Zambia FISP - Proposed Indexes Report, 2021/22
1. Overview
This report provides details on the proposed structure of the FISP Weather Insurance Index for the 2021/22 season. It is not an official calculation of index payouts. The accuracy and correctness of calculations and data for the index payouts are the responsibility of the financial partners in the FISP project. Please notify us of any errors found in this report or in accompanying datasets.
The structure and parameters of this proposed index reflect input from several key stakeholders. The Ministry of Agriculture was responsible for collecting and reviewing the farmer data against which the index was calibrated, and also gave input on the payout frequency and weighting of the index. Additionally, a FISP Design Team - composed of technical experts from MoA, the World Food Programme, Mayfair and ACRE - were responsible for reviewing the timing of the index windows in each district.
For any questions about this report, please contact Daniel Osgood, deo@iri.columbia.edu.
2. Index Structure and Processes
2.1 Perils
The specific perils covered by the index depend on the part of the country. The FISP design team worked with IRI to designate three “Zones” of coverage:
- Zone 1 focuses on drought as the main hazard, and excess rainfall as the secondary hazard,
- Zone 2 focuses on excess rainfall as the main hazard, and drought as the secondary hazard, and
- Zone 3 has equal amounts of coverage for both drought and excess.
For a full list of the Zone designations, see Section 4.
2.2 Indexes
Focusing on these two dominant perils - drought and excess rainfall - a standardized index is calibrated to the rainfall patterns and cropping calendar for each district. The index is optimized to provide the best protection for each district while being as standardized and homogeneous as possible.
The index is designed with the goal of providing a meaningful payout for the worst 10% years of the the historical dataset for the main hazard in that Zone, and the worst 5% of years for the secondary hazard in that Zone. Based on input from the design stakeholders, the design goal was to balance the maximum payouts received with a reasonable payout frequency, to arrive at a point where increases in one would lead to likely unacceptable decreases in the other.
For a typical district, the proposed index would have paid out about 1 year out of 8 (5 payout years out of the last 40) and have a maximum payout of approximately 1000 ZMK in the past 40 years (assuming a maximum liability of 2000 ZMK, a minimum payout of 200 ZMK, a premium of 100 ZMK and a loading cost of 30%). This proposed index would have an estimated average payout of approximately 65 ZMK, with zero payout years included in the average (details on these pricing estimates in Section 3).
This payout frequency was determined after consultation with the MoA on the optimal balance between the regularity and size of index payouts. More details on the scenarios considered by the MoA can be found in this document: Zambia FISP Pricing Scenarios
The index is triggered using the CHIRPS satellite estimates of rainfall, freely available from IRI or NOAA, For each zone, the satellite information for the 10km x 10km pixel is averaged over the level 2 administrative boundaries, reflecting the rainfall for that district.
To address the key times of the season, 4 separate index windows have been developed for each peril: An early and a late simple sum window, and an early and a late rolling average window. Calculation of these windows are described in greater detail in Section 3. The timing of the windows in each district have been tuned to reflect that area’s climatology and cropping patterns. The specific coverage dekads for each location and each window can be found in Table 4.2 further down in the report.
