero Zazo and Sarita Subramanian provided outstanding research asssistance. Views expressed in this paper are the authors and should not be attributed to the World Bank, Federal Reserve Bank of New York or the Federal Reserve System. xgine@worldbank.org, rtownsen@uchicago.edu, and james.vickery@ny.frb.org.

2 1. Introduction Exposure to drought amongst rural households in India and other countries should, at least in principle, be largely diversifiable. This is because deficient rainfall is exogenous to the household, and not likely to be strongly correlated with the systematic risk factors, such as aggregate stockmarket returns, that are relevant for a well-diversified representative investor. With this principle in mind, the goal of rainfall index insurance is to allow households, groups and governments to reduce their exposure to weather risk by purchasing a contract that pays an indemnity during periods of deficient (or excessive) rainfall. Advocates argue that index insurance is transparent, inexpensive to administer, enables quick payouts, and minimizes moral hazard and adverse selection problems associated with other risk-coping mechanisms and insurance programs. See World Bank (2005), Barnett and Mahul (2007), Giné, Townsend and Vickery (2007) and the other papers in this session for more details. This paper uses historical rainfall data to estimate the distribution of payouts on a realworld rainfall index insurance product offered since 2003 to households in the state of Andhra Pradesh in southern India. The product is sold to farmers by BASIX, a microfinance institution, and rainfall risk is underwritten by the insurance firm ICICI Lombard and their reinsurers. Our empirical strategy is based on the presumption that, since rainfall is close to a stationary process, we can use past historical rainfall data to calculate a putative history of insurance payouts for insurance contracts written against the 2006 monsoon. We then perform several statistical exercises to better understand the properties of insurance payouts, focusing on three topics. Firstly, what is the shape of the unconditional distribution of payoffs? Does the insurance contract pay off regularly, providing income during periods of moderately deficient rainfall? Or does it operate more like disaster insurance, rarely paying an indemnity, but providing a very high payout during the most extreme rainfall 1

3 events? Our evidence suggests the truth is closer to the second statement. Studying insurance contracts linked to 14 different rainfall gauges, we estimate the probability of receiving a positive payout on any single phase of the insurance contract to be only around 11 per cent; furthermore, half the total value of indemnities are triggered by the highest-paying 2 per cent of rainfall events. The maximum indemnity, which is paid in approximately 1 per cent of cases, provides a rate of return to the policyholder of 900 per cent. However, on average, the insurance appears expensive; we estimate that insurance premiums are around three times as large as expected payouts. Second, we study the correlation of payouts cross-sectionally and through time. Serially and spatially correlated rainfall shocks are likely to be more difficult for households to insure against by other means (eg. precautionary savings, or inter-household transfers), implying potentially larger benefits of the rainfall insurance product. However, dependence in payouts is also likely to increase the risk exposure of a financial institution, such as ICICI Lombard or a reinsurer, who holds a portfolio of insurance contracts on its balance sheet (since dependence reduces the diversification benefits of pooling contracts). Perhaps unsurprisingly because we consider insurance contracts in a particular geographic region, we find payoffs are significantly positively correlated across contracts. However, there are still significant diversification benefits from pooling; the standard deviation of payouts on an equally-weighted basket of 11 contracts is around half as large as the average standard deviation of the individual contracts. Although the rainfall index used to calculate payoffs is serially correlated, we find much less temporal dependence in insurance payoffs themselves, which reflect only the tail of the rainfall distribution. Third, we find that, as well as being correlated across contracts, payouts are negatively correlated with growth in Indian GDP per capita. This suggests that some component of 2

