3. DISEÑO Y MARCO METODOLOGICO
3.1. LA OBSERVACION
As has been developed above, two value-added data sets are available for
analyzing any number of policy alternatives designed to handle catastrophic yield risk: 1) the Judet data; and 2) the simulated farm data for each Judet and crop. A number of alternatives that either use Judet area-yield s or farm yields or some combination of the two will be examined. This section systematically examines the relative costs and the profile of risk for a number of alternatives. In the next section, weather-based insurance alternatives are examined for a specific region (Southeast Romania).
This report examines the following options: 1) Area Base Insurance:
Liability = Price x Hectares x Judet Expected Yield
where hectares would be the farmer’s plantings (or the total hectares in the Judet when performing this analysis)
The index trigger is set in two different fashions:
1) As a percent of the Judet expected yield (80%, and 90%)
2) At various frequency levels for the Judet yield (1 in 5; 1 in 7; 1 in 10; & 1 in 20 year events).
2) Multiple-peril Crop Insurance:
Indemnity = max(0, Farm Yield Trigger – Actual Farm Yield) * Price * Hectares where farm yield triggers are examined for 60%, 70%, and 80% of the farm expected farm yield
3) Area-yield Insurance with Individual Payments
Indemnity = max(Multiple-peril Payment, Area-yield Payment)
Area-yield at 1 in 7 and 1 in 10; Farm Yield at 60% & 70% with the same indemnity payouts as presented above
Liability Trigger Index Yield Realized Trigger Index , Indemnity × − =max 0
6: Alternative Programs for Catastrophic Yield Risk GlobalAgRisk Report November, 2002
Results
Results are developed for the value at risk portfolio of the five crops. Since the analysis is performed using this weighted average of crop value across Romania and with the 33 years of crop-yield risk, a rather complete profile of risk is possible. As an
illustration of the tracking of two very different programs, Figure 6 presents the historic loss cost for the AYP that is based on triggers set at 1 in 7 years and the 60% coverage for a MPCIP. Again, the higher loss cost values in the more recent years is evident, especially considering that 2002 may be at about the same level as 2000.
0% 5% 10% 15% 20% 25% 1968 1973 1978 1983 1988 1993 1998 Year Loss Cost 1 in 7 AYP MPCI @60% Figure 6: Historic Loss Cost Estimates for Area- yield 1 in 7 Year Trigger and MPCIP set
at 60% Coverage.
Given different crop insurance program designs one can also make cross comparisons. Figure 7 provides a direct comparison of an area- yield program (AYP) with a multiple-peril crop insurance program (MPCIP) for the aggregate loss cost or pure premium. Farm yields will nearly always have more variance than area-yields. Thus, as expected, the MPCIP program cost curve is greater than the AYP curve. The curves also have the expected shape; the increase at an increasing rate as the coverage increase (deductible decreases). Estimates of the loaded premiums are also presented. These loads are based on expert judgment and industry standards. The loading assumptions are presented in the table below. Clearly these loads will be much greater for the MPCIP versus the AYP. Offering MPCIP at any coverage levels in excess of 70% is certainly not practical.
6: Alternative Programs for Catastrophic Yield Risk GlobalAgRisk Report November, 2002 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 60 65 70 75 80 85 90 95 100 Coverage Level
Premium Rates Multiple Peril Pure Premium
Multiple Peril Loaded Premium
Area Yield Pure Premium Area Yield Loaded Premium
Figure 7: Comparison of pure and loaded premiums for MPCI versus AYP
Loading Premium Rates
Regardless of who pays for the insurance – the farmer, the government, or some combination – the Hazel ratio clearly communicates that all cost should be considered. This study considers all cost in sequence by expanding the A (administrative cost) in the Hazel equation to include a number of factors presented below.
