Table 7 Back-testing Weekly Returns in the Futures Market, 1979-2012

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 27 16 11 29 20 11 25 12 5
Cotton 23 13 10 31 18 9 23 9 5
Oats 25 17 11 26 15 7 21 5 2
Soybeans 26 17 13 23 13 8 16 8 4
Wheat 17 10 8 30 14 9 24 10 5
Live cattle 17 12 8 14 8 4 13 6 3
Orange juice 28 19 15 28 16 8 24 12 3
Sugar 21 14 10 18 11 6 13 5 1
Average 23.0 14.8 10.8 24.9 14.4 7.8 19.9 8.4 3.5
(Expected) (12.5) (6.3) (3.1) (12.5) (6.3) (3.1) (12.5) (6.3) (3.1)
Rejected tests 6 6 8 6 6 5 5 0 0
Panel (b): Number of VaR-exceedances in right tail
Corn 37 27 19 23 12 4 15 6 2
Cotton 30 22 17 24 15 7 20 8 3
Oats 21 13 7 12 7 4 10 5 5
Soybeans 23 13 10 19 10 3 17 3 1
Wheat 35 23 18 24 15 10 18 11 4
Live cattle 18 11 8 20 9 4 17 6 3
Orange juice 32 24 20 22 13 7 18 9 2
Sugar 18 12 6 18 9 4 13 4 1
Average 26.8 18.1 13.1 20.2 11.2 5.4 16.0 6.5 2.6
(Expected) (12.5) (6.3) (3.1) (12.5) (6.3) (3.1) (12.5) (6.3) (3.1)
Rejected tests 6 6 6 4 3 1 0 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 520 weeks 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 week exceeds the VaR estimate based on the past 520 weeks (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