Session 26 L, Issues in Agricultural Insurance. Moderator: Remi Villeneuve, FSA, FCIA. Presenters: Lysa Porth, MBA, Ph.D. Remi Villeneuve, FSA, FCIA

Transcription

1 Session 26 L, Issues in Agricultural Insurance Moderator: Remi Villeneuve, FSA, FCIA Presenters: Lysa Porth, MBA, Ph.D. Remi Villeneuve, FSA, FCIA

2 Lysa Porth, MBA, Ph.D. Assistant Professor and Guy Carpenter Chair in Agricultural Risk Management and Insurance Warren Centre for Actuarial Studies and Research, Asper School of Business, University of Manitoba, Canada Issues in Agriculture Insurance 2015 SOA Annual Meeting and Exhibit October 11-14, Austin, TX

3 Broadening the Role of Actuaries Agricultural Insurance Importance Actuarial Challenges Current Research Examples

4 Broadening the Role of Actuaries Agricultural Risk Management and Insurance is an important and growing market for the actuarial community. Few actuaries are involved and specialized in this area. Developed significantly over recent years, and is often considered the fastest growing line of business in Property and Casualty companies. Direct global agricultural insurance premiums increasing: US$8 billion in 2005 US$30 billion in 2013

5 Guy Carpenter Research Chair in Agricultural Risk Management and Insurance Warren Centre for Actuarial Studies and Research, I.H. Asper School of Business, University of Manitoba, Canada First of its kind in the world from a combined actuarial and agricultural economics perspective. Jointly funded by: Guy Carpenter & Company ( and Agriculture and Agri-Food Canada ( Increase the pace of innovation. Multi-stakeholder approach. Strengthen public-private partnerships. Specialized research opportunities. Foster the teaching of actuarial students and shape the next generation of actuaries trained in P&C generally, and agribusiness specifically.

6 International Agricultural Risk, Finance and Insurance Conference (IARFIC) Agricultural Economics Statistics Plant Science Actuarial Science Finance Climatology Risk Management Insurance

7 International Agricultural Risk Management and Research Group Optimal Loss Experience Forecasting Weather, Climate, and the Environment Pricing Framework Crop Insurance Pricing Framework Livestock Mortality Insurance Optimal Crop Insurance Risk Transfer Feasibility of Hedging for Risk Management Demand for Agricultural Index-based Insurance. Data Collection, Storage and Analytics

8 Importance of Agricultural Insurance Can help improve the productivity of agriculture. Environment is rapidly changing: more complex agri-supply chain, climatic changes that may be increasing the frequency and severity of natural disasters, and increased price volatility due to changes in market structure and sensitivity. Agricultural insurance is an important part of ensuring long-term stability and growth of the agriculture sector. Facilitating access to credit, Helping to reduce the negative impacts of natural catastrophes, and Encouraging investment in improved production technology.

9 Actuarial Challenges Agricultural sector faces a number of unique challenges regarding insurability. Government Involvement Expected Yields Pricing Self-sustainability Actuarial foundations have become increasingly important to help ensure the long term sustainability of programs.

10 CURRENT RESEARCH EXAMPLE: A Credibility-based Yield Forecasting Model for Crop Reinsurance Pricing and Weather Risk Management Co-Authors: Wenjun Zhu Assistant Professor, School of Finance, Nankai University, China Ken Seng Tan University Research Chair Professor Department of Statistics and Actuarial Science, University of Waterloo

11 A Credibility-based Yield Forecasting Model Forecasting crop yield is critical for agricultural insurance ratemaking. However, in the presence of systemic weather risk, there are many challenges to efficiently and accurately forecast crop yields: Effects of possible climate changes, selecting predicting variables, Restating crop mix, and modeling geographical differences across regions.

12 A Credibility-based Yield Forecasting Model Objectives of research is to address these difficulties by developing a new crop yield forecasting model and reinsurance pricing framework. Integrating weather risks and production information from different geographical regions. Proposing scientific approach to restate yields through consideration of changing crop mix over time.

13 A Credibility-based Yield Forecasting Model Representativeness of Data Evolution of farming practices creates difficulties for loss modeling given that historical data become less representative of the current experience. Examples: Mixed cropping crop rotation changes in biotechnology increases in commodity prices changes in crop mix A scientific restatement approach for historical yield data helps to ensure that the historical observations are good indicators of future crop production.

