Assessing the diversification risk of a single equity market: evidence from the largest European stock indexes

Figure 1

Descriptive statistics of six European stock index prices (for the period 2008–2018)

	DAX	FTSE 100	CAC 40	FTSE MIB	MDAX	IBEX 35
Mean	59.60722	21.86251	72.62883	16.02681	67.01549	25.12312
Median	58.14654	19.65725	73.66524	17.49506	68.14011	26.01219
SD	14.85281	2.105744	7.065241	2.625164	6.056982	1.991045
Skewness	0.565189	–0.251102	–0.265694	–0.414151	–0.112697	0.215631
Kurtosis	4.159295	3.056694	1.952011	2.622373	3.124191	3.018854
Jarque-Bera	15.19295	4.960236	2.968939	6.409951	4.165313	8.456301
Probability	0.000152	0.000294	0.000621	0.000657	0.000219	0.000806
No. of companies	30	100	40	40	60	35
Observations	3,025	3,025	3,025	3,025	3,025	3,025

The results of risk level (diversification benefits) linked with the six different portfolios

Years	Portfolio (A) DAX	Portfolio (B) FTSE100	Portfolio (C) CAC40	Portfolio (E) FTSE MIB	Portfolio (F) MDAX	Portfolio (G) IBEX35	All Portfolios (ABCEFG)
2008	1.83	0.23	1.38	0.21	2.35	0.37	0.33
2009	4.86	0.85	3.68	0.95	7.05	0.94	1.45
2010	2.89	0.47	3.04	0.82	3.34	1.13	1.12
2011	1.48	0.19	1.17	0.28	2.41	0.42	0.42
2012	3.33	0.25	3.10	0.73	3.80	0.57	0.88
2013	1.66	0.19	1.34	0.29	1.35	0.50	0.82
2014	1.89	0.21	2.02	0.32	1.10	0.49	0.50
2015	1.12	0.18	0.94	0.22	1.44	0.33	0.27
2016	2.95	0.41	2.05	0.33	2.16	0.48	0.61
2017	1.40	0.21	1.72	0.36	1.89	0.31	0.51
2018	1.61	0.12	1.83	0.37	2.33	0.39	0.36

Average risk and return tradeoffs for different poolings of the portfolios (stock indexes), 2008–2018