Hazel: (I + A) / P < 1
The pure premiums that come from the pure loss cost history must be loaded in a logical and consistent fashion. Reinsurance loads are generally associated with the variance of the loss cost. The higher the variance, the greater the reinsurance loads. One method for loading reinsurance cost is to use the standard deviation from the loss cost. For the MPCI programs, a relatively simple 40% load is imposed by multiplying the standard deviation by 0.40. For example, with MPCI 60 in the table below the loaded reinsurance premium would be calculated as follows:
Loaded Reinsurance Premium = LC + (STD x 0.40) = 3.8 + (4.1 x 0.40) = 5.4% The actual premium load = 1 – (5.4 / 3.8) or 42%
6: Alternative Programs for Catastrophic Yield Risk GlobalAgRisk Report November, 2002 adjustment for a MPCI program very high. Thus, even the high load factors presented in Table 5 may be too conservative for the Romanian setting.
Table 5: Loading Pure Premium Rates
MPCI 60 MCPI 70 AYP 80 AYP 90
Pure Premium (Loss Cost) 3.8% 6.4% 2.9% 5.0% Standard Deviation on Loss Cost 4.1% 5.3% 3.9% 5.2%
Reinsurance Load 40% 40% 20% 20%
Actual Reinsurance Load 42% 33% 26% 21%
Moral Hazard & Adverse Selection 30% 35% 2% 2%
Claims & Loss Adjustment 13% 13% 5% 5%
General Administration 15% 15% 5% 5%
Sales Agents 15% 15% 5% 5%
Total Load Factor (1 + percent
load) 215% 211% 143% 138%
Loaded Premiums 8.2% 13.6% 4.2% 6.9%
While the assumptions used to load the rates should be questioned and reexamined by others, the general direction of the loads are logical and provide a consistent basis for developing estimates of what the market would charge. The total load factors can also be referenced as a rather simple index of the efficient of the risk programs. Obviously, the question of the degree of basis risk for all these programs will be important. Assessing the basis risk is beyond the scope of this report, primarily due to data constraints.
Assessing the Correlated Risk Issue
The correlated risk among the Judets is a major issue. Various programs can now be analyzed to examine this issue in more detail and to motivate recommendations. The historic loss cost values can be used to develop a probability distribution function of losses. This will be referred to as the loss function. Figure 8 presents the hypothetical loss function for two very different types of crop insurance: 1) private hail and 2)
multiple-peril. As the figure suggests, the losses around a target loss ratio of 60% for the private hail insurance are more symmetrical and have a very low probability of exceeding a loss ratio of 100%. Hail losses are generally not correlated across a wide area. Thus, it is unlikely that in any one year nearly all farmers would have a hail loss. By contrast, the MPCI losses include payments for all perils, including drought. When there is a drought in one area, it is likely that many surrounding areas are also suffering. Even though the average loss ratio for the hypothetical MPCI is 60%, these correlated risks create a MPCI loss function that has a long thick tail above the 100% loss ratio. Understanding the shape the loss function and the probability that losses will be above 100% is critical for assessing the sustainability of any insurance program. Keep in mind that these losses are used to justify government subsidies for MPCI through the world.
6: Alternative Programs for Catastrophic Yield Risk GlobalAgRisk Report November, 2002
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 Hypothetical MPCI Loss Function
Hypothetical Private Hail Loss Function
Figure 8: Hypothetical loss function for private hail versus MPCI
Without considering loaded premium rates, the odds of exceeding the loss ratio of 100% are roughly 1/3. The odds of exceeding 200% for most programs are roughly 15%. Even with loaded rates for reinsurance, the alternatives that are examined here generally have a 25% chance of exceeding a loss ratio of 100%. The odds of exceed losses in excess of two times the loaded premiums are at least 1 in 10 for most programs examined after the reinsurance loads have been imposed. Undoubtedly, the private markets in Romania are not prepared to take on this type of risk. To consider the potential value of these losses requires some assumptions about participation. Even with a conservative participation rate of 10% for these five crops, there would be roughly $150 million of exposure. Loss cost values that exceed 20% are not uncommon for the programs examined in this report. At a loss cost of 20%, indemnities for a $150 million program would be $30 million. These are very large losses for the insurance industry in Romania. If the participation rate were 50%, the losses for a year with a loss cost of 20% could exceed $150 million ($750 million of exposure x 0.20%).
7: Forecasting Costs for Romanian Crop Insurance Law GlobalAgRisk Report November, 2002