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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