Zambia FISP: Pricing Scenarios and Feedback, 2021/22
0. Background
This report provides details on the proposed structure of the FISP Index for the 2021/22 season, and asks for MoA feedback on key points. 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.
For any questions about this report, please contact Daniel Osgood, deo@iri.columbia.edu
0.1 Key Decision Points
In any index insurance project, there are a couple key decision points that must be considered:
Which times of year and which hazards should the insurance cover? Since budgets are limited, index insurance tends to focus only those risks which are most critical for farmers’ harvests. For instance, some places may be more vulnerable to a late onset of rainfall than an early end, or more vulnerable to an excess of rainfall than drought.
- The FISP technical design team has worked to define many of these parameters - described in Sections 1 and 5 - for each district in the country.
- One remaining choice is how to weigh each component of the index in the final calculation of payouts, discussed in Section 2.
How should the insurance payout budget be allocated over time? We know that each farmer pays a fixed premium per year, and that in the long term, the sum total of insurance payouts cannot exceed the amount of money collected from premiums. Knowing this, there are many potential ways to allocate the payout funds. Consider the following illustrative example:
(NB - this example is only meant to illustrate the type of decision faced. It does not reflect the actual FISP index parameters, which are discussed in Section 1.)
A project collects 100 ZMK in premiums from each farmer.
We have 10 years of data on weather conditions from the project.
Thus, considered over a 10-year horizon, the total payouts for each farmer cannot exceed 100*10 = 1000 ZMK.
We will assume for this example that the maximum liability (highest possible payout) of the index is also 1000 ZMK, although it could potentially be lower.
One way to allocate that 1000 ZMK would be to pay it all out (100% of the maximum liability) in the single worst year:
- Another option would be to allocate 500 ZMK (50% of the maximum liability) over the top two worst years:
- A third option would be to spread it out over the top 5 worst years (i.e. any year that was below average), but only pay 200 ZMK (20% of the maximum liability) in each of those years:
This document presents several such allocation scenarios for the proposed FISP national insurance index, and is meant to help the reader work through the implications of the choice.
0.2 Basis of Document
This document presents several payout frequency scenarios for the FISP insurance index, 2021/22 season.
The scenarios presented draw from the work of the FISP technical design team, who have worked with MoA and IRI to determine some key parameters of the index - namely the input datasets, the timing of the index windows in each district, and the zones of coverage for each hazard - in advance. These parameters are described in greater detail in Section 5.
The bad harvest year data against which the index was evaluated also comes from an MoA / WFP / IRI collaborative exercise, in which MoA officers visited almost 1,000 camps across the country for focus group discussions with farmers.
Per guidance from MoA, the premium which farmers are to pay for the insurance product will remain the same in 2021/22 - 100 kwatcha. The sum insured (aka maximum liability) is 2000 kwatcha, and the minimum payout in a year is 200 kwatcha.
0.3 Outline
Taking these inputs as a guide, Section 1 of this document presents several potential index payout frequency scenarios with similar long-term cost.
In the second part of the document, we present suggested weights for each component of the index, given a payout frequency scenario from Section 1. These weights are based on the relative importance of each hazard to farmers, as estimated from the data.
For each of these decision points - payout frequency and index component weights - we ask for your feedback on the best way forward. There are feedback forms embedded in this document, which we ask you to complete as you read through it.
The rest of the document presents details of the proposed index. In the third part of the document, we summarise how the long-term average payout of the index is distributed geographically, given a representative payout scenario from Sections 1 and 2.
In the fourth part of the document, we summarise the historical distribution of potential payouts from the index, drawing from the same scenario as Section 3. Using this, we can explore how diversified the proposed risk portfolio appears to be.
The fifth and final part of the document presents full, downloadable tables of the index payouts and parameters (windows, triggers, exits) for every district.
1. Payout Scenarios
1.1 Financial Constraints
The premium farmers pay each year is 100 kwatcha, the sum insured (maximum payout) for the index is 2000 kwatcha - the cost of the FISP inputs - and the minimum payout is 200 kwatcha. Taking these parameters as given, any financially viable payout scenario for the index must not exceed the amount of money the product is bringing in.
For example, if we were to evaluate the index over the last 40 years (approximately the length of the satellite record), then the total payouts for each farmer over that period must not exceed 4,000 (100 ZMK premium * 40 years) kwatcha.
We also want to account for loading cost in our payout budget. Empirically estimating the loading cost is a complex subject that requires knowledge of the national distribution of payouts over time - discussed further in Section 4. For the time being, we will assume a loading cost equal to 30% of the premium (30 ZMK) - approximately the same as last year’s loading - for the following scenarios. If the premium paid by farmers cannot exceed 100 ZMK, the loading cost must be absorbed by a reduction on the payout budget. This means the effective payout budget for these scenarios is 2,800 kwatcha (100-30*40).
There are many potential payout scenarios that could meet these financial constraints. For instance, we could allocate our total 40-year payout budget on a single year when we knew there was catastrophic risk. Or, we could spread our budget over smaller payouts in a number of years, letting farmers cover any additional risk themselves - or through complementary assistance programs like savings groups.
1.2 Budget Allocation Scenarios and Risks Covered
The specific risks covered by the index depend on the part of the country. The FISP technical 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 map of the Zones, see Section 3. For a full list of Zone designations, see Section 5.
This section presents three scenarios for how to allocate payouts:
- The first scenario represents a large proportion of the payout budget allocated to just a few risk years - corresponding to 2 years out of the last 40 being covered for the main hazard in each Zone.
- The second scenario represents a moderate proportion of the payout budget allocated to more risk years - corresponding to 4 payout years out of 40 for the main hazard in each Zone, and 2 years out of 40 for the secondary hazard.
- Finally, the third scenario represents a small proportion of the payout budget allocated to many risk years - corresponding to 8 payout years out of 40 for the main hazard in each Zone, and 4 years out of 40 for the secondary hazard.
For each hazard, both the early and late season are covered, with a separate coverage window for each. The timing of the windows in each district have been tuned by the FISP Technical Team to reflect that area’s unique climate and cropping practices. For each hazard, both simple sum (targeting specific parts of the season) and rolling average (targeting dry spells over any point in the season) windows are offered.
1.3 Scenarios Visualized
The following graphs present the historical payouts of the index under each coverage scenario, for an average farmer in a representative district from each Zone.
For discussion purposes, we also consider scenarios where the premium is increased to 150 ZMK and the effective payout budget, including loading, is 4,200 ZMK.
NB: The scenarios pictured assume each hazard is weighted according to the default index weights, described in the following section.
Zone 1 Sample - Drought-Focused, 100 ZMK Premium
Zone 1 Sample - Drought-Focused, 150 ZMK Premium
Zone 2 Sample - Excess-Focused, 100 ZMK Premium
Zone 2 Sample - Excess-Focused, 150 ZMK Premium
Zone 3 Sample - Both Drought and Excess, 100 ZMK Premium
Zone 3 Sample - Both Drought and Excess, 150 ZMK Premium
Decision Point #1 - Which Scenario do you believe best balances frequency of payouts with level of coverage?
Please indciate which you would prefer in the form below. Your feedback will inform the final design of the index.
2. Determining Weights of Index Components
2.1 Types of Index Windows
In addition to the payout frequency, there is a choice of how to weigh each component of the index in the payout calculation (described fully in Section 5). Weights should reflect how important each period of the season is to farmers’ harvest.
As mentioned in Section 1, the new FISP index offer two types of windows: simple sum, and rolling average. Each has its advantages and disadvantages.
A simple sum over the window is best for capturing extended droughts (example #1 below). If rainfall is consistently low over the window, a simple sum will pick this up. However, it may not trigger for brief cessations of rainfall.
A rolling average is somewhat more complex. It has two steps: First, average rainfall is calculated over each 20-day period in the window. Then, the lowest value out of those rolling averages is identified. This is what is used to calculate the trigger.
A rolling average is suited for identifying temporary pauses, late onsets or early stops of rainfall (scenario #2 below). However, it may not trigger for a window in which rainfall was consistently somewhat below average.
Both types of windows can be combined, and can act as complementary to one another. Additionally, multiple windows can be placed throughout the season, to cover key times of vulnerability.
It is important to link the choices regarding window timing and calculation to the key risks which farmers report. These may vary from place to place.
Window Example #1 - Extended Drought:
Window Example #2 - Brief Dry Spell:
2.2 Suggested Weights
By default, each window - early season drought, late season drought, early season excess, etc. - is weighted according to how well its payouts match with farmers’ reported risk years. Components with a greater degree of matching are given proportionally greater weight in the index.
The following tables present the suggested weights for each Zone based on the above method. These could be further revise to reflect the subjective importance of each hazard.
Please note that these suggested weights are derived from a statistical model, which has its limitations. For example, if two windows tend to cover the same years, the model will arbitrarily choose one and not the other. Thus, it is important to have a common-sense review of these suggestions, and tie the final choice of weights to expert judgment about which times of the season are most important.
Decision Point #2 - How should each window be weighted in the calculation of the index?
Please indciate which you would prefer in the form below. Your feedback will inform the final design of the index.
The following sections illustrate how the payouts from the proposed index would be distributed, both geographically (section 3) and over time (section 4), and what its parameters would be (section 5).
These sections assume we follow payout frequency Scenario 2 and use the default weights for each index component. These assumptions will be updated following MoA feedback.
