Assessment of the risk management potential of a rainfall based insurance index and rainfall options in Andhra Pradesh, India.

Veeramani, Venkat N. ; Maynard, Leigh J. ; Skees, Jerry R. 等

Abstract

Crop insurance is an alternative risk management technique available to farmers for stabilizing their revenue risk. Schemes based on area yield index are in operation for quite some time. Here a basic mechanism for the operation of rainfall index insurance and rainfall derivatives is developed. Instead of direct premium subsidies that are distorting, premium subsidy is taken as a function of adverse deviation of rainfall from the mean. A sensitivity analysis at different revenue elasticity levels with respect to rainfall was performed. Potential for private insurer's and reinsurer's participation exists with rainfall based index and options.

JEL Classification: G13, G22, Q14.

Introduction

In 2001-02, farmers in the state of Andhra Pradesh, Karnataka, and Punjab committed suicide over recurring crop losses due to drought, pests, and diseases. The crop loss data for the period 1985 to 2002 provided by the General Insurance Corporation's crop insurance cell categorized drought (70 percent) as the major source of crop loss followed by excess rainfall (20 percent) (Parchure, 2002). This shows the enormous dependency of crop production on rainfall. Higher dependency of agriculture on rainfall means that successive failures resulting from monsoons could leave the cash starved farmers in a debt cycle. The sheer size of the population involved in agriculture and the fact that 60 percent of the crop production is done under rainfed conditions highlight the need for income stabilization programmes for the farmers. Traditional insurance programmes are unsuitable for insuring agricultural risk mainly due to the presence of systemic risk. Presence of high correlation between rainfall and crop losses makes rainfall based crop insurance an attractive option for insuring agricultural risk.

Current Insurance Programmes

Crop Insurance was first introduced as a pilot scheme in 1978. Crops covered under the pilot scheme are paddy, wheat, millets, oilseeds and pulses. Until 2000, crop insurance schemes targeted the crop loans distributed by the loaning agency. Practically, insurance was not available for farmers without crop loans. The central and the state governments at a 2:1 ratio shared the crop insurance risk. "Rashtriya KrishiBeema Yojana" is the latest crop insurance scheme available to farmers. The central and the state governments under this programme share crop insurance risk equally. This scheme is fairly structured with different levels of indemnity and it covered all major crops grown in India. Indemnity payments are calculated based on an area yield index. A lower premium rate (approx. 4%) is charged for liability amounts up to 150 percent of the trigger yield. Liability amounts above 150 percent of the trigger yield attract an actuarial premium rate. Under this scheme a 50 percent premium subsidy is provided to small and marginal farmers. Losses up to 200 percent of the premium are covered by the insuring agency and losses above 200 percent are covered by a corpus fund set up by the government.

Area yield index programmes overcome most of the moral hazard and adverse selection problems but presence of basis risk is a major disadvantage of crop insurance programmes based on an index. U.S. crop insurance programme results have shown that the level of participation did not increase even with higher levels of premium subsidies. Higher premium subsidies also provided an incentive for the farmers to take more risky activities (Skees, 1999). Although the crop insurance scheme is effective in increasing the participation level of the farmers (0.7 million in 1992 to 1.3 million in 1999) in the state of Andhra Pradesh, high compensation payments (386 percent of the premium collected) discouraged full scale implementation of the programme. Extending the programme to include non-loaned farmers is met with skepticism as the payment rate for non-loaned farmers averaged 3 times that of loaned farmers (Parchure, 2002). The crop insurance programme was in fact beneficial to the farmers but it had a negative influence on the government budget. The current trend towards disinvestment of the public sector means that, increasingly, the government wants to shy away from ad hoc disaster payments. Transferring excess risk to international reinsurers is a viable alternative to disaster payments and reinsurance by the government. But international reinsurers are reluctant to reinsure crop insurance risk from developing countries mainly due to the lack of reliable crop yield data. If the current area yield index insurance numbers are an indication, encouraging private participation in insurance programmes will not be a reality.

In India, BASIX and ICICI Lombard introduced rainfall insurance as an experimental scheme covering small farmers in Mahabubnagar, Andhra Pradesh last year. Insurance based on rainfall and area yield indices have similar characteristics except for the availability of reliable rainfall data for long periods and low administrative cost in the case of rainfall insurance.