4 rainfall risk against which the contracts insure is aggregate to the Indian economy, and in turn, that spreading rainfall risk internationally (eg. through financial markets, or a non-indian reinsurer) may improve risk-sharing. 2. Background and Methodology The insurance product we study was developed by the general insurer ICICI Lombard, and is designed to insure smallholder farmers against deficient rainfall. It has been offered to households since ICICI Lombard partners with local financial institutions to market the product to households; in Andhra Pradesh this role is fulfilled by BASIX, a microfinance institution. Giné, Townsend and Vickery (2007) and Cole and Tufano (2007) provide more background details about BASIX and the insurance product. Giné et. al. also estimate the cross-sectional deterninants of household insurance takeup, based on a 2004 household survey. Below we summarize the design of ICICI Lombard rainfall insurance contracts, focusing on policies sold in Andhra Pradesh in Policies cover rainfall during the Kharif (monsoon season), which is the prime cropping season, running from approximately June to September. The contract divides the Kharif into three phases roughly corresponding to sowing, podding/flowering and harvest. In 2006, unlike some previous years, farmers were allowed to purchase different numbers of contracts across phases. Phase payoffs are based on accumulated rainfall between the start and end dates of the phase, measured at a nearby reference weather station or rain gauge 1. The start of the first phase is triggered by the monsoon, namely, Phase 1 begins on the first date on which accumulated rain since June 1 exceeds 50mm or July 1 st if accumulated rain since June 1 st is below 50mm. 1 Some adjustments are made to raw accumulated rainfall when constructing the index used to calculate payoffs. First, daily index rainfall is capped at 60mm (ie. if >60mm of rain falls in a day, only 60mm is added to the cumulative rainfall index); conversely, rainfall <2mm is ignored for the accumulated rainfall index. These adjustments are meant to reflect that heavy rain may generate water runoff, resulting in a less than proportionate increase in soil moisture, while very light rain is likely to evaporate before it soaks into the soil. We take these adjustments into account when constructing our dataset of estimated insurance payouts. 3

5 The payout structure within each phase is illustrated in Figure 1. Payouts in the first two phases are linked to low rainfall. An upper and lower threshold is specified; the policy pays 0 if accumulated rainfall exceeds the upper threshold, or strike. Otherwise, the policy pays Rs. 10 for each mm of rainfall deficiency relative to the strike, until the lower threshold, or exit, is reached. If rainfall is below the exit, the policy pays a fixed, higher indemnity of Rs Phase 3 has the same collar structure, but in reverse, namely it pays out only when rainfall is above the strike, meant to correspond to unusually heavy rainfall during the harvest season that may cause damage to crops. [INSERT FIGURE 1] Depending on the individual policy, the reference weather station is of one three types: an IMD (Indian Meteorological Department) station, mandal rainfall station (a mandal is a local geographic area roughly equivalent to a US county) or one of a network of automated rain gauges installed by ICICI Lombard. IMD rainfall data is considered to be more reliable than data from mandal stations, and there is also a longer and more complete history of past rainfall, making it easier for ICICI Lombard to estimate expected payouts to policyholders. However, many villages are not close to an IMD station. An additional disadvantage is that IMD data takes approximately two months to be certified, delaying the process of calculating and settling payouts to policyholders. ICICI Lombard rain gauges are concentrated in areas far from other rain stations, where the basis risk from writing contracts on IMD or mandal stations would be excessively high. Our analysis focuses on contracts written against IMD rainfall stations, which have the longest span of historical data for constructing a putative dataset of insurance payouts. Our source data consists of terms on contracts indexed to 14 different IMD stations in Andhra Pradesh (one contract per station), as well as IMD s dataset of historical rainfall for each 4