14 A Credibility-based Yield Forecasting Model Extreme weather events often lead to wide spread losses across many geographic regions. An integrated yield model that combines meteorological and climate data may be beneficial. A major challenge faced with integrating yield and weather information is: How to efficiently select weather variables from a complex set of correlated weather variables. Reduce the dimension of explanatory variables to an acceptable number.

15 A Credibility-based Yield Forecasting Model In this paper, a comprehensive weather index system is considered to describe the nonlinear relationship of weather variables and crop yields. Three model selection algorithms are proposed by combining: Screening Regression (SR) Principal Component Analysis (PCA) Cross Validation (CV) to efficiently help to achieve the goal of model selection and dimension reduction

16 A Credibility-based Yield Forecasting Model Data Detailed farm-level crop yield data set from Manitoba, Canada. 216 types of crops 19,238 farms from 1996 to Weather data is the Adjusted and Homogenized Canadian Climate Data (AHCC) from Environment Canada. Daily temperature (maximum, minimum, and mean) from 24 weather stations Daily precipitation from 30 weather stations. Missing weather data is handled via Ordinary Kriging method.

17 A Credibility-based Yield Forecasting Model Crop Mix Restatement In order to ensure that the crop yield data observed historically is a good indicator of future crop production, it is necessary to pre-process the yield data using a procedure commonly known as restatement. Particularly important in the context of agriculture for reasons such as: Evolution of technology Improved farming practice Changes in weather conditions Any other factor that may have a significant impact on crop production over the years

18 A Credibility-based Yield Forecasting Model Crop Mix Restatement Over the years there have been many different types of crops produced, so unrealistic to restate each and every single crop. Instead, focus on restating a representative crop mix, to provide a better reflection of the current risk profile. Identify main crop mix that municipality has been producing in recent years, defined as the minimum number of crops that cover at least 90% of the total farming acres over the most recent 5 years. Define optimal crop mix, which consists of the main crop mix and others, to capture the remaining crops. Assumed to be representative of next year s faming practice and hence used as a benchmark for restating historical crop yields.

19 A Credibility-based Yield Forecasting Model Weather Index System High severity and low frequency nature of agricultural risks, mean that insurers often cede a portion of the risk to private reinsurers. Reinsurers are often faced with data limitations, and seek to improve loss forecasting approaches. A detailed weather index system is developed based on temperature and precipitation information. Temperature thresholds: θ 1 =6 to 10 C; θ 2 =0 to 4 C; θ 3 =26 to 30 C Precipitation thresholds: λ 1 = first quantile of historical precipitation; λ 2 = second quantile of historical precipitation

20 A Credibility-based Yield Forecasting Model Weather Index System Developed monthly and annually, using daily observations. Aggregation functions are divided into three types: Average Index: Using function avg, the average indices provide aggregate measures of weather conditions during a defined period. Extreme Events: Using function min and max, these indices describe extreme events during a defined period. Extreme Days: Using function cot, these indices count the number of days during a defined period experiencing extreme weather conditions. Construct a 140-dimensional design matrix, where each column is an explanatory variable and each row is one year observation for the corresponding variables.

21 A Credibility-based Yield Forecasting Model Weather Index System Common modeling practices, such as all possible subset method or stepwise methods, can be long and tedious and may not lead to an optimal model with a high-dimensional design matrix. Paper considers three model selection algorithms : Screening Regression (SR): reduces dimensionality and allows only those important explanatory variables in the regression model. Principal Component Analysis (PCA): transforms original highly correlated variables into uncorrelated principal components, retaining variation of data. Cross Validation (CV): identifies optimal threshold of screening, and limits the overfitting problem.

22 A Credibility-based Yield Forecasting Model Tradeoff between insample and out-ofsample forecasting. SR has best in-sample fitting, but, produces relatively large out-ofsample forecasting errors with large SD. PCASR and SPCAR, although slightly worse than the SR in the insample forecasting, have better performance in the out-of-sample forecasting.

