Index insurance: contract designIndex insurance: contract design

Daniel Osgood (IRI)deo@iri.columbia.edu

Material contributed by:

Miguel Carriquiry, Ashok Mishra, Nicole Peterson, Megan McLaurin

The International Research Institutefor Climate and Society

Cooperative Design

Cooperative design steps

• Stakeholders determine– Premium constraint– Payout frequency target

• Set initial guess for optimizer– Pursue strategies that target alternate risks (eg sowing vs flowering)

• Computer optimization (“tuning”):– Using performance measures, WRSI based loss– Optimize upper triggers to:

• Minimize variance of (losses - insurance payments)• Subject to specified maximum insurance price

• Compare contracts performance against information sources looking for contract strengths and vulnerabilities

• Adjust parameters to round numbers so that client does not get misimpression that design information is higher accuracy than it is

• Communicate results with stakeholders

– Correct years for correct reasons– Is coverage what clients demand?

• Adapt contracts and models

• Typically trade-offs: Must sacrifice something for gain

• Iterate

Starting point—initial parameters• Sowing parameters

– WRSI model assumptions, farm, expert input• Sowing window beginning, end• Sowing trigger

– Cost information• Failed sowing payout

• Phase parameters– Number of phases

• Balance crop and climate seasonal phases

– Beginning, end of each phase• WRSI assumptions, farmer, expert input

– Upper trigger• Deductible based on WRSI• Investigate targeting alternate drought risks

– Exit• Financial constraint for payout condition

– Maximum payout per phase• Cost, loss information

• Maximum total payout– Cost, loss information, financial constraints

Contract Performance Evaluation• For a given premium

How well does contract reduce risk?– Risk = Variance of hypothetical farmer with

• Yield loss driven reductions in revenues• Insurance payouts

– When comparing contracts with same premium, better performing contract has lower:

• Var(Losses – Insurance payouts)

– Computer optimizer• Minimizes variance subject to price constraint • Adjusts upper triggers: Balances deductibles between phases to provide most risk reduction for price

• Other important metrics– Correlation

• Useful measure • Not for design algorithms--correlation is not identical to risk faced

– Client’s perspective: Are insurance payments in critical years?

• Useful, but not enough of a criterion to identify optimum• Because of price and pay frequency constraints, typically more

tough years than payments• So design deductible to find which bad years can be covered

most cost effectively

Tuning Contract parameters• Upper trigger (deductible)

– Computer optimization– Payout rate constraint– Evaluate alternate strategies

• Exit– If premium low enough, can increase to increase

coverage without changing payout rate

• Phase timing– Adjust to target risk more effectively or to address

client demand

• Sowing window, condition– Adapt to reflect season timing, risks reported, price,

payout constraints

• Note– If farmers are farming, risks must be reasonable– If insurance is not, revisit information on practices

Losses

• Insurance – Not for 1% reduction from best year in history

– For worst year out of 5 or 10

• Use appropriate loss proxy– Role: indicator to balance protection between

phases to most cost effectively reduce risk

– Absolute magnitude • Only changes weighting between larger and

smaller losses

– Losses, not small reductions from best year

• Generate proxy– Zero for good years

– Approximate magnitude of cash losses• Tune magnitude to weigh optimizer to reward

higher/lower payout frequencies

Parameter iteration

• Upper trigger– Deductible– Payout frequency– Type of protection– Optimizer

• Exit– Does not impact freq.– Increases coverage, price– Catastrophe

• Phase length, timing– Target vulnerabilities– If too tight may be out of sync– Trade off: Split up/long

• In general, contract – Mostly determined by cost, payout

constraints– Want most cost effective protection

Phase Payout function 2006

0

25

50

75

100

125

150

175

200

225

250

275

300

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Kwacha

Mv

ula

Ra

infa

ll (

mm

)

1970 1980 1990 2000

020

0040

0060

00Chitedze Groundnut Loss based on Daily WRSI, seasonal KY

years

loss

LossPayLoss-Pay+E[Pay]

1992 1994 1996 1998 2000 2002

050

010

0015

0020

0025

0030

00Chitedze Groundnut Historical Loss

years

loss

LossPayLoss-Pay+E[Pay]

1970 1980 1990 2000

020

0040

0060

00Chitedze Groundnut Simulated

years

loss

LossPayLoss-Pay+E[Pay]

• Upper triggers: 35 35 220 • Exits: 30 30 20

• Price rate (target, actual): 0.07, 0.083

Pearson’s Correlation

Years Payouts % Payyears in worst 1/4

WRSI 0.54 45 9 78

Historical Yields (all Groundnut)