3. Geographic Distribution of Payouts
Given a payout frequency scenario discussed in Section 1 and component weights discussed in Section 2, we can visualize the geographic distribution of long-term average payout. In general, we should expect areas to have similar average payouts, particularly those with similar climate patterns.
3.1 Average Payout Frequency Distribution
The following graph shows the frequency distribution of average payout over districts in each zone:
100 ZMK Premium
150 ZMK Premium
3.2 Average Payout Distribution Mapped
The following map shows the same data plotted geographically:
100 ZMK Premium
150 ZMK Premium
4. Historical Distribution of Payouts
4.1 Motivation
Finally, we can explore the historical distribution of potential payouts for our chosen payout scenario. We would like our insurance product to have a diversified portfolio of risks - that is, when one Zone presents a large payout, the others should present low or no payouts.
The diversification of the insurance risk portfolio affects the loading cost. If payouts across the country tend to all fall on the same years, the product will have a higher tail risk; that is, the insurer has to hold a larger amount of capital to cover the biggest probable payouts, and the loading cost should be higher. In contrast, if payouts tend to be distributed in different years in each Zone, the insurer has to hold less capital in reserve, and the loading cost should be lower.
As an illustration of the benefits of diversification, we can consider the following stylized example:
- The maximum liability for each farmer is 2000 ZMK, and the pure risk premium (not including loading) is 100 ZMK.
- Let us assume that the index makes one full payout for each farmer once in history, and 0 in every other year.
- Let us also assume that each of the three Zones has the same number of enrolled farmers.
- The loading cost is estimated as the difference between the average payout and the highest payout possible, times the cost of borrowing (assumed to be 5% here):
(Highest payout - average payout)*0.05
- If all Zones pay out during the same year, the highest possible payout, averaged over the Zones, is:
(2000 + 2000 + 2000) / 3 = 2000 ZMK
Loading cost = (2000 - 100)*0.05 =
95 (95% of pure risk premium)
- If two of the Zones pay out during the same year, the highest possible payout is:
(2000 + 2000 + 0) / 3 = 1333 ZMK
Loading cost = (1333 - 100)*0.05 =
~61 (~60% of pure risk premium)
- If each Zone pays out in a different year, the highest possible payout is:
(2000 + 0 + 0) / 3 = 666 ZMK
Loading cost = (666 - 100)*0.05 =
~28 (~30% of pure risk premium)
- The actual calculation of loading cost is more complex, but based on the same principle. To approximate how diversified our proposed index would be, we can look at the historical distribution of payouts over each Zone and year - pictured below.
4.2 Plot of Historical Payouts
These calculations are weighted by the total number of participating farmers in each district, as estimated from the FISP 2020/21 program data.
100 ZMK Premium
150 ZMK Premium
4.3 Estimated Total Liability
Finally, we can estimate what the total liability for the entire FISP project would have been in each year, and compare this to the estimates from the current FISP index. NB: As in 4.2, all of these estimates are based off of the total number of enrolled farmers from 2019/20. This means that some of the estimated historical payouts shown here are not exactly equal to those years’ actual payouts.
Pre-2019/20 estimates are calculated using the index’s previous sum insured and minimum payout values: 1,700 ZMK and 85 ZMK, respectively.
The estimated loss ratio is 63% for the proposed index, 100 ZMK premium version, 59% for the 150 ZMK premium version, and 48% for the current FISP index.
For reference, the actual payouts for 2018/19, 2019/20 and 2020/21 are 93,519,016 ZMK, 27,594,922 ZMK and 4,105,358 ZMK, respectively.
5. Full Index Details
All of the figures presented in this section are based on the payout scenario and weights chosen above, and a 100 ZMK premium.
5.1 Historical Payouts
For a description of how the raw (0-1 scale) payouts are used to generate the combined payout, see section 5.5.
5.1.1 Combined Index Payouts (ZMK Per Farmer)
5.1.2 Raw Payouts by Window
5.2 Index Windows
5.2.1 Windows, in Decads
5.2.2 Decad Reference Table
5.3 Index Triggers and Exits
All values are expressed in mm of rainfall unless otherwise noted.
5.4 Rainfall Data
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
5.5 Index Payout Formula
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.
5.5.1 Computing Triggers
The index has multiple windows - described in Section 1 - each of which is designed to cover a different peril and time of the season.
For each window, the start and end times for each district (shown in Table 5.2.1) are 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.
For each location, the rainfall is spatially averaged over the administrative boundary. For the proposed indexes, the exits are set with a full loss calibrated to 90% of the worst rainfall event observed. The trigger is 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 (see Section 1 for more details on this).
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
5.5.2 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, where the weights are defined according to Section 2.
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.
5.5.3 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” - described in Section 1 - 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, 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.
Payouts are capped at the maximum liability, 2,000 ZMK. Any payouts less than the minimum of 200 ZMK are set to 0.