23 A Credibility-based Yield Forecasting Model SPCAR reduces the dimension to a few dominant explanatory variables. Empirical analysis shows great variations across municipalities.

24 A Credibility-based Yield Forecasting Model In agricultural ratemaking, geographical heterogeneity is typically ignored. Should have stable and homogeneous risk portfolios, and pricing should be based on historical loss data.

25 A Credibility-based Yield Forecasting Model New Credibility Estimator This geographical heterogeneity indicates that the traditional pricing method for crop reinsurance may fail to consider the spatial differences in the reinsurer's risk portfolio. A new credibility estimator that integrates weather information and considers the geographical heterogeneity is proposed. Let us assume that there are d risk categories, and let i.i.d random variable θ i describes the ith risk category, i = 1; ; d. In practice, the risk category can be referred to as different geographical regions, different insurance or reinsurance companies, etc.

26 A Credibility-based Yield Forecasting Model The classic regression credibility estimator can be expressed as: where is a 1xp design matrix for risk category i, and is a px1 vector of regression coefficients. The other parameters are defined as:

27 A Credibility-based Yield Forecasting Model Introduce auxiliary variable to reduce the risk of model misspecification, which is related to crop yield using the correlation coefficients between crop yield and the auxiliary variable. Compare the forecasting results of the new credibility estimator with SPCAR (which was shown to have the best out-of-sample forecasting ability), as well as the classical regression credibility estimator.

28 A Credibility-based Yield Forecasting Model

29 Current Research Example: Spatial Dependence & Aggregation in Weather Risk Hedging Co-Authors: Wenjun Zhu Assistant Professor, School of Finance, Nankai University, China Ken Seng Tan University Research Chair Professor Department of Statistics and Actuarial Science, University of Waterloo Chou-Wen Wang Professor, Department of Finance, National Kaohsiung First University of Science and Technology, Taiwan, Kaohsiung

30 SYSTEMATIC WEATHER RISK AND AGRICULTURAL INSURANCE Weather risk is systematic and undiversifiable. Outside the control of human management widespread and spatially correlated, impacting many farms within a region. Weather risk will not be eliminated by pooling, must be managed through various risk transfer techniques. Agricultural insurers and reinsurers are major weather risk underwriters

31 RISK TRANSFER, AGRICULTURAL INSURANCE High loss ratios compared to other lines of business in the P&C sector 1. To help manage the insurers exposure to losses, reinsurance is an important part of the risk management strategy. A study from Q-Re shows that almost 80% of global downside risk for agricultural insurers are reinsured 2. Reinsurers are high aggregators of risk, and are particularly exposed to catastrophic events. 1. Woodard and Garcia, Schneider and Ross, 2013

32 HEDGING WEATHER RISKS In some cases, hedging weather risks with financial instruments may be a compliment or alternative to traditional reinsurance. Potential reduced cost Improved market efficiency. Examples: Reduced administration costs: no loss checking and adjusting Reduce information asymmetry: indemnities are based on a specific weather event rather than actual farm losses. Statistical inference viewpoint: often large volumes of reliable weather data records in daily frequency.

33 RESEARCH QUESTIONS Develop and compare different weather hedging strategies for agricultural insurers and reinsurers. Necessity of weather hedging (hedged vs. unhedged portfolio) Importance of assumed dependence structure Geographical aggregation effect on hedging effectiveness Refine the statistical weather variable modeling to improve the hedging performance. Nonstationarity; Seasonality; Multidimensionality; Incomplete nature of the market Existing stochastic weather models are typically designed for modeling only a single region Exception of the work by Okhrin et al. (2013)

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35 Data Daily temperature ( ) from 8 provinces in Canada, from Adjusted and Homogenized Canadian Climate (AHCC). Alberta (AB), Saskatchewan (SK), British Columbia (BC), Manitoba (MB),Ontario (ON), New Brunswick (NB), Nova Scotia (NS), and Quebec(QC)

36 Data Descriptive annual statistics, temperatures recorded in Celsius.

37 Data

38 Temperature Dynamic To describe the non-stationarity and seasonality nature of the temperature data, many statistical models propose to decompose the DAT dynamic as 1 : 1. Alexandridis and Zapranis (2013); Okhrin et al. 2013

