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

Bouri, Elie; Salisu, Afees A.; Gupta, Rangan

doi:10.1186/s40854-023-00464-8

Financial Innovation

Table 3 Economic significance

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
Sector stock	Model	\(\varvec{Gamma} = {\mathbf{3}}\;\varvec{and}\;\varvec{Theta} = {\mathbf{6}}\)				\(\varvec{Gamma} = {\mathbf{3}}\;\varvec{and}\;\varvec{Theta} = {\mathbf{8}}\)
Composite	HA	0.1582	6.3683	0.1569	0.0518	0.2180	11.0590	0.2166	0.0573
	WN	0.3786	9.9721	0.3772	0.1112	0.4942	18.0405	0.4928	0.1099
Consumer Discretionary	HA	0.4717	78.2085	0.4686	0.0502	0.6115	139.5238	0.6085	0.0494
	WN	− 2.4630	121.1427	− 2.4670	− 0.2263	− 3.3025	215.4363	− 3.3065	− 0.2269
Consumer Staples	HA	− 0.3913	10.6121	− 0.3919	− 0.1286	− 0.5171	18.6920	− 0.5177	− 0.1260
	WN	0.2351	3.2580	0.2344	0.1150	0.3054	5.7784	0.3047	0.1156
Energy	HA	0.4169	50.9515	0.4145	0.0545	0.5448	90.7675	0.5424	0.0543
	WN	− 3.8934	69.5225	− 3.8960	− 0.4702	− 5.1918	123.5344	− 5.1944	− 0.4696
Financials	HA	− 0.3992	12.8728	− 0.4004	− 0.1189	− 0.5129	22.0292	− 0.5140	− 0.1151
	WN	− 0.5381	37.2313	− 0.5394	− 0.0927	− 0.7365	66.3159	− 0.7378	− 0.0938
Health Care	HA	− 1.1088	29.4945	− 1.1097	− 0.2092	− 1.4770	52.4270	− 1.4778	− 0.2078
	WN	− 0.6532	29.7704	− 0.6546	− 0.1248	− 0.8836	52.8847	− 0.8851	− 0.1253
Industrials	HA	− 0.7841	20.0793	− 0.7856	− 0.1811	− 1.0216	34.3436	− 1.0230	− 0.1790
	WN	− 0.1195	33.2669	− 0.1214	− 0.0255	− 0.1797	59.6844	− 0.1816	− 0.0268
Information Technology	HA	0.5007	12.2098	0.4972	0.1354	0.6604	21.5676	0.6569	0.1363
	WN	− 0.1611	43.8404	− 0.1648	− 0.0285	− 0.2399	79.7341	− 0.2436	− 0.0299
Materials	HA	− 0.2289	19.4588	− 0.2300	− 0.0581	− 0.3026	34.2687	− 0.3038	− 0.0564
	WN	− 0.0533	18.5352	− 0.0543	− 0.0188	− 0.0884	33.1728	− 0.0895	− 0.0201
Real Estate	HA	− 1.3669	29.4363	− 1.3680	− 0.2570	− 1.8207	52.2294	− 1.8218	− 0.2557
	WN	− 0.9325	25.9896	− 0.9334	− 0.1883	− 1.2618	46.2730	− 1.2627	− 0.1895
Telecommunication Services	HA	0.3155	73.2586	0.3129	0.0336	0.4156	130.2285	0.4130	0.0340
	WN	− 0.8051	74.4048	− 0.8076	− 0.0965	− 1.0965	133.5648	− 1.0990	− 0.0973
Utilities	HA	0.2550	6.5103	0.2536	0.0891	0.3363	11.6497	0.3349	0.0905
	WN	0.4724	10.3612	0.4710	0.1382	0.6230	18.6182	0.6216	0.1380

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

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