ETF策略系列：科技ETF配置及基于Garch-EVT的再平衡优化策略

⚫ ⚫ ⚫ ⚫    -0.8-0.6-0.4-0.200.20.40.60.811.20.00.10.10.20.20.30.30.40.4 𝛽 （2.43 Calmar 𝑟𝑡 = 𝜇 + 𝜖𝑡𝜖𝑡 = 𝜎𝑡𝑧𝑡𝜎𝑡2  =  𝜔 + ∑ 𝛼𝑖𝑝𝑖=0𝜖𝑡−𝑖2    + ∑ 𝛽𝑗𝑞𝑗=0 𝜎𝑡−𝑗2𝑟𝑡𝜇𝜖𝑡σ𝑡z𝑡𝜔𝛼𝑖βj∑𝛼𝑖𝑝𝑖=0∑βjqj=0z𝑡z𝑡~𝐺𝐸𝐷(𝑣)𝑣ARCH<2 𝑓(𝑥; 𝜉, 𝛽) = 1𝛽 (1 + 𝜉 𝑥 − 𝜇𝛽)−1𝜉−1𝜇𝜉𝜉𝜉𝜉𝛽 𝑉𝑎𝑅𝛼 = 𝜇 + 𝛽𝜉 [(𝛼 ·)−𝜉 − 1]Threshold = Quantile𝛼·𝜃(𝑅𝑜𝑙𝑙𝑖𝑛𝑔𝑅𝑒𝑡𝑢𝑟𝑛𝑠)𝛼θ 𝐽𝐵 =𝑛6𝑆2 +𝐾−324𝐻0𝐻1 Δ𝑦𝑡 = 𝛼 + 𝛽𝑡 + 𝛾𝑦𝑡−1 − ∑𝜙𝑖𝑝𝑖=1Δ𝑦𝑡−𝑖 + 𝜖𝑡𝛼𝛽𝑡𝛾𝜙𝑖𝜖𝑡𝐻0 𝛾𝐻1 𝛾 ≠ 05101520253035-0.07625-0.06125-0.04625-0.03125-0.01625-0.001250.013750.028750.043750.058750.073750.088750.103750.118750.133750.148750.163750.1787550ETF05101520253035-0.06625-0.05625-0.04625-0.03625-0.02625-0.01625-0.006250.003750.013750.023750.033750.043750.053750.063750.073750.083750.09375ETF0510152025303540-0.07875-0.06875-0.05875-0.04875-0.03875-0.02875-0.01875-0.008750.001250.011250.021250.031250.041250.051250.061250.071250.081250.09125ETF0.000.200.400.600.801.001.201.401.601.80-0.10-0.050.000.050.1050ETF0.000.200.400.600.801.001.201.401.601.80-0.10-0.050.000.050.10ETF0.000.200.400.600.801.001.20-0.10-0.050.000.050.10ETF𝜌𝑘 =0𝑘𝑘 = 𝐸[(𝑦𝑡 − 𝜇)(𝑦𝑡−𝑘 − 𝜇)]𝑘0𝜌𝑘𝜌𝑘𝜌𝑘𝜙𝑘𝑘𝜙𝑘𝑘 = 𝜌𝑘 − ∑𝜙𝑘−1,𝑚𝑘−1𝑚=1𝜌𝑘−𝑚1 − ∑𝜙𝑘−1,𝑚𝑘−1𝑚=1𝜌𝑚𝜙11 = 𝜌1𝜙𝑘𝑚 𝑒𝑡𝑒𝑡2 = 𝛼0 + ∑ 𝛼𝑖𝑒𝑡−𝑖2𝑞1+ 𝜖𝑡,𝐻0:𝛼𝑖 = 0𝐻1𝛼𝑖 ≠ 0𝐿𝑀 = 𝑛 · 𝑅2𝜒2(𝑞)𝑅2-0.20.00.20.40.60.81.01.20 3 6 9 1215182124273033363950ETF(ACF)-0.20.00.20.40.60.81.01.20369 12 15 18 21 24 27 30 33 36 39ETF(ACF)-0.20.00.20.40.60.81.01.20369 12 15 18 21 24 27 30 33 36 39ETF(ACF)-0.20.00.20.40.60.81.01.20 3 6 9 12 15 18 21 24 27 30 33 36 3950ETF(PACF)-0.20.00.20.40.60.81.01.20369 12 15 18 21 24 27 30 33 36 39ETF(PACF)-0.20.00.20.40.60.81.01.20 3 6 9 12 15 18 21 24 27 30 33 36 39ETF(PACF) 00.020.040.060.080.10.120.140.160.180.20.0000.0050.0100.0150.0200.0250.0300.0350.04050ETF50ETF()00.020.040.060.080.10.120.0000.0020.0040.0060.0080.010ETFETF()00.020.040.060.080.10.120.0000.0020.0040.0060.0080.010ETFETF()𝐵𝐼𝐶 = 𝑙𝑛(𝑛)𝑘 − 2𝑙𝑛(𝐿)𝐿𝑘𝑛min 𝑍 = −(𝑤𝑇𝜇 − 𝐶𝑉𝑎𝑅𝛼(𝑤))∑ 𝑤𝑖 = 1𝑛𝑖=1𝑤𝑖 ≥ 0 (𝑖 = 1,2, … , 𝑛)𝑤𝜇𝐶𝑉𝑎𝑅𝛼(𝑤)𝛼𝑤𝑖𝑛