39 Temperature Dynamic In studying the Canadian DAT we find: This equation illustrates some stylized general properties of daily temperature data, such as cyclical and seasonal trending. Does not capture the distinctive characteristics of Canadian DAT. Lower temperatures that appear with higher frequency and more extreme values in the winter. Propose to add a shock term Δi(t) The DAT decomposition becomes:

40 Temperature Dynamic with Wavelet Analysis Justify the terms in the DAT decomposition and determine the compositions of the seasonal parts using wavelet analysis. Decompose series into a time-frequency space, providing detailed analysis of the variability of the data. Daubechies 10 are the most commonly used discrete wavelet transforms (DWT). The residual parts are estimated with a heteroskedastic model with the general hyperbolic (GH) family Alexandridis an Zapranis (2013); Bellini (2005); Benth and Benth (2005)

41 Temperature Dynamic with Wavelet Analysis Wavelet Analysis of Historical Temperatures in Manitoba, 2001 to 2011 (Approximations) Wavelet Analysis of Historical Temperatures in Manitoba, 2001 to 2011 (Details)

42 Multisite Temperature Modeling with LSHAC After removing the serial correlations from the DAT data and performing the GH probability transformation according to the previous model, next we must appropriately model the joint distribution of the resulting pseudo sample. Propose a copula approach, which creates a flexible and realistic multivariate distribution modelling framework 1. Choosing an appropriate high-dimensional copula can be challenging because of dimensionality. 1. Joe (1997); McNeil et al. (2010)

43 Multisite Temperature Modeling with LSHAC Almost all applications of HAC models rely on the Gumbel copula or the Clayton copula, which have been verified to fulfill the compatible conditions 1. If the HAC models are constructed from mixed generators involving different families, we must verify the compatible conditions on a case-by-case basis. Hering et al. (2010) circumvent this hard-to-check compatible condition by constructing the HAC models via Levy Subordinators. Zhu et al. (2014) provide estimation methodology and empirically test the efficiency of the LSHAC models. 1. Embrechts et al. (2003)

44 Structure of the LSHAC The spatial dependence of the temperature processes of eight Canadian provinces are modeled and analyzed with the LSHAC model.

45 Structure of the LSHAC

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47 Spatial Dependence Estimation Results Based on BIC >50% of the estimated LSHAC models perform better than the Gaussian copula (88.76 imp BIC). The LSHAC models are more efficient with better fitting abilities and smaller sets of parameters. The LSHAC models <=9 parameters and Gaussian has 28 parameters. All-GM-HAC (most common HAC in empirical analysis 1 ). Estimation limited, each node restricted as a GM copula. BIC Imp. of All-GM-HAC = (compared to best LSHAC model of 88.76). GM-LSHAC and CL-LSHAC CL-LSHAC models are perform slightly better, possibly due to difference in tail dependence properties. 1. Okhrin et al. (2013)

48 Hedging Weather Risks An insurance company holds business lines over 8 provinces in Canada, where the hedging portfolio can be any subset of B. The weather risk exposure of the company is in the form of financial weather contracts on HDD sold to producers. Three hedging strategies: Local hedging (from only one province) Three parts local hedging Two parts local hedging One part local hedging (all provinces)

49 Results Overview Necessity of hedging weather risk: all hedging strategies perform better compared to unhedged portfolio. Importance of dependence structures: LSHAC model always has the best hedging performance compared to the independent and Gaussian copula. Geographical aggregation effect: effectiveness of the hedging strategies is dependent on the geographical aggregation effect. Higher levels of aggregation result in more effective hedges.

50 Results Necessity of Hedging Weather Risk Variance Reduction Simulated hedging error densities for local, global and unhedged strategies show that both local and global hedging strategies reduce the portfolio of risk. Hedging Efficiency One Part Global > 96% Local-ON > 35% VAR and CTE One Part Global: VAR 0.01 =92.21% and CTE 0.01 = 95.34% AB: VAR 0.01 = 82.07% and CTE 0.01 = 89.22%

51 Results Importance of Dependence Structure LSHAC assumption reduces downside risk of portfolio further than independent assumption. Reduction in Downside Risk in Millions VAR 0.01 CTE 0.01 LSHAC $ $ Independent $ $