6 station. Rainfall data is measured at a daily frequency, and spans the period and then However the span of available data is different for different stations, and there also are scattered individual months and years where all or some data is missing. Across 14 stations, there are 1089 individual contract phases for which at least some rainfall data is available. However, for 135 phases, data is missing for part of the contract period. We drop these from our analysis, leaving a sample of 954 phases for which we have complete daily rainfall to calculate payoffs. Applying the terms of each contract to the historical rainfall data for the relevant station, we then calculate the hypothetical payout on the contract for each station, phase and year. (In other words, we calculate what each contract would have paid if it had been available in past years.) Data on estimated payouts and information on contract features are presented in Table 1. As the right hand column of the table shows, there is significant variation across stations in the amount of historical data available. At the upper end, there are 91 phases of complete rainfall data for Anantapur (equivalent to 30 1/3 years). However for Adilabad and Nalgonda, only a small amount of rainfall data is available (8 and 18 phases respectively). [INSERT TABLE 1] The first two columns of Table 1 present summary statistics on estimated payouts. Strikingly, the insurance provides an indemnity in only 10.7 per cent of phases. Additionally, the average putative historical payout is low relative to premiums, 29.7 rupees, compared to an average premium of 99.9 rupees. Even taking into account the administrative costs of operating and selling insurance, this expected payout appears quite low relative to premiums. However, the insurance may still be valuable to policyholders if provides a high payout during times when the household s marginal utility of consumption is extremely high. 5

7 The table also summarizes the main contract features of each phase, namely the value of the strike and exit. These values differ significantly across stations, reflecting differences in average historical rainfall. 3. Distribution of payouts Further evidence on the distribution of payouts is presented in Figure 2. The x-axis for both graphs is payout rank, based on ranking payouts in increasing order of size. Figure 2a plots payout amount against payout rank. The payout is zero until the 89 th percentile, reflecting that an indemnity is paid in only 11 percent of phases. The 95 th percentile of payouts is around Rs In a small fraction of cases (around 1 percent), the insurance pays out the maximum indemnity of Rs. 1000, yielding a return on the average premium of around 900 per cent. Figure 2b plots cumulative payouts against payout rank (ie. the y-axis measures the fraction of the sum of all indemnities from phases whose payout rank is less than x). The figure shows that around half of the value of all indemnities are generated by the highest-paying 2 per cent of phases. [INSERT FIGURE 2] These calculations suggest that the ICICI Lombard policies we study are primarily designed to insure against extreme tail events of the rainfall distribution. Without further evidence on the sensitivity of household consumption to rainfall shocks of different types, it is difficult to say whether this is close to the optimal insurance design. For example, Paxson (1992) and Jacoby and Skoufias (1998) find that, on average, the consumption of rural households in Thailand and India respectively are quite close to fully insured against rainfall fluctuations. However, they do not consider whether the degree of consumption insurance is lower for very large shocks, which would, for example, be more likely to exhaust the household s stock of precautionary savings. 6

8 From the perspective of an insurance provider such as ICICI Lombard, such a fat-tailed distribution of payouts implies that a comparatively large amount of capital must be held against policies whose risk is not transferred to reinsurers. This may in turn be expensive, because of informational frictions in raising external finance or tax disadvantages in holding capital (Zanjani, 2002; Froot, 1999; Froot and Stein, 1998). The size of the required capital buffer will depend on the value of policies held, the extent to which reinsurance is used and correlation of payouts across contracts and through time. We present some evidence on these correlations in the next section. 4. Dependence in insurance payoffs Estimates of time-series and cross-sectional dependence in insurance payouts is presented in Table 2. Standard errors in all regressions are clustered by time period (ie. by a variable interacting phase x year). [INSERT TABLE 2] The first part of the table presents results of a regression of phase payout on the mean payout on all other contracts during the same phase-year. 2 This regression reveals a significant degree of dependence; the coefficient on mean payout is 0.6, significant at the 1 per cent level. The R 2 is 0.083, implying a correlation coefficient of Thus, although payouts are clearly spatially correlated, the majority of the variation in payouts is idiosyncratic. Stated differently, the average standard deviation in phase payouts across the 11 contracts for which we have close to a continuous history of rainfall data is Rs The standard deviation of mean payouts across these 11 contracts is Rs (compared to a value of Rs if payoffs were uncorrelated across contracts). Thus, holding an equally-weighted 2 We exclude the contract whose payoffs are the dependent variable from the calculated mean payoff, to avoid any mechanical correlation with the mean. The coefficient in our regression will be zero if the underlying individual insurance payouts are uncorrelated within a given phase-year. 7

