Table 6 Back-testing Monthly Returns in the Spot Market, 1928-2014

From: On agricultural commodities’ extreme price risk

Distribution: Normal Generalized EVT Heavy-tailed
  1.00% 0.50% 0.25% 1.00% 0.50% 0.25% 1.00% 0.50% 0.25%
Panel (a): Number of VaR-exceedances in left tail
Corn 14 10 6 19 11 6 8 2 0
Cotton 15 12 11 16 11 5 8 2 1
Oats 12 9 5 17 10 3 6 1 0
Soybeans 13 9 7 16 8 1 7 2 1
Wheat 17 12 7 17 9 6 10 5 0
Live cattle 6 4 3 9 4 3 4 1 0
Orange juice 11 9 7 19 13 9 7 0 0
Sugar 6 4 3 9 4 1 3 1 1
Average 11.8 8.6 6.1 15.2 8.8 4.2 6.6 1.8 0.4
(Expected) (6.7) (3.3) (1.7) (6.7) (3.3) (1.7) (6.7) (3.3) (1.7)
Rejected tests 4 6 5 6 6 3 0 0 0
Panel (b): Number of VaR-exceedances in right tail
Corn 12 9 8 11 6 4 7 5 4
Cotton 24 19 16 16 9 5 8 2 2
Oats 18 14 10 15 7 4 10 3 2
Soybeans 13 7 5 8 5 4 5 4 4
Wheat 22 17 14 22 11 7 13 7 2
Live cattle 15 9 7 12 8 5 6 2 0
Orange juice 19 17 14 14 10 4 11 3 2
Sugar 25 19 17 16 7 4 5 0 0
Average 18.5 13.9 11.4 14.2 7.9 4.6 8.1 3.2 2.0
(Expected) (6.7) (3.3) (1.7) (6.7) (3.3) (1.7) (6.7) (3.3) (1.7)
Rejected tests 7 7 7 5 4 1 1 0 0
  1. Note: The table reports the number of VaR-exceedances in the back-testing procedure. We estimate the VaR with a rolling-window of 360 months based on the normal distribution, the generalized EVT distribution using the estimator of Fraga Alves et al. (2009) and the power law tail distribution. For each commodity, we count how often the return in any particular month exceeds the VaR estimate based on the past 360 months (a “VaR-exceedance”). The lines labelled “average” and “expected” report the average number and expected number of VaR-exceedances for accurate VaR estimates for each column. The bottom line reports the number of unconditional coverage tests that were rejected at a 5 percent significance level for each column