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J. Risk Financial Manag. 2021, 14, 440 10 of 15 Figure 5. Density of Bitcoin: COVID era. 3.3. Similarity with Select Asset Classes In this part, we apply the same method to test the equality of densities for daily returns of Bitcoin and stocks in different industry groups. The data for daily stock returns in different industries comes from Kenneth R. French 30 Industry Portfolios2. We use the daily average value weighted returns for 30 industry portfolios data. The 30 indus- try portfolios include: Food Products (Food), Beer and Liquor (Beer), Tobacco Products (Smoke), Recreation (Games), Printing and Publishing (Books), Consumer Goods (Hshld), Apparel (Clths), Healthcare (Hlth), Medical Equipment, Pharmaceutical Products, Chemi- cals (Chems), Textiles (Txtls), Construction and Construction Materials (Cnstr), Steel Works Etc (Steel), Fabricated Products and Machinery (Fabpr), Electrical Equipment (Elceq), Au- tomobiles and Trucks (Autos), Aircraft, ships, and railroad equipment (Carry), Precious Metals, Non-Metallic, and Industrial Metal Mining (Mines), Coal (Coal), Petroleum and Natural Gas (Oil), Utilities (Util), Communication (Telcm), Personal and Business Services (Servs), Business Equipment (Buseq), Business Supplies and Shipping Containers (Pa- per), Transportation (Trans), Wholesale (Whlsl), Retail (Rtail), Restaraunts, Hotels, Motels (Meals), Banking, Insurance, Real Estate, Trading (Fin), Everything Else (Other). We apply the nonparametric entropy metrics test of equality of densities proposed in (Renyi 1961), described above, where f1 = f (x) and f2 = f (y) are the marginal densities of daily returns of Bitcoin and stocks in different industries, respectively. From Table 4, we calculated the entropy measures between Bitcoin and select asset classes. During pre-COVID period, the density of Bitcoin daily return has smallest distance with the density of Coal industry daily return. The Sρ between these two densities is 0.02 and statistically significant. The density of Bitcoin daily return also has small distances with densities of Steel Works Etc, as well as Precious Metals, Non-Metallic, and Industrial Metal Mining industries, with Sρ values of 0.07 and 0.09, respectively. During COVID era, the density of Bitcoin daily return has smallest distance with the density of Business Supplies and Shipping Containers, Utilities, Tobacco Products and Restaraunts, Hotels, Motels industries daily returns, with Sρ values of 0.03. Comparing Sρ before and after the COVID-19 outbreak, we conclude that the values of Sρ decrease generally in all cases. This is consistent with our findings with stock indexes in the previous section, which indicates that forecasting cryptos’ performance could be more feasible during COVID era.PDF Image | Contrasting Cryptocurrencies with Other Assets
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