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Table 6 Economic significance (75:25 data split with GARCH based 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

0.2527

1.89E−05

0.2527

51.8445

0.3171

3.35E−05

0.3171

50.0171

 

WN

0.2537

1.85E−05

0.2537

52.6391

0.3185

3.28E−05

0.3185

50.7792

Consumer discretionary

HA

0.2299

2.88E−05

0.2299

37.7162

0.2879

5.12E−05

0.2879

36.3875

 

WN

0.2346

2.94E−05

0.2346

38.2143

0.2938

5.22E−05

0.2938

36.8585

Consumer staples

HA

0.1150

9.44E−07

0.1150

90.0166

0.1401

1.68E−06

0.1401

86.8932

 

WN

0.1619

4.24E−06

0.1619

65.2402

0.2002

7.54E−06

0.2002

62.9133

Energy

HA

0.1053

1.73E−05

0.1053

18.6993

0.1276

3.07E−05

0.1276

18.0533

 

WN

0.1020

1.66E−05

0.1020

18.2954

0.1234

2.94E−05

0.1234

17.6695

Financials

HA

0.1856

1.55E−05

0.1856

40.1856

0.2309

2.75E−05

0.2309

38.7731

 

WN

0.1913

1.61E−05

0.1913

40.8373

0.2382

2.86E−05

0.2382

39.3970

Health Care

HA

0.2108

4.06E−06

0.2108

90.9209

0.2633

7.23E−06

0.2633

87.7234

 

WN

0.2061

4.06E−06

0.2061

88.6021

0.2573

7.22E−06

0.2573

85.4844

Industrials

HA

0.2554

1.08E−05

0.2554

69.3924

0.3206

1.92E−05

0.3206

66.9491

 

WN

0.2635

1.10E−05

0.2635

71.1749

0.3309

1.95E−05

0.3309

68.6510

Information Technology

HA

0.0907

4.49E−05

0.0907

9.4319

0.1089

7.98E−05

0.1089

9.1118

 

WN

0.0897

4.49E−05

0.0897

9.2772

0.1076

7.98E−05

0.1076

8.9623

Materials

HA

0.1730

1.15E−05

0.1730

42.8836

0.2147

2.05E−05

0.2147

41.3808

 

WN

0.2146

1.97E−05

0.2146

42.1344

0.2681

3.51E−05

0.2681

40.6387

Real Estate

HA

0.1176

1.39E−06

0.1176

76.5535

0.1435

2.46E−06

0.1435

73.9247

 

WN

0.1542

6.10E−06

0.1542

51.2772

0.1905

1.09E−05

0.1905

49.4629

Telecommunication Services

HA

0.1960

1.10E−05

0.1960

50.8572

0.2443

1.95E−05

0.2443

49.0645

 

WN

0.1958

1.11E−05

0.1958

50.5779

0.2440

1.97E−05

0.2440

48.7952

Utilities

HA

0.2332

4.11E−06

0.2332

101.4970

0.2921

7.30E−06

0.2921

97.9237

 

WN

0.2456

4.63E−06

0.2456

101.3130

0.3080

8.24E−06

0.3080

97.7250

  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