Table 5.

The optimal asset allocation and the measure of its risk diversification.

	dj-wt			dj-go			dj-ch
	ρ	w 1	R a	ρ	w 1	R a	ρ	w 1	R a
Overall	0.2561	0.9524	0.0641	−0.0089	0.5024	0.0823	0.0245	0.9643	0.0695
Pre	0.2395	0.9454	0.0522	0.0117	0.4974	0.0769	0.0239	0.9701	0.0608
Post	0.3107	0.9755	0.1034	−0.0776	0.5189	0.1003	0.0263	0.9454	0.0980
	dj-eu			dj-bi			dj-et
	ρ	w 1	R a	ρ	w 1	R a	ρ	w 1	R a
Overall	0.0053	0.2533	0.0377	0.0234	0.9511	0.0883	0.0759	0.9862	0.0736
Pre	−0.0438	0.3057	0.0188	−0.0118	0.9532	0.0809	0.0455	0.9880	0.0641
Post	0.1670	0.0810	0.0998	0.1393	0.9441	0.1127	0.1759	0.9803	0.1048
	dj-li			wt-go			wt-ch
	ρ	w 1	R a	ρ	w 1	R a	ρ	w 1	R a
Overall	0.0358	0.9732	0.0735	0.0528	0.1143	0.0344	0.0063	0.7666	0.0240
Pre	0.0038	0.9767	0.0644	0.0544	0.1044	0.0324	−0.0156	0.7745	0.0171
Post	0.1412	0.9618	0.1032	0.0473	0.1469	0.0406	0.0785	0.7407	0.0469
	wt-eu			wt-bi			wt-et
	ρ	w 1	R a	ρ	w 1	R a	ρ	w 1	R a
Overall	0.0678	0.0276	0.0102	0.0508	0.7229	0.0497	0.0498	0.8636	0.0351
Pre	0.0521	0.0343	−0.0022	0.0422	0.7341	0.0399	0.0516	0.8990	0.0186
Post	0.1192	0.0058	0.0512	0.0792	0.6860	0.0819	0.0439	0.7473	0.0891
	wt-li			go-ch			go-eu
	ρ	w 1	R a	ρ	w 1	R a	ρ	w 1	R a
Overall	0.0486	0.8230	0.0238	0.0035	0.9597	0.0479	0.4507	0.0667	0.0168
Pre	0.0436	0.8391	0.0130	−0.0029	0.9595	0.0553	0.4486	0.1025	0.0083
Post	0.0651	0.7701	0.0595	0.0248	0.9603	0.0238	0.4576	−0.0508	0.0448
	go-et			go-li			ch-bi
	ρ	w 1	R a	ρ	w 1	R a	ρ	w 1	R a
Overall	0.1047	0.9959	0.0421	0.0538	0.9730	0.0470	0.0315	0.4274	0.0868
Pre	0.0822	0.9953	0.0448	0.0293	0.9686	0.0524	0.0265	0.4257	0.0816
Post	0.1786	0.9979	0.0332	0.1341	0.9875	0.0294	0.0477	0.4329	0.1039
	ch-et			ch-li			eu-bi
	ρ	w 1	R a	ρ	w 1	R a	ρ	w 1	R a
Overall	0.0112	0.6165	0.0689	0.0279	0.5783	0.0491	0.0791	0.9883	0.0171
Pre	−0.0181	0.6334	0.0619	0.0131	0.5838	0.0462	0.0229	0.9791	0.0090
Post	0.1077	0.5608	0.0919	0.0765	0.5603	0.0585	0.2636	1.0185	0.0438
	eu-et			eu-li
	ρ	w 1	R a	ρ	w 1	R a
Overall	0.0694	1.0002	0.0110	0.0370	0.9951	0.0118
Pre	0.0278	0.9972	−0.0013	−0.0245	0.9898	0.0022
Post	0.2060	1.0099	0.0515	0.2392	1.0127	0.0433

1. “dj” denotes the Dow Jones Industrial Average index in the stock market; “wt” and “go” represent the WTI crude oil and gold in the commodity market, respectively; “ch” and “eu” denote the Chinese yuan (CNY) and Euro in the currency market, respectively, and “bi,” “et,” and “li” denote the abbreviations of Bitcoin, Ethereum, and Litecoin in the cryptocurrency market, respectively. 2. ρ denotes the average value of correlation for a pair of assets during a specific period. w₁ is the average weight forecast of the first component asset of the minimum variance portfolio (MVP) based on the MDWI approach of Su (41) or Kroner and Ng (42). 3. R^a denotes the realized risk-adjusted returns of the MVP, which is obtained by the return of the MVP divided by the standard deviation of the MVP. 4. The bold font in columns “ρ” (or “R^a”) for a specific pair of assets denotes the largest value when the values of “ρ” (or “R^a”) for three periods are compared with each other. 5. The italic font in columns “ρ” (or “R^a”) for a specific pair of assets denotes the smallest value when the values of “ρ” (or “R^a”) for three periods are compared with each other.