9 portfolio of contracts results in significant reduction in the variance of payouts, although the extent of variance reduction is reduced by the spatial correlation in payouts across contracts. The second part of Table 2 presents evidence on time-series correlations in payouts. These correlations are of interest for several reasons. First, rainfall shocks are likely to be more difficult for households to smooth if they are persistent (eg. under the permanent income hypothesis, the sensitivity of consumption to current income is increasing in the persistence of the shock). Second, serial correlation in payoffs will increase the portfolio risk for the provider of insurance, in this case ICICI Lombard, since a shock to capital relating to insurance losses will in expectation be followed by further shocks in later periods. Third, temporal dependence in rainfall and payouts may allow insurance purchasers to take advantage of a kind of stale pricing opportunity. If contract terms and pricing are set far in advance, the actuarial value of the contract may change significantly between when terms are set and the start of the phase, while the contract price has not changed. An alert customer could in principle take advantage of this lack of price updating by delaying their purchase decision until just before the start of the phase, and then adjusting the size of their purchase to reflect the change in contract actuarial value since the terms were set. Zitzewitz (2006) provides evidence of this kind of late trading behavior amongst US mutual fund investors. We estimate three regressions, in which the dependent variable is in turn (i) the rainfall index used to determine payouts (ii) the payout and (iii) a dummy if the payout is > 0. We regress each variable on all three variables lagged one phase (since we regress on lagged values, we estimate this regression for the second and third phases only). We find significant serial correlation in rainfall, but not in insurance payouts. The coefficient on lagged rainfall is 0.4, significant at the 1 per cent level, demonstrating that periods of low rainfall are quite persistent. However, none of the three lagged variables is statistically significant in predicting 8

10 the level of payouts, or the payout dummy variable. The lower degree of persistence in payouts reflects that indemnities reflect only the tail of the distribution. 5. Correlation with Aggregate Variables Finally, we estimate correlations between insurance indemnity payments and several aggregate variables, including GDP growth and stock returns. Such correlations could plausibly be nonzero, because rainfall shocks are likely to be spatially correlated across regions, and the Indian economy is quite dependent on the agricultural sector. Therefore, extreme rainfall events may represent a non-trivial productivity shock for the overall Indian economy. Any positive correlations with aggregate risk factors also potentially indicates that the required rate of return on the insurance product should not be the risk-free interest rate, but instead a rate that reflects its positive factor loadings on systemic risk factors. (Although contracts resemble a collar option, they cannot be priced by arbitrage a la Black and Scholes (1973), because the underlying rainfall index is non-tradeable. See Richards, Manfredo and Sanders (2004) for a discussion of methods to price weather derivatives.) [INSERT TABLE 3] We estimate a simple linear regression to investigate these correlations. Results are presented in Table 3. The top half of the Table estimates correlations with macroeconomic variables: growth in Indian GDP per capita, inflation, innovations in short and long-term interest rates and US GDP growth. Standard errors are clustered by year, since the macroeconomic data is available only at an annual frequency. Either 38 or 30 years (depending on the variable) of macroeconomic data is available to be merged with our payout dataset. Our main finding is that insurance payouts are negatively correlated with growth in Indian GDP per capita. This is significant at the 10 per cent level in the bivariate specification, and the 5 per cent level in the multivariate model. The magnitude of the coefficient is quite 9