For each location, the rainfall is spatially averaged over the administrative boundary and the indexes are calibrated to the crop calendars and rainfall amounts in the location, and are based on a scientific understanding of crop and water stress models. The start and end of each index is set by considering the following:
- Local expert opinion through the use of the index optimization tool
- Precision of satellite measurements during the window
- Rainfall patterns during the window with the greatest risk for crop production
- How absence / excess of rainfall during the window agrees with actual on-the-ground crop loss, as reported by farmers
- Output of crop and water stress models
2.3 Validation
Below are the main strategies followed to evaluate the performance of the indexes:
- Agreement of payout with farmer design team reported “bad years” and expert reviewed bad years
- If there would have been a payout in the severe regional drought years
- Agreement of index with MoA provincial yield data when available
- Local and expert feedback
2.4 Data Sources
The indexes are triggered based on the UC Santa Barbara Climate Hazards center InfraRed Precipitation with Station (CHIRPS) Dekadal data. The official source of this data, and its documentation are at the URLs below
https://data.chc.ucsb.edu/products/CHIRPS-2.0/
https://www.chc.ucsb.edu/data/chirps
The IRI Data Library also serves this data set at the URL below:
http://iridl.ldeo.columbia.edu/SOURCES/.UCSB/.CHIRPS/.v2p0/.dekad/.prcp/
Data can be downloaded for a specific pixel by replacing the coordinates with the appropriate lat/lon in the URL below:
http://iridl.ldeo.columbia.edu/SOURCES/.UCSB/.CHIRPS/.v2p0/.dekad/.prcp/dataselection.html
3. Index Calculation
Calculating the index payouts involves three steps: 1) Computing trigger values over each window, 2) computing combined indices for drought and excess from each window, and 3) normalizing the sum of payouts from the combined indices to meet a budget.
3.1 Computing Triggers
Index triggers are calibrated with the goal of providing a meaningful payout for the worst 10% years of the the historical dataset for the main hazard in that Zone, and the worst 5% of years for the secondary hazard in that Zone.
In trigger and exit calculations, missing data is filled with historical averages for that day. Unless specified otherwise, any supplementary precipitation data provided with this report uses this missing data protocol.
There are two types of windows: sum and rolling average. For sum windows, the formula below determines the payout for any maximum liability when index values are between the trigger and exit.
Payout = (1 – ((Capped Rainfall Sum Over Window – Exit) / (Trigger – Exit)))*Max Liability
While for rolling average windows, the formula is:
Payout = (1 – ((Min(2 Dekad Rolling Average of Rainfall Over Window) – Exit) / (Trigger – Exit)))*Max Liability
3.2 Computing Drought and Excess Combined Indices
After all windows’ 0-1 index values are calculated, combined sub-indices are calculated for drought and excess. These sub-indices are a weighted average of the payouts in each window. The weights of each component are detailed in Table 4.5. These weights were determined by considering both the correspondence between each window’s payouts and farmers’ reported bad years as well as feedback from the MoA.
The drought and excess sub-indices have equal weight in the final combined payouts - Zones only differ in terms of the payout frequency of drought vs excess, not their weights in the combined index.
Before monetary payout values are computed, a final normalization step is applied: the combined payouts are adjusted such that the top 10% of payouts are retained for the dominant hazard, and the top 5% are retained for the secondary hazard. This step is done to make the final frequency of payouts more predictable.
3.3 Computing Potential Payout Monetary Values
Finally, we assign monetary values to the payouts. This step is done for illustrative purposes only, and should not reflect a final pricing decision.
We begin with an overall “payout budget”, representing the maximum cumulative amount per farmer that could be paid out over the historical record of the data (40 years).
Our 0-1 combined index values for drought and excess are added together (equally weighted, as described above), then those values are normalized such that their sum equals the payout budget. For example, if there is only 1 payout in history, the entire payout budget will be placed on that year. If there are two equally sized payouts in history, half the payout budget will be placed on each. If there is one 100% payout and one 50% payout, 2/3rds of the payout budget will be placed on the first year and 1/3rd on the second - and so on.
In this illustration, payouts are capped at the maximum liability, 2,000 ZMK. Any payouts less than the minimum of 200 ZMK are set to 0.
4. Full Index Parameters & Results
4.1 Historical Payouts
4.1.1 Combined Index Payouts (ZMK Per Farmer)
4.1.2 Combined Index Summary Statistics
4.1.3 Raw Payouts by Window
4.2 Index Windows
4.2.1 Windows, in Decads
4.2.2 Decad Reference Table
4.3 Index Triggers and Exits
All values are expressed in mm of rainfall unless otherwise noted.