Objectives

Skees et al. (1999, 2001), Miranda (1991), Martin et al. (2001), and Mahul (2000) explored the possibility of using rainfall in developing insurance products. Using the elasticity of revenue with respect to rainfall, this study develops a basic mechanism for operating a rainfall based crop insurance product. Direct premium subsidies are production distorting and inherently expensive. In this study a non" production distorting premium subsidy schedule is developed based on the methodology suggested by Parchure (2002). Even with the availability of reliable weather data for long periods, international reinsurers may not be interested in reinsuring crop insurance risk from a developing country like India. This study explores the use of derivative instruments to hedge against extreme losses faced by the insurers.

Data and Methodology

In this study historic monthly rainfall for the Coastal Andhra Pradesh subdivision for 130 years from 1871 to 2000 is used (data provided by the Indian Institute of Tropical Meteorology). Rice is the major food crop grown in this subdivision and most of it is grown during the kharif season. The rice crop also has the highest insurance utilization rate of 82.5 percent with an average claim rate of 326 percent. The state level rice yield, farm harvest price and minimum support price for the period 1981-2000 is collected from Ministry of Finance, Government of India and used as proxy for the subdivision due to data limitations. Four years moving average yield and the maximum of farm harvest price and minimum support price is used to calculate the liability. The wholesale price index for agricultural products is used to normalize the prices.

Since the rice crop is sensitive to drought more than flooding, different limits are used to calculate the payment percentage for the downside risk (drought) and upside risk (flooding). Loss payment starts whenever the actual rainfall is above or below the strike rainfall. The rice crop requires 1000 to 1200mm of water: around 250 to 300mm per month if grown completely under rainfed conditions. Less water is required from germination stage to seedling stage and also from grain maturation stage until harvest (150 to 175 mm). From tillering to dough grain stage higher levels of water are required (600-800 mm). Due to uneven distribution of rainfall, daily rainfall data should be used to develop the strike values appropriate for each growth stage. Since daily rainfall data for long periods is not available, this article uses historic average monthly rainfall as the strike rainfall for individual months from June to October.

In the case of downside risk a limit of half of strike is used to identify full payment. Between strike and the limit for all the months a percentage payment is used. In the case of upside risk the payment starts after the deviation in monthly rainfall is greater than twice the strike value for June, July, and August. For September the payment starts at 1.5 times the strike rainfall and for October the payment starts at 1.25 times the strike rainfall. These limits were set based on the water requirement for the rice crop.

For developing a season based rainfall index one can take the average of monthly payment percentages but the occurrence of extreme losses in a particular month that could destroy the crops may lead to erroneous payment calculations. Hence premium calculation is done for individual months.

The method suggested by Skees et al. (2001) for calculating the payment percentage, indemnity and the premium rate is used here

Payment Percentage (drought) = (Strike Rain - Actual Rain/Strike Rain) (1)

Payment Percentage (flooding) = (Actual Rain - Upper Strike Rain/Actual Rain) (2)

Indemnity = Payment Percentage x Liability (3)

Premium rate = (Average Indemnity/Average Liability) * Loading (4)

Loading is the hiking of the premium to cover losses due to unforeseen events or to build cash reserves or to cover the monitoring cost (Skees et al., 1999). In this study loading is done by adding 33 percent of the standard deviation of the indemnity to the premium. The insurer is assumed to take payment risk up to 1.5 times the premium collected and for losses beyond 1.5 times the premium the insurers can either reinsure or hedge using rainfall options. Reinsurance premium rates are calculated based on the premium rates formula (4) above. A countercyclical premium subsidy schedule is used in this study.

Premium subsidy = f (adverse deviation of rainfall from the mean) (5)

Hedging Using Rainfall Options

The idea of using climatic events for insurance payments is not new; trading based on Heating Degree Days (HDD) and Cooling Degree Days (CDD) are available for quite some time now (Turvey, 1999). This study considers both the upper bound and lower bound risk. The payoff function for call and put options is given below

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

where, L2 is the lower limit, L1 is the upper limit, strike is a choice variable, X is the actual rainfall level, and [lambda] is the predetermined monetary value of the rainfall index. The strike values for both the upside and downside risk and the limits for the downside risk are similar to those used for rainfall insurance. In the case of upside risk the limit is fixed at four times the historic mean for June, July and August monthly options, and 3 and 2.5 times the historic mean for September and October, respectively. For rainfall beyond the limits on both sides the payout will equal the amount at the limit.