11 large, a 1 percentage point decline in GDP growth is associated with an increase in payouts of Rs. 4-5 (ie. around 15 per cent of average contract payouts). In unreported regressions, we repeat these regressions using accumulated rainfall, rather than insurance payoffs, as the dependent variable. We find results that are similar, although estimated more precisely; the coefficient on rainfall is positive in both bivariate and multivariate specifications, statistically significant at the 1 per cent level in both cases. Taken at face value, this finding suggests that measured rainfall and payouts, beyond being spatially correlated within Andhra Pradesh, have a component which is also aggregate to the the Indian economy as a whole. One implication of this finding is that remittances from urban workers to family members in drought-striken areas may be somewhat constrained as a means of sharing risk, since transfers within risk-sharing groups cannot smooth shocks that are aggregate to the group as a whole (Townsend, 1994). The finding also potentially strengthens the case that ICICI Lombard should attempt to hedge its exposure to weather risk arising from rainfall insurance. Froot, Scharfstein and Stein (1993) show that when external finance is costly due to informational frictions or other factors, firms should minimize exposure to shocks that reduce cashflows during periods when credit constraints are most binding. This provides a potential rationale for ICICI Lombard using a foreign reinsurer to underwrite the insurance policies; such a reinsurer s balance sheet would be less exposed to Indian macroeconomic risk. Such considerations are currently relatively unimportant given the small amount of rainfall insurance coverage being sold, however, it may become more relevant as the market grows over time. We note that ICICI Lombard does in fact already use reinsurers to hedge its exposure to rainfall risk, despite the limited amount of coverage it writes, a decision that must be motivated by the existence of some kind of frictions in raising external capital. 10

12 The second half of Table 3 estimates correlations with stock returns, namely the Indian SENSEX index and the US S&P 500. For each phase, year and station, we calculate stock returns between the start and end dates of the phase, and convert them to an annualized rate. Thus, returns match up exactly to the period covered by the contract, rather than just the year of the contract, as for the macroeconomic data. We find that payoffs are uncorrelated with Indian stock returns, and slightly positively correlated with S&P 500 returns. 6. Conclusions We summarize the design of a rainfall insurance product offered to households in semi-arid India, and present evidence on the statistical properties of insurance payouts. We reach three main findings: (1) Insurance payoffs are concentrated in the extreme tail of adverse rainfall events; (2) Insurance premia appear high relative to expected payoffs; (3) Insurance payoffs are correlated cross-sectionally, and also appear to be correlated with Indian output growth. Our finding that a component of rainfall risk is aggregate, perhaps even at the level of the Indian economy, suggests that other risk sharing mechanisms like inter-household transfers, and sales of assets into local asset markets, may be of only partial help for insuring consumption against rainfall shocks. This potentially underlines the benefit of explicit rainfall insurance. However, correlations in insurance payoffs combined with the fat-tailed payoff distribution suggests that a financial institution such as ICICI Lombard who underwrites a large quantity of rainfall insurance, may face significant balance sheet risk. The use of reinsurers whose cashflows are less sensitive to Indian risk factors, or the issuance of financial market instruments linked to rainfall insurance payouts, are likely. Finally, we emphasize that many of our conclusions are somewhat speculative, and that much more research is needed to evaluate the promise of rainfall insurance. For example, to shed further light on optimal contract design, both theoretical and empirical work is needed to 11