52 Results - Geographical Aggregation Effect Results support the hypothesis that the effectiveness of the hedging strategy is dependent on the geographical aggregation effect. Hedging Errors VAR 0.01 CTE 0.01 Best Local -$ $ Hedging Three Parts -$ $ Two Parts -$ $ One Part -$ $191.56

53 Thank You! Lysa Porth, MBA, Ph.D.

54 Issues in Agricultural Insurance Rémi Villeneuve, FSA, FCIA Chief Actuary, Agriculture and Agri-Food Canada 2015 SOA Annual Meeting October 12 th, 2015

55 Agenda Background Coverage Setting Premium Rate Setting Assessment of Selfsustainability Conclusion 2

56 Background: Agricultural Insurance in Canada Agricultural Insurance in Canada = AgriInsurance Government-sponsored program Eligible perils: weather, diseases or pests Various rider options (eg. unseeded acreage benefit) Various deductible options for producers (from 10% to 50%) 3

57 Background : Government Agencies Canada USA Actuarial consultants are hired by provinces to certify: Probable Yield Methodologies Premium Rate Methodologies Assessment of Self-Sustainability of provincial insurance programs Federal Government s actuarial team within Agriculture and Agri-Food Canada (AAFC): Reviews and approves provincial certifications Approves changes to the program Monitors compliance with the program in terms of Federal Regulations and actuarial guidelines Risk Management Agency (RMA) operates and manages the Federal Crop Insurance Corporation (FCIC) FCIC provides crop insurance to American farmers and ranchers Private-sector insurance companies sell and service the policies RMA: Develops and/or approves the premium rate Administers premium and expense subsidies Approves and supports products Reinsures companies Develops Products Monitors compliance of the program 4

58 Background : Canada versus the United-States Crop Year 2012 Canada 1 USA 2 Policies (Million) Premium ($ Billion) Exposure ($ Billion) Acres Insured (Million) Agriculture and Agri-Food Canada 2 United States Department of Agriculture Fact sheet 5

59 Background : Agricultural Insurance in Canada Proportion of Total Liability (%) by Province Provinces deliver and administer the Program Federal Government shares administrative and premium cost Premium cost share: 60% government / 40% producer 1.7 Participation: 68% Average deductible: 25%

60 Background: Yield Based Plans Multi-peril individual coverage Multi-peril risk-area based coverage Single peril coverage (eg. hail) Whole farm coverage Proxy crop coverage 7

61 Background: Yield Based Plan - Common Additional Benefits Quality Loss Coverage Reflects loss in indemnity Assessment Same quality for whole province Unseeded Acres Benefit Long-term average loss Reseeding Benefit Establishment Benefit Salvage Benefit 8

62 Coverage Setting: Premium Amount Formula Dollar Premium = Number of Acres x Probable Yield (Bushel/Acre) x Unit Price (Dollar/Bushel) x (1 Deductible) x Premium Rate 9

63 Coverage Setting: Acres Description Producer must insure all acres Indemnity based on yield calculated on all acres Issues Risk-splitting Risk area boundaries Credibility Premium = Acres x Probable Yield x Unit Price x (1 Deductible) x Premium Rate 10

64 Coverage Setting: Probable Yield Description Probable yield is the producer s expected production Calculated based on historical individual production Adjusted for quality of the crop Calculated by risk area or per individual producer Premium = Acres x Probable Yield x Unit Price x (1 Deductible) x Premium Rate 11

65 Coverage Setting: Probable Yield (continued) Issues Stability vs. Responsiveness Probable yield following a catastrophic year or very good year New Plans A crop that has never been insured before: How do we determine probable yield? A crop that was insured, but has never been grown by a producer: Can we expect the same performance? New Producer A producer that has never grown or insured anything: What probable yield can we expect? Individual Yield vs. Area Yield Individual experience better reflects production practices Area yield can also be used to establish insurance coverage Premium = Acres x Probable Yield x Unit Price x (1 Deductible) x Premium Rate 12

66 Coverage Setting: Probable Yield (continued) Issues Credibility How do we define credibility? How do we define the credibility complement? Should credibility be calculated the same way as traditional P&C products? Limited research on agricultural insurance credibility available There is variation in calculation of the full credibility standard between provinces Premium = Acres x Probable Yield x Unit Price x (1 Deductible) x Premium Rate 13

