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Table 1 The first four columns present the reduction in economic cost achieved in explaining exponential variations in the levels of the ETF’s

From: Zero covariation returns

Economic cost reductions in explaining   Economic cost reductions in explaining
exponential variations of ETF’s   exponential variations of SPX
Numerator Linear ratio to SPX Linear plus SPX rsvm ratio to SPX rsvm plus SPX Linear ratio Linear vector rsvm ratio rsvm vector
XLB 0.0258 0.2144 0.0383 0.3810 0.0070 0.1626 0.0099 0.3389
XLE 0.0518 0.2123 0.0335 0.3524 0.0015 0.1209 0.0708 0.3327
XLF 0.0248 0.1060 0.2361 0.3363 0.0064 0.0502 0.0510 0.2827
XLI 0.1772 0.1298 0.1187 0.3645 0.1277 0.1010 0.0968 0.3205
XLK 0.0788 0.0539 0.0823 0.3788 0.0269 0.0483 0.0781 0.2928
XLP 0.0212 0.0320 0.0002 0.0515 0.0555 0.0818 0.1153 0.3746
XLU 0.0985 0.1970 0.0026 0.1405 0.1331 0.0844 0.2153 0.2949
XLV 0.0026 0.1199 0.0355 0.2565 0.0022 0.1505 0.0497 0.3636
XLY 0.0979 0.0286 0.2210 0.2233 0.0903 0.0551 0.2754 0.3465
  1. The variables used are the ratio of price to spx (S&P 500 index) and the two variables separately. Prediction is by linear regression or support vector machine regression. The last four columns switch to explaining exponential variations in the level of the spx index using the ratio to the ETF and the two variates of the ETF and the spx index separately