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 soybean 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 soybeans in Brookings County, South Dakota.
Figure 1 shows the revenue risk in Brookings County, South Dakota. The estimate is based on historical soybean yields1, historical and current South Dakota soybean prices, and the historical relationship between soybean yields and price. The predicted trend yield for soybeans in this simulation was 52 soybean bushels per acre in Brookings County, South Dakota. The yield uncertainty we used in the revenue simulations was 11%. This simulation was based on an expected futures price for November soybean 2018 futures of $8.50 with 18% volatility and assumed basis of -$1.31. This simulation was performed on September 26, 2018. In order for the analysis to more accurately reflect individual farm risk, a producer may need to alter the assumptions of the simulation, such as the percent of yield uncertainty. Value-at-risk is a dynamic measure that incorporates real-time changes in yield and price uncertainty.
In this illustration, we can show what value-at-risk is for soybean production in Brookings County for a given time period. 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 $369 per soybean acre, minus the 1st percentile of revenue which is $274 per soybean acre (yellow area). The difference between the expected value and the 1st percentile is the 10-day 99% VaR at $95 per soybean acre (green area). The 10-day 99% VaR amount of $95 means that over the next ten days there is a 99 percent chance that the operation will not lose more than $95 per soybean acre from changes to yield or prices.
In addition, this calculation can be done with insurance and hedging (top graph). In the case of insurance, the 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 $341 per soybean acre, minus the 1st percentile of revenue which is $292 per soybean acre (yellow area). The difference between the expected value and the 1st percentile is the 10-day 99% VaR at $49 per soybean acre (green area). The 10-day 99% VaR amount of $49 means that over the next ten days there is a 99 percent chance that the operation will not lose more than $49 per soybean acre.
In this analysis, we included an insurance liability of $381 per soybean acre, and a producer insurance premium of $28 per acre. When we included the insurance, the 10-day 99% VAR was reduced from $95 per soybean acre to $49 per acre.
By comparing the bottom graph that shows no insurance with the top graph that incorporates insurance, you will notice the ‘yellow tail’ is longer. This represents that there is a greater probability that revenues could be lower without insurance than with insurance. The insurance scenario shown in the top graph compensates for these lower revenue occurrences by including an indemnity payment in the revenue per acre calculation--up to the insurance liability.
You will also notice the scenario without insurance shows a higher expected revenue at $369 per acre, while the insurance scenario shows a slightly lower expected revenue at $341 per acre. This occurs because the insurance premium is made and lowering the expected revenue. The graph illustrates the tradeoff between increasing expected returns without insurance with the risk reducing benefits of having insurance.
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 example, if an operation had $49 per acre 10-day 99% VaR, then according to this rule of thumb, a 1,000-acre soybean operation would need between $147,000 and $196,000 in working capital to tolerate the risk that is assumed.
Figure 1. Histogram plot of the Revenue Risk for Soybean Production in Brookings County, South Dakota in 2018.
This material is based upon work supported by USDA/NIFA under Award Number 2015-49200-24226.
1Soybean trend yield was calculated using historical yield data from 1998 to 2017.