Portfolios	Stock indexes	Omega, average	SD, average	Correlation coefficient, average	No. of stock indexes	WAR (%)	No. of stocks
Portfolio (AB)	DAX + FTSE100	0.69	3.04	0.30	2	6.33	129
Portfolio (AC)	DAX + CAC40	2.17	4.65	0.42	2	0.17	70
Portfolio (AE)	DAX + FTSE MIB	0.87	3.22	0.40	2	0.56	69
Portfolio (AF)	DAX + MDAX	2.26	4.65	0.41	2	0.08	77
Portfolio (AG)	DAX + IBEX35	0.96	3.66	0.39	2	0.05	62
Portfolio (BC)	FTSE100 + CAC40	0.64	2.89	0.27	2	6.30	139
Portfolio (BE)	FTSE100 + FTSE MIB	0.52	2.19	0.26	2	5.12	138
Portfolio (BF)	FTSE100 + MDAX	0.56	2.96	0.26	2	7.11	146
Portfolio (BG)	FTSE100 + IBEX35	0.47	2.27	0.26	2	4.95	131
Portfolio (CE)	CAC40 + FTSE MIB	0.91	3.09	0.42	2	0.96	79
Portfolio (CF)	CAC40 + MDAX	2.03	4.34	0.42	2	0.04	87
Portfolio (CG)	CAC40 + IBEX35	0.85	3.28	0.42	2	0.03	72
Portfolio (EF)	FTSE MIB + MDAX	0.59	3.12	0.38	2	0.67	86
Portfolio (EG)	FTSE MIB + IBEX35	0.58	1.93	0.38	2	0.66	71
Portfolio (FG)	MDAX + IBEX35	0.59	3.45	0.35	2	0.00	79
Portfolio (ABC)	DAX + FTSE100 + CAC40	0.78	3.32	0.30	3	5.67	169
Portfolio (ABE)	DAX + FTSE100 + FTSEMIB	0.64	2.77	0.28	3	4.73	168
Portfolio (ABF)	DAX + FTSE100 + MDAX	0.70	3.38	0.29	3	6.32	168
Portfolio (ABG)	DAX + FTSE100 + IBEX35	0.60	2.85	0.28	3	4.55	161
Portfolio (ACE)	DAX + CAC40 + FTSE MIB	1.14	3.71	0.40	3	0.87	109
Portfolio (ACF)	DAX + CAC40 + MDAX	2.16	4.58	0.41	3	0.17	117
Portfolio (ACG)	DAX + CAC40 + IBEX35	1.14	3.88	0.41	3	0.03	102
Portfolio (AEF)	DAX + FTSEMIB + MDAX	0.89	3.66	0.39	3	0.57	101
Portfolio (AEG)	DAX + FTSEMIB + IBEX35	0.79	2.99	0.37	3	0.62	101
Portfolio (AFG)	DAX + MDAX + IBEX35	0.99	3.99	0.38	3	0.07	109
Portfolio (BCE)	FTSE100 + CAC40 + FTSE MIB	0.60	2.67	0.27	3	4.72	178
Portfolio (BCF)	FTSE100 + CAC40 + MDAX	0.65	3.24	0.27	3	6.29	186
Portfolio (BCG)	FTSE100 + CAC40 + IBEX35	0.57	2.74	0.27	3	4.54	171
Portfolio (BEF)	FTSE100 + FTSE MIB + MDAX	0.53	2.73	0.26	3	4.25	185
Portfolio (BEG)	FTSE100 + FTSE MIB + IBEX35	0.48	2.16	0.25	3	3.99	170
Portfolio (BFG)	FTSE100 + MDAX + IBEX35	0.49	2.80	0.26	3	4.96	178
Portfolio (CEF)	CAC40 + FTSE MIB + MDAX	0.93	3.57	0.40	3	0.96	126
Portfolio (CEG)	CAC40 + FTSE MIB + IBEX35	0.73	2.79	0.41	3	0.58	111
Portfolio (CFG)	CAC40 + MDAX + IBEX35	0.89	3.72	0.40	3	0.00	119
Portfolio (EFG)	FTSE MIB + MDAX + IBEX35	0.60	2.91	0.36	3	0.67	118
Portfolio (ABCE)	DAX + FTSE100 + CAC40 + FTSEMIB	0.71	3.06	0.29	4	4.39	208
Portfolio (ABCF)	DAX + FTSE100 + CAC40 + MDAX	0.79	3.53	0.29	4	5.67	216
Portfolio (ABCG)	DAX + FTSE100 + CAC40 + IBEX35	0.69	3.13	0.29	4	4.21	201
Portfolio (ABEF)	DAX + FTSE100 + FTSE MIB + MDAX	0.65	3.11	0.28	4	4.75	215
Portfolio (ABEG)	DAX + FTSE100 + FTSEMIB + IBEX35	0.58	2.66	0.284	4	3.75	200
Portfolio (ABFG)	DAX + FTSE100 + MDAX + IBEX35	0.61	3.18	0.287	4	0.87	208
Portfolio (ACEF)	DAX + CAC40 + FTSEMIB + MDAX	1.16	3.92	0.39	4	0.55	141
Portfolio (ACEG)	DAX + CAC40 + FTSE MIB + IBEX35	0.90	3.35	0.39	4	4.57	141
Portfolio (ACFG)	DAX + CAC40 + MDAX + IBEX35	1.16	4.04	0.39	4	0.05	149
Portfolio (AEFG)	DAX + FