Alternativas teóricas

The modelled results for Enugu are shown in Figure A4.18. Over the 30-year period 1981 to 2010 there would have been a total of 5 modelled contract payouts relating to excess rain or a frequency of 1 payout in every 6 years. To begin with there would have been a sowing failure payout in 2001 due to the very high rainfall in the first dekad of 171 mm or considerably above the 135 trigger threshold resulting in an indemnity of Naira 24,000. This is followed by one full Phase 1 Germination failure payout of Naira 24,000 in 1997, one Phase 2, Vegetative stage maximum payout of Naira 30,000 and finally two Phase 3 flowering and yield formation excess rain payouts in payouts in 1984 and again in 1995 when a maximum payout would have been made. The average pure loss cost or burning rate is 8.6% for this example.

Similar modelled results are obtained for the excess rain contracts for maize in Kaduna, Cross River (Calabar) Lagos (Ikeja) namely a high number of modelled excess rainfall claims based on the accumulated per phase rainfall data.

The major drawback of this excess rainfall analysis for Enugu maize is that there is (1) no correlation at all between the cumulative excess rainfall payouts and the WRSI calculated optimal yields over the 30 year period and (2) there is no correlation between excess rain payouts and the actual state-level time-series yields for maize grown in Enugu from 1994 to 2010. In other words, if one were to offer a three-phase cumulative excess rainfall cover in Enugu, it is possible

that the payouts triggered by the rainfall index may have no correlation whatsoever, with maize crop yield and revenue losses on the ground. (Figure 4.19).

Similar modelled results are obtained for the excess rain contracts for maize in Kaduna, Cross River (Calabar) Lagos (Ikeja) namely, a high number of modelled excess rainfall claims in each of the phases based on the accumulated per phase rainfall data. However, the modelled results are not deemed safe to recommend the design of maize excess rainfall contracts on this basis. The finding that excess rain events as measured by rainfall exceeding 50 mm in a 24 hour period are very frequent during the growing season suggests that future research should be conducted using this definition of excess rain either in conjunction with a cumulative rainfall contract or by itself.

Figure A4.18. Enugu Maize: Cumulative per Phase Excess Rainfall Contract Payouts

Source: Authors

Figure A4.19. Enugu Maize: relationship between WRSI calculated yield potential for maize and actual state-level annual yields maize.

4.9.

Pricing of Weather Index Insurance Contracts

In general the premium charged for a weather index contract can be broken down as follows:

Original Gross Premium = Expected Loss + Risk Margin + Administrative Costs

A detailed description of the issues and methods for pricing weather index insurance contracts is included as Module 7 of the ARMT-IRI WII Training modules and can be downloaded from the FARMD website as noted in the introduction to this annex. The World Bank’s pricing methodology is termed the “Return on Risk” (ROR) approach to WII pricing.

The expected loss is calculated as the pure loss cost rate and which may be based on historical burning cost data only, for example for the 30 years of rainfall data which has been modelled for Nigeria. Alternatively monte-carlo simulation may also be employed to extend the analysis of the average loss cost to any number of specified iterations – for example 10,000 iterations (years). According to the level of confidence the contract designer has in the underlying weather data, including factors such as the number of years and percentage missing data, standard procedures are outlined in the World Bank training materials to adjust the expected loss by fitting confidence limits to the estimated parameter (the average loss cost) and correcting the number of year’s data for missing values. The output is termed the Adjusted Expected Loss (AEL).

For the purposes of adding a security margin to cover both infrequent, but potentially catastrophe weather event years a standard procedure is to calculate the 1 in 100 year expected probable maximum loss (again using monte carlo simulation) and according to the risk carrier’s (underwriter’s) perception of risk and his required rate of return to accept this risk, a percentage of the PML value is then taken as a security load. It is also fairly common for underwriters to accept the security load as a contribution to their expected profit margin

The technical rate is defined by: Technical Rate = AEL + Security Load

As a guideline, the final technical rate after addition of the security load may often be double the average pure loss cost rate.

In order to derive the final commercial premium rate (or Original Gross Premium rate), underwriters will gross-up the Technical Rate by their A&O (acquisition and own operating costs) which include brokerage and the companies fixed and variable expenses for administering the WII business. A&0 expenses will commonly add between 25% and 35% percentage points to the Technical Premium rates. If local taxes such as insurance stamp duty and VAT (Value Added Tax) are levied on crop insurance, then the A&O loadings will be correspondingly higher.

Given the very poor fit of the maize and rice rainfall deficit contracts modelled for the selected stations in Nigeria, it is not appropriate to calculate illustrative commercial premium rates applying to these rainfall deficit prototype contracts. Local interest groups should, however, be very aware that rainfall deficit WII contracts commonly cost at least 7.5% to 10% and premium rates of 15% and more my apply in high drought risk situations.

Appendix 4.1: Note on WRSI Model

The FAO Water Requirement Satisfaction Index (WRSI) establishes how production of a crop grown in a microclimate can be indexed to rainfall amount and distribution. A description follows of the WRSI model and its inputs and assumptions.