67 Coverage Setting: Probable Yield (continued) Issues Trend How prudent should we be with trend factors? How long will the trend continue? Is it reasonable to project trends for several years? Premium = Acres x Probable Yield x Unit Price x (1 Deductible) x Premium Rate 14

68 Coverage Setting: Probable Yield (continued) Issues Trend Should the trend be uniformly applied to all areas? Should the trend be uniformly applied to all producers? 2.1% 0.4% Premium = Acres x Probable Yield x Unit Price x (1 Deductible) x Premium Rate 15

69 Coverage Setting: Probable Yield (continued) Issues Pressure on trend from optimistic producers and industry 53% Increase in 10 Years (2025) Premium = Acres x Probable Yield x Unit Price x (1 Deductible) x Premium Rate 16

70 Coverage Setting: Probable Yield (continued) Issues Increase in disease incidence that may affect the trend 30% % Incidence of a Disease Affecting Crop on Previous Slide 25% 20% 15% 10% MB SK AB 5% 0% Premium = Acres x Probable Yield x Unit Price x (1 Deductible) x Premium Rate 17

71 Coverage Setting: Probable Yield (continued) Issues Change in agricultural practices affect yield trend Traditional Apple Orchard Modern Apple Orchard Premium = Acres x Probable Yield x Unit Price x (1 Deductible) x Premium Rate 18

72 Coverage Setting: Unit Price Description Different price options are offered to a producer Base price option Low price option Variable price option In-Season price option Contract price option Issues Premium setting for the variable price option Needs to be in line with market price (not always available) Premium = Acres x Probable Yield x Unit Price x (1 Deductible) x Premium Rate 19

73 Coverage Setting: Deductible Description Producer has choice of deductible between 10% - 50% Lower government cost share for deductible below 20% with a high premium rate Issues Credibility Lacks necessary data to calculate premium at each deductible for all crops Actual yield not in a claim position is not always collected Premium = Acres x Probable Yield x Unit Price x (1 Deductible) x Premium Rate 20

74 Premium Rate Setting Historical Indemnity Rates (Loss to coverage ratio) Adjusted Indemnity Rates Adjusted to current condition Credibility or conversion to common coverage level Excess losses Average Selected Premium Rate Conversion to selected coverage level Provincial to individual rate Smoothing Uncertainty Margin Discount / Surcharge Balance Back Factor Self-Sustainability Load Private Reinsurance Load Premium Rate Premium = Acres x Probable Yield x Unit Price x (1 Deductible) x Premium Rate 21

75 Premium Rate Setting (continued) Issues Stability vs. Responsiveness Fluctuation after very good/bad years Communication with producer on how the methodology works Loading for catastrophes How are catastrophic years considered? Deterministic vs. Stochastic Complexity of the model Should follow probable yield responsiveness Premium = Acres x Probable Yield x Unit Price x (1 Deductible) x Premium Rate 22

76 Premium Rate Setting (continued) Issues Area Rate vs. Individual Rate Availability of data Unfair for very good/bad producers Discount / Surcharge Discount for good years or discount for good producers? Producer s attachment to a discount Premium = Acres x Probable Yield x Unit Price x (1 Deductible) x Premium Rate 23

77 Assessment of Self-Sustainability Description: Catastrophic financial position of the program is: The 5 th percentile of stochastically simulated fund balances at the end of year 5, using the current financial position as the starting point. Criteria for the Program to be considered self-sustainable, using the catastrophic financial position as the starting point : The first positive mean of stochastically simulated annual fund balances is prior to the end of year 15, and; The first positive 20 th percentile of stochastically simulated annual fund balances is prior to the end of year

78 Assessment of Self-Sustainability (continued) Issues Grouping crops together Should all crops be modelled together? If not, what crops should be grouped together? Simulating a catastrophic year What frequency and severity should be used for a catastrophic year? How quickly can it change over time? 25

79 Conclusion Agricultural insurance offers traditional roles for actuaries in a non-traditional sector Key actuarial techniques are still under development More research is being done as the sector is expanding 26

80 Thank You 27