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Table 7 Economic significance (80:20 Data Split with 20-day annualized realized volatility)

From: The predictive power of Bitcoin prices for the realized volatility of US stock sector returns

Sector stock

Model

Returns

Volatility

CER

SR

Returns

Volatility

CER

SR

\(\varvec{Gamma} = {\mathbf{3}}\;\varvec{and}\;\varvec{Theta} = {\mathbf{6}}\)

\(\varvec{Gamma} = {\mathbf{3}}\;\varvec{and}\;\varvec{Theta} = {\mathbf{8}}\)

Composite

HA

− 1.6221

3.97E+01

− 1.6233

− 0.2633

− 2.1671

7.06E+01

− 2.1683

− 0.2624

 

WN

− 0.9601

3.00E+01

− 0.9612

− 0.1820

− 1.2704

5.26E+01

− 1.2716

− 0.1803

Consumer Discretionary

HA

− 1.3803

8.61E+01

− 1.3831

− 0.1528

− 1.8357

1.52E+02

− 1.8386

− 0.1517

 

WN

− 1.2221

8.67E+01

− 1.2251

− 0.1353

− 1.6256

1.53E+02

− 1.6286

− 0.1342

Consumer Staples

HA

− 0.6852

1.11E+01

− 0.6859

− 0.2164

− 0.9199

1.98E+01

− 0.9206

− 0.2154

 

WN

− 1.9433

3.00E+01

− 1.9442

− 0.3616

− 2.6162

5.33E+01

− 2.6172

− 0.3635

Energy

HA

0.1294

7.66E+00

0.1266

0.0333

0.1830

1.26E+01

0.1802

0.0410

 

WN

− 1.1441

5.24E+01

− 1.1470

− 0.1632

− 1.5271

9.29E+01

− 1.5299

− 0.1623

Financials

HA

− 0.2931

4.07E+01

− 0.2948

− 0.0518

− 0.3833

7.11E+01

− 0.3850

− 0.0499

 

WN

− 0.4288

3.23E+01

− 0.4305

− 0.0821

− 0.5669

5.65E+01

− 0.5686

− 0.0804

Health Care

HA

− 1.1077

8.78E+00

− 1.1081

− 0.3865

− 1.4868

1.57E+01

− 1.4872

− 0.3852

 

WN

0.3674

3.43E+00

0.3666

0.1781

0.4776

6.10E+00

0.4768

0.1782

Industrials

HA

− 2.0448

5.71E+01

− 2.0467

− 0.2755

− 2.7280

1.02E+02

− 2.7298

− 0.2744

 

WN

− 0.5362

2.83E+01

− 0.5380

− 0.1078

− 0.7163

5.02E+01

− 0.7181

− 0.1064

Information Technology

HA

− 1.3994

1.08E+02

− 1.4015

− 0.1381

− 1.8720

1.92E+02

− 1.8740

− 0.1377

 

WN

− 0.5430

8.78E+01

− 0.5451

− 0.0619

− 0.7297

1.56E+02

− 0.7318

− 0.0615

Materials

HA

− 1.1526

2.21E+01

− 1.1533

− 0.2530

− 1.5410

3.93E+01

− 1.5417

− 0.2518

 

WN

0.4039

3.98E+00

0.4031

0.1837

0.5424

6.96E+00

0.5417

0.1914

Real Estate

HA

− 1.4401

2.09E+01

− 1.4407

− 0.3234

− 1.9296

3.71E+01

− 1.9302

− 0.3228

 

WN

− 1.2866

2.17E+01

− 1.2873

− 0.2841

− 1.7162

3.85E+01

− 1.7169

− 0.2825

Telecommunication Services

HA

− 1.8706

4.44E+01

− 1.8721

− 0.2864

− 2.4926

7.87E+01

− 2.4941

− 0.2851

 

WN

0.6459

1.97E+01

0.6441

0.1370

0.8455

3.58E+01

0.8437

0.1351

Utilities

HA

− 0.7391

3.44E+01

− 0.7405

− 0.1324

− 0.9799

6.07E+01

− 0.9813

− 0.1306

 

WN

− 0.5224

2.62E+01

− 0.5236

− 0.1093

− 0.6884

4.59E+01

− 0.6897

− 0.1071

  1. HA is the historical average model while WN is the Westerlund and Narayan (2012, 2015) type distributed lag model that accommodates salient data features such as endogeneity, persistence, conditional heteroscedasticity and structural breaks. A given predictive model that incorporates Bitcoin (logged) as a predictor is said to yield economic gains over the compared benchmark whenever such model construct yields maximum returns, CER and SR; and minimum volatility. The figures in bold letterings are cases where our WN-type predictive model provides some economic gains over the benchmark historical average model. Also, the cases of negative SR indicate that the returns of the corresponding stocks are lower than the risk free asset used in the computation of economic significance; however, the decision remains based on the maximum SR