Premium= - (EV + 0.25*SD) (8)

The premiums charged for the options are calculated based on the expected return of the options (EV) and the options' standard deviations (SD).

Results

Studies by Rao, Ray and Rao (1988) give the range of elasticity of output with respect to rainfall for different crops for different states in India. They found the output elasticity of rice with respect to rainfall is in the range of 0.7 to 0.8 during the 1980s. Here rainfall insurance analysis is performed over three different revenue elasticity levels (0.4, 0.5, and 0.6).

As expected, the relative risk of rainfall for the kharif season is lower (coefficient of variation is 19.63 percent) than the relative risk for individual months (coefficient of variation values: June 47.22 percent, July 35.43 percent, August 36.41 percent, September 34.61 percent, October 51.22 percent). The descriptive statistics for historic monthly rainfall are given in table 1. The distribution of rainfall in the case of October has a longer tail on both sides. Hence the probability of excess loss payments is higher in the month of October. For June, the possibility of loss payment due to drought has a higher frequency than due to flooding. The probability density function approximations for rainfall distributions for individual months are available upon request.

Calculated insurance premium with and without loading for the three revenue elasticity levels is given in table 2. The actuarially fair premiums and the leaded premiums are in the range of 12 percent to 32 percent and 16 percent to 43 percent of the liability, respectively. If a revenue elasticity of 0.5 is assumed, the actual premiums are in the range of 8 percent to 21 percent. The actual premiums are relatively higher when compared to the premium rates charged in the current insurance programmes (approx. 8% before subsidy). The results are summarized in table 1. The reinsurance premiums for protection against excess losses are in the range of 4 percent to 14 percent, 4 percent to 12 percent, and 3 percent to 10 percent for revenue elasticities of 0.6, 0.5, and 0.4, respectively.

The premium paid follows a downward slope on either side of the strike for adverse deviation of rainfall from the mean. The more adverse the deviation of rainfall from the mean, the lower the premium charged by the insurer thereby acting purely as a countercyclical payment. The payment mechanism is decoupled in the sense that it neither affects the production decision of the farmers nor their risk orientation. As the revenue elasticity increases the decrease in the premium paid is steeper for adverse deviations in rainfall from the mean. An example for the calculation of premium subsidies is given in appendix 1. Results obtained using formula 5 are given in table 3.

The coefficient of variation of revenue with and without insurance is given in table 4. Results clearly show that the relative risk decreases with insurance versus without insurance. There is a marginal decrease in relative risk under a fair insurance outcome when compared to the loaded insurance outcome. The difference in the coefficient of variation of revenue between monthly indices (June, September, and October have higher relative risk than July and August) provides opportunities for swapping risk between months. The payment percentages between months are distributed within a smaller region.

A farmer may not be concerned about excess rainfall, while he wants to protect against revenue loss because of low rainfall. On the other hand, a grain handler will be more concerned about excess rainfall as it will lead to grain spoilage and storage losses. The financial institutions might want to hedge their portfolio of crop loans against default. Rainfall call and put options can meet this demand. Put rainfall options would be appropriate for a farmer who wants to protect against drought and call rainfall options would be appropriate for a farmer who wants to protect against flooding. Price of a unit of rainfall derived in the premium subsidy calculation is used here. The premium charged for the call and put options and also for swaps is given in table 5.

The payout structures of the call and put options and for the swaps are shown in figures 1 to 10. The premium paid by the insurer for a swap is less than the premium for a pure put or call option.

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Conclusion

A high correlation between revenue loss and rainfall motivated interest in rainfall based insurance products in recent years. The widespread availability of reliable data for long periods makes it attractive to private insurers and reinsurers and helps developing countries explore both domestic and international markets for risk sharing. Rainfall based indices reduce moral hazard and adverse selection and also avoid the problem of an extensive margin. The rainfall insurance also faces basis risk. A high correlation between the index and the individual's risk is important for reducing basis risk. The crop losses due to rainfall tend to be evenly distributed thereby reducing basis risk.

