Evaluating crop insurance options for 2014
click image to zoom A 5% gross revenue VAR, for example, shows the value at which 5% of the possible outcomes fall below, and 95% of the outcomes exceed - in other words a 1 in 20 worst event. A 1% VaR shows a characteristic of "extreme risk" representing a 1 in 100 year analog probability. The table below shows the 1% VARs for the various insurance products and elections to better help appreciate the relatedness of payments to revenue shortfall. Notice that with no insurance, the 1% VAR for revenue is about $419 meaning that in 1% of the cases, revenue would be below that value. Using YP insurance increases the lower tail to about $460. Using ARP would increase that extreme outcome to about $481. However, the RP policies add over $150 to the lowest outcome compared to no-insurance. RP and RP-HPE do a far better job of "cutting off the low tail" of the revenue distribution and provide substantially better downside risk protection due to their ability to trigger based on either yield or price level movements. A producer considering covering $550 in total production costs would thus likely find higher elections of the revenue products most appealing.
The final information presented in the graph below helps summarize the impacts across the lower tail of the revenue distribution. The bottom axis gives levels of gross revenue with insurance payments, less premiums paid. The vertical axis shows the probability of occurrence. Because distributions with higher likelihood of higher revenue are preferred, lines to the bottom and right are preferred to those above and to the left in this graph. The dark blue line provides the possible revenue outcomes with no insurance. For example, there is about a 5% chance of revenue with no insurance being below $535 and a 10% chance of revenue being below $580, a 25% chance of being below $660, and so on without insurance. Purchasing insurance has two types of consequences on the revenue distribution -- first, it shifts the whole schedule left by the amount of the premium. Then, it adds back payments to outcomes covered by insurance, there by shifting specific portions of the revenue distribution back to the right. Ideally, insurance should make payments when revenue is lowest and not make payments when revenue is highest resulting in an overall shift in the revenue distribution to the right at lower revenue levels, and resulting in lower revenues when only premiums are paid and no indemnities are paid (top portion of the curves are not shown in the graph, but would be shifted to the left of the no-insurance case). As can be seen in the graph, AYP actually reduces the revenue distribution relative to no insurance over most of the lower half (probability less than 50%) of the revenue distribution. YP (omitted from the graph) has almost no effect compared to no insurance, roughly covering its own cost, but not much more or less. RP 85% and RP-HPE 85% do the best job of "cutting off the tail" of the revenue distribution with minimum revenues of roughly $580-600 guaranteed in most cases. The ARP outcomes are interesting in that they pay back more than premiums over a large range of revenues, but do not protect against particularly severe revenue shortfalls. Further, in years with high crop revenue they actually cost the most in terms of total revenue due to their higher initial premiums.
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