13 improve our understanding of the types of weather and other shocks against which household consumption is not well insured. References Barnett, Barry and Olivier Mahul, 2007, Weather Index Insurance for Agriculture and Rural Areas in Lower Income Countries, American Journal of Agricultural Economics, this issue. Cole, Shawn and Peter Tufano, 2007, BASIX, Harvard Business School Case Froot, Kenneth A. (ed), 1999, The Financing of Catastrophe Risk, University of Chicago Press. Froot, Kenneth and Jeremy Stein, 1998, Risk management, capital budgeting, and capital structure policy for financial institutions: an integrated approach, Journal of Financial Economics, 47, Froot, Kenneth, David Scharfstein, and Jeremy Stein, 1993, Risk Management: Coordinating Corporate Investment and Financing Policies, Journal of Finance, 48, Giné, Xavier, Robert Townsend and James Vickery, 2007, Patterns of Rainfall Insurance Participation in Rural India, working paper. Jacoby, H. and Skoufias, E., 1998, Testing Theories of Consumption Behaviour Using Information on Aggregate Shocks : Income Seasonality and Rainfall in Rural India, American Journal of Agricultural Economics 80, p Paxson, Christina H., 1992, Using Weather Variability to Estimate the Response of Consumption to Changes in Transitory Income in Thailand, American Economic Review, 82, Richards, Timothy, Mark Manfredo and Dwight Sanders, 2004, Pricing Weather Derivatives, American Journal of Agricultural Economics, 86, Townsend, Robert (1994) Risk and Insurance in Village India, Econometrica 62, May, World Bank, 2005, Managing Agricultural Production Risk: Innovations In Developing Countries, World Bank Agriculture and Rural Development Department, World Bank Press. Zanjani, George, 2002, Pricing and Capital Allocation in Catastrophe Insurance, Journal of Financial Economics 65, Zitzewitz, Eric, 2006, American Economic Review (Papers & Proceedings). 12

14 Figure 1: Structure of Insurance Contract BASIX rainfall insurance divides the monsoon season into three phases. The graph below shows how rainfall during the phase translates into the insurance payout for the phase. Figures in brackets are actual trigger points and payouts for Phase 1 of the contract for Mahboobnagar IMD station. Payout in Phase 1 Max Payout (1000Rs) (600Rs) Exit (10mm) [equivalent to crop failure] Strike (70mm) Rainfall during Phase 1 13

15 Figure 2: Distribution of Payoffs 1a. Payout amounts in rupees, in increasing order of payout amount Payout amount Payout rank 1b. Cumulative payout distribution, ordered by payout amount Cumulative payout Payout rank 14

16 Table 1: Summary Statistics Table relates to rainfall insurance contracts written against 14 IMD rainfall stations in Andhra Pradesh, India, in Estimates of average payouts are based on historical IMD rainfall data from and Note that in all cases, insurance contracts pay out 10Rs per mm of rainfall deficiency relative to the strike, until the exit is reached. Beyond the exit (ie. below the exit in the case of Phases 1 and 2, and above the exit for Phase 3), the insurance pays out a fixed payout of Rs average payout per phase percent positive payouts average premium per phase mean Phase 1 Phase 2 Phase 3 value of rainfall index strike exit strike exit strike exit Number of obs. (phases) By station Adilabad % Andolemedak % Hanmakonda % Begumpet % Anantapur % Bhadrachalam % Kalingapatnam % Khammam % Kurnool % Mahbubnagar % Nandyal % Nizamabad % Kadapa % Nalgonda % By phase One % Two % Three % By decade 1960s % s % s % s % s % All observations %

17 Table 2: Correlations Amongst Contract Payoffs Standard errors in all regressions are clustered by time period (ie. phase x year). Cross-sectional correlation in payouts payout Mean payout, other gauges 0.603*** (5.10) R N 932 Estimated standard deviations of payouts: average σ across individual gauges: σ of average gauge payout: 60.8 Time-series correlation in payouts rainfall index payout dummy for payout > 0 dummy for payout > 0 (t-1) (-0.20) (-0.19) (0.20) payout (t-1) (1.48) (0.07) (-0.17) rainfall index (t-1) 0.410*** (4.65) (-0.85) (-0.40) R N

18 Table 3: Correlation of Payouts with Systematic Risk Factors Macro variables (annual data): Dependent variable in all columns: insurance payout India real GDP per capita (% change) * ** (-1.90) (-2.17) US real GDP (% change) (0.60) (0.92) India inflation (growth of GDP deflator) (0.25) (-1.08) Change in short interest rate, India (0.10) (0.30) Change in long interest rate, India (0.44) (0.57) R Number of observations T Annualized stock returns (phase data): Dependent variable: insurance payout India SENSEX index (-0.42) (-0.52) US S&P * (1.38) (1.80) R Number of observations T