Actuarial premium rates arrived at after accounting for the elasticity of revenue with respect to rainfall is higher than the current crop insurance premium levels. Higher premium rates obtained in this study are consistent with the results obtained in recent studies dealing with rainfall insurance. Higher premium rates discourage participation in crop insurance programmes. One way to get lower premium rates is to use an optimization technique to get the strike and the limit values subject to a constraint on the premium rate. Opportunities for risk swapping between months even within a single locality exist because of the presence of variations in the distribution of rainfall between months. Risk swapping between localities provides opportunities for reducing the premium rates.

Instead of a direct 50 percent premium subsidy to farmers, a countercyclical mechanism was used to calculate the premium subsidy received by the farmers. The premium subsidy received by the farmers was formulated as a function of the adverse deviation in rainfall from the mean.

From the insurer's risk perspective, reinsurance of excess loss over that covered by the insurer is comparable to that of protecting the excess loss by means of options. Since the loss effect of rainfall on output is predominant and tends to have an even distribution, rainfall options might be better suited to protect against excess losses.

Government regulation requires that 5 percent (Rs. 15 billion) of the premium collected by the general insurance companies should be from the rural areas and 10 percent (Rs.240 billion) of the total investment made by these companies should be in the rural areas. Establishing such a rural network proved a difficult task for both Indian and foreign private insurance companies. Availability of rainfall options would be very attractive to these companies as it satisfies both of the regulatory requirements (Parchure, 2002). Financial institutions and investment bankers can hedge their funds on these rainfall options. Since agriculture occupies a significant part of the economy adverse deviation in rainfall can affect the stock markets and traders can protect themselves by hedging their stock with rainfall options. Hence, an effective secondary market can be developed based on the portfolio principle. Although higher premium rates identified in this article may discourage the demand for insurance products, rainfall based crop insurance products are quite attractive to institutional investors and have vast potential in encouraging private participation in crop insurance.

Appendix I

Data for year 2000 are used in this example. The average yield of rice was 2,841 kg/ha, price per kg of rice was Rs. 5.00, and the average revenue obtained was Rs.14,205. If the revenue elasticity with respect to rainfall was 0.6 then the actuarial premium charged will be 13.0 percent (Rs. 1,847 for the month of July). If the direct 50 percent subsidy is considered then the farmer pays Rs. 923.5 as premium and gains an equal amount as income not lost by means of the premium payment.

Here we consider the increasing premium subsidy schedule with increasing adverse deviation of rainfall from the mean. One percent adverse deviation in rainfall causes the revenue to decrease by 0.6 percent. If income were to decrease by 13.0 percent (full premium paid) then the adverse deviation in rainfall should be 21.66 percent from the mean.

21.66 percent adverse deviation in rainfall = Rs. 1847

1 percent adverse deviation in rainfall = Rs. (1847 / 21.66) = Rs. 85.27

For every 1 percent adverse deviations in rainfall from the mean the premium paid by the farmer decreases by Rs.85.27 which is given as subsidy to the farmer. If the maximum subsidy payable is restricted to the total premium collected then the maximum subsidy paid would be Rs.1,847.

REFERENCES

Mahul, O. and D. Vermersch (2003), "Hedging Crop Risk With Yield Insurance Futures and Options," European Review of Agricultural Economics, Vol. 27, No. 2, pp. 109-126.

Martin, S.W., B.J. Barnett and K.H. Coble (2001), "Developing and Pricing Precipitation Insurance," Journal of Agricultural and Resource Economics, Vol. 26, No. 1, pp. 261-274.

Miranda, M.J (1991), "Area-Yield Crop Insurance Reconsidered," American Journal of Agricultural Economics, Vol. 73, pp. 233-242.

Monthly Sub-divisional Rainfall Data (1871-2000), Indian Institute of Tropical Meteorology, Pune, India 2001.

Parchure, R (2003), "Varsha Bonds & Options Capital Market Solutions for Crop Insurance Problems," Paper presented at the 5th Global Conference of Actuaries, New Delhi, India.

Rao, H.C.H., S.K. Ray and K.S. Rao (1988), Unstable Agriculture and Droughts: Implications for Policy, Vikas Publications House, New Delhi.

Skees, J.R., P. Hazell and M.J. Miranda (1999), "New Approaches to Crop Yield Insurance in Developing Countries," EPTD Discussion paper No.55, IFPRI, Washington, DC.

Skees, J.R., S. Gober, P. Varangis, R. Lester and V. Kalavakonda (2001), "Developing Rainfall Based Index Insurance in Morocco," The World Bank, Policy Research Working Paper 2577.