0.66 12 4 50

Crop simulation

0.30 43 8 50

Ranking of losses and payouts

RANK YEAR LOSS PAYOUT? [1,] 1995 7641.140 1 [2,] 1973 6542.680 1 [3,] 1966 6324.398 0 [4,] 1996 6315.617 1 [5,] 1990 5903.817 0 [6,] 1984 5660.633 1 [7,] 2005 5598.026 1 [8,] 1970 4929.469 1 [9,] 1992 4904.982 0[10,] 1997 4459.438 1[11,] 1968 4400.516 0 [12,] 1969 4296.916 1 [13,] 1980 4235.219 0 [14,] 1994 4136.128 0 [15,] 2004 3921.972 0 [16,] 1979 3513.749 0 [17,] 2000 3399.898 0[18,] 1983 3399.299 0[19,] 2001 3367.294 0[20,] 2006 3347.076 0[21,] 2002 3218.283 1[22,] 1967 3070.731 0[23,] 1962 0.000 0[24,] 1963 0.000 0[25,] 1964 0.000 0

[26,] 1965 0.000 0[27,] 1971 0.000 0[28,] 1972 0.000 0[29,] 1974 0.000 0 [30,] 1975 0.000 0[31,] 1976 0.000 0[32,] 1977 0.000 0[33,] 1978 0.000 0[34,] 1981 0.000 0[35,] 1982 0.000 0[36,] 1985 0.000 0[37,] 1986 0.000 0[38,] 1987 0.000 0[39,] 1988 0.000 0[40,] 1989 0.000 0[41,] 1991 0.000 0[42,] 1993 0.000 0[43,] 1998 0.000 0[44,] 1999 0.000 0[45,] 2003 0.000 0

Nicole Peterson, CRED

Insurance Contract developed with Farmers

Stakeholder input drives contracts

• Look for:– Do stakeholders understand contracts?

– Do stakeholders show evidence of negotiating in their own interests?

– Do stakeholders understand basis risk and what is not covered?

– Insightful complaints

• Malawi stakeholders have been very active, driven design– Original CRMG project proposal was for stand

alone Maize Insurance

– Malawi stakeholders proposed groundnut bundle

Some Stakeholders

Malawi Groundnut contract bundle• Farmer gets loan (~4500 Malawi Kwacha or ~$35) for:

– Groundnut seed cost (~$25, ICRSAT bred, delivered by farm association)

– Interest (~$7), Insurance premium (~$2), Tax (~$0.50)– Prices vary by site

• Farmer holds insurance contract, max payout is loansize– Insurance payouts on rainfall index formula– Joint liability to farm “Clubs” of ~10 farmers– Farmers in 20km radius around met station

• At end of season– Farmer provides yields to farm association– Proceeds (and insurance) pay off loan– Remainder retained by farmer

• Farmers pay full financial cost of program• Only subsidy is data and contract design assistance • Partners: Farmers, NASFAM, OIBM MRFC, ICRSAT, Malawi

Insurance Association, the World Bank CRMG, Malawi Met Service, IRI, CUCRED

Exploratory analysis: Hypothetical Historical Payouts of Drought Insurance 2005 Contracts for Groundnuts in Lilongwe, Malawi

0

200

400

600

800

1000

1200

1400

1600

1800

1961 1966 1971 1976 1981 1986 1991 1996 2001

Year

Pay

ou

t (K

wac

ha)

Exploratory Analysis: Standardized Seasonal Rainfall Anomaly Predictions (October) vs Payouts from Groundnut Insurance

0

200

400

600

800

1000

1200

1400

1600

1800

-1.2

-1.1 -1

-0.7

-0.5

-0.3

-0.1

0.0

3

0.1

6

0.2

2

0.2

5

0.3

3

0.4

4

0.5

9

0.6

9

0.8

2

1.1

5

1.4

5

Predicted anomaly (standardized)

Pa

yo

ut

(Kw

ach

a)

Visions for climate risk management

• Malawi farmers– Knew about Enso impacts on precipitation– Would like to adjust practices to take advantage of

seasonal forecasts but are unable to obtain appropriate fertilizer and seed

– We are researching and cooperatively developing packages that provide price incentives, risk protection, and strategic input availability so farmers can take advantage of forecasts

– No ‘historical’ payouts for La Nina years for many stations

– ICRSAT would like to develop seeds to compliment these packages

– Fundamental research on insurance, production, and forecast necessary

– When asked how they adapt to climate variability and change farmers reported that they signed up for the index insurance program.

1985 1990 1995 2000

50000

100000

150000

Non-Hybrid ENSO shifted Land Allocation Based on Historical District Yields

Year

Gross R

evenue (

MK

W)

Enso BasedStandard

Adjusting insurance price with forecast may increase profits

Climatology correlations important• Northern and Southern Malawi

– “opposite” Enso phase response– Location of north-south dividing line challenging to forecast

• But climate info still very valuable for insurance

• Potential for natural hedge– By strategic pooling of contracts from the north and south, total risk can be reduced, reducing costs of

insurance – Pool Kenya with Malawi?

• Negative correlations, forecast potentially very valuable in Central America

306

308

310

312

314

316

318

320

322

324

326

0 10 20 30 40 50 60 70 80 90 100

Percent Lilongwe

Pre

miu

m (

Kw

ach

a)

Forecast issues

• Seasonal forecasts have information • Future: to build system robust to forecasts

– Multi year contracts, contract sale before forecast

– Build contracts that avoid losses using forecast

• Important once pilots grow sufficiently