Written collaboratively by Lisa Elliott and Matthew Elliott.

Calculating farm value at risk can be done using the tools we have made available through links below. Figure 1 is a histogram plot of the revenue risk for corn production in Brookings County South Dakota in 2018. A histogram measures the density of the 500 simulations of revenue using a best fitting copula model. The simulations are transformed to current levels of revenue value-at-risk estimates given changes to real-time market and yield data. In this case, the simulations are measuring the revenue distribution per acre for corn in Brookings County, South Dakota.

The default estimate of yield is based on a historical trend yield model^{1}. The relationship of yield to price is based on the historical relationship between corn yields and price in a particular county and state. The years used to determine the trend yield and price-yield relationship can be adjusted by adjusting the beginning year. The predicted trend yield in this simulation was 187 bushels per acre in Brookings County, South Dakota for 2018. The default yield uncertainty is the standard error of the trend yield model. This percent of yield uncertainty reflects the deviations from trend that occurred during the annual production cycle in Brookings County for a given probability. However, if one were to calculate value-at-risk after a crop is completely harvested, the yield uncertainty would be 0% since the producer would know with 100% probability the yield. Likewise, if the value-at-risk calculation is only for 10 trading days, the amount of yield uncertainty should be adjusted from an annual uncertainty level to a level that reflects potential changes to expected yield during those 10 trading days. For example, yield uncertainty during the early periods of reproduction such as during pollination are likely to be higher for a 10 day period than during a 10 day period when grain fill is mostly complete. The user can adjust the level of yield uncertainty that corresponds with their selected value-at-risk time period, and so the uncertainty is reflective of changes to yield during the production cycle of the commodity.

The expected price of the simulated revenue is the last futures price for the selected futures contract minus the current basis. The contract symbols used are symbols used by Barchart.com for the various commodities that value-at-risk can be measured in the tool. For example, the December Futures contract for corn in 2018 is ZCZ18. The default price uncertainty—or price risk—is determined by the latest implied volatility of the selected futures contract. Implied volatility is derived from option prices currently traded for the same underlying futures contract. For example, when we calculated the value-at-risk in Figure 1, the implied volatility for the December 2018 futures contract was 18.8%. Implied volatility is a way to measure potential future fluctuations in the price of a futures contract. Implied volatility is always stated in an annual term, but for value-at-risk calculations, the annual volatility is adjusted to reflect volatility during the specified period the user is calculating value-at-risk.

In order, for the analysis to more accurately reflect individual farm risk, a producer may need to alter the assumptions of the modeling, such as the percent of yield uncertainty and the annual, expected volatility to price. Value-at-risk is dynamic as yield and price uncertainty changes occur as time passes, including over the production cycle as yield production becomes more certain.

In this illustration, we can show what value-at-risk is for a given moment. For example, without any hedging or insurance (bottom graph), a 10 day 99% VaR is calculated by taking the expected value, or value where there is a 50% chance of being above or below, in this case it is $587 per acre, minus the 1 percentile of revenue which is $447 (yellow area). The difference between the expected value and the 1 percentile is the 10-day 99% VaR of $140 (green area). The 10-day 99% VaR amount of $140 means that over the next ten days, there is a 99 percent chance that the operation will not lose more than $140 per acre. Likewise, there is only a 1% chance that the operation would lose more than $140 per acre over the next ten days.

However, the top graph can include changes to value-at-risk because of hedging or insurance. In this analysis, with an insurance liability of $535 per acre and a producer premium of $31, the 10-day 99% VAR was slightly reduced from $140 per acre to $121. In this analysis, a 12% yield uncertainty around the expected yield of 187 bushels per acre was used, since it was closer to the end of the production cycle.

By comparing the bottom graph that shows value-at-risk if there was no insurance or hedging compared to the top graph that incorporates insurance, the ‘yellow tail’ is longer which illustrates that there are greater probabilities of lower revenues without insurance. The with insurance scenario shown in the top graph puts a ‘cap’ at potential losses that results in an insurance indemnity payment with the revenue is found to be less than the liability. However, the scenario without insurance shows a higher expected revenue at $587 per corn acre, while the insurance scenario shows a slightly lower expected revenue at $556 per corn acre. This lower expected revenue but less risk illustrates the tradeoff between the premium paid for the insurance to gain the lower probability of extreme loss events.

The banking sector typically requires firms to have 3 to 4 times the amount of working capital compared to a 10-day 99% VaR. So, for this example, if an operation had $140 per acre 10-day 99% VaR. Then according to this rule of thumb, a 1,000-acre corn operation would need between $420,000 and $560,000 in working capital to absorb the level of risk that is assumed.

Figure 1. Histogram plot of the Revenue Risk for Corn Production in Brookings County, South Dakota in 2018.

*This material is based upon work supported by USDA/NIFA under Award Number 2015-49200-24226.*

^{1}Corn trend yield was calculated using historical yield data from 1998 to 2017.