Skees, J.R (1999), "Agricultural Risk Management or Income Enhancement?" The Cato Institute, Vol. 2, pp. 4-9.

Turvey, C.G (1999), "Weather Insurance, Crop Production, and Specific Event Risk," Paper presented at the annual meetings of the AAEA, Nashville TN.

Venkat N. Veeramani, Graduate Research Assistant, Department of Agricultural Economics, University of Kentucky.

Leigh J. Maynard, Associate Professor, Department of Agricultural Economics, University of Kentucky.

Jerry It. Skees, H.B. Price Professor of Agricultural Policy, Department of Agricultural Economics, University of Kentucky.

Table 1: Historic Monthly Rainfall Descriptive Statistics

 Coefficient
 Mean Standard of
Months (mm) Deviation Variation (%) Skewness

June 88.30 41.69 47.22 0.97
July 132.49 46.95 35.43 0.85
August 134.38 48.93 36.41 0.56
September 151.66 57.66 34.61 0.48
October 213.35 109.28 51.22 0.28

 Max. Min.
Months Kurtosis (mm) (mm)

June 0.82 25.2 239.7
July 1.35 46.8 315.5
August 0.41 28.5 292.0
September -0.24 31.6 322.9
October -0.59 12.7 476.3

Table 2: Insurer's and Reinsurer's Premium for Individual Months for
Different Revenue Elasticity (Re) Levels

(Numbers are in percentages)

 Insurer Premium

 Fair Loaded RE RE RE

Months (0.6) (0.5) (0.4)

June 29.9 39.7 23.8 19.8 15.9
July 12.9 17.2 10.3 8.61 6.89
August 11.8 15.9 9.5 7.95 6.36
September 32.3 42.9 25.7 21.4 17.1
October 32.4 43.1 21.5 21.5 17.2

 Reinsurer Premium

 RE RE RE

Months (0.6) (0.5) (0.4)

June 11.35 10.32 9.10
July 4.34 4.05 3.58
August 4.95 4.42 3.80
September 13.54 11.93 10.07
October 13.13 11.47 9.80

Table 3: Decrease in Premium Paid by the Farmer for 1 Percent Adverse
Deviation of Rainfall From the Mean

(Numbers are in Rupees)

 Revenue Revenue Revenue
 elasticity elasticity elasticity
Month of 0.4 of 0.5 of 0.6

June 26.76 29.90 33.05
July 20.32 22.57 24.83
August 22.56 24.99 27.42
September 23.13 25.87 28.62
October 35.29 39.85 44.41
Average 25.61 28.64 31.67

Table 4: Payment Percentage and Coefficient of Variation (CV) at
Different Revenue Elasticity (RE) Levels

(Numbers are in percentages)

 Payment CV of
 Percentage revenue

 RE RE RE RE RE RE
 (0.6) (0.5) (0.4) (0.6) (0.5) (0.4)

Revenue Without -- -- -- 49.99 49.99 49.99
Insurance
Fair Insurance -- -- -- 20.91 20.68 19.86
Revenue With 13.01 10.80 8.67 20.10 19.95 19.81
Insurance

Month Wise

June 13.51 11.26 9.01 35.12 34.45 33.82
July 9.70 8.08 6.46 20.31 20.32 20.14
August 10.44 8.70 6.96 22.14 22.02 21.89
September 11.78 9.80 7.85 35.72 34.98 34.28
October 19.61 16.30 13.07 32.12 31.36 30.64

Table 5: Premium Charged for Call, Put and Swap for
Different Monthly Options and Revenue Elasticity (RE) Levels

(Numbers are in Rupees)

 RE-0.4 RE-0.5

Months Put Swap Call Put Swap Call

June 497.66 352.57 78.15 556.22 394.05 87.34
July 211.24 1386.86 13.70 234.76 199.19 15.22
August 254.99 223.93 9.36 282.67 244.36 10.38
September 256.17 185.34 97.88 152.70 160.57 109.33
October 151.56 217.35 475.59 171.19 366.45 537.18

 RE-0.6

Months Put Swap Call

June 614.62 435.42 96.51
July 258.14 228.34 16.74
August 309.90 272.15 11.38
September 317.09 229.41 121.16
October 190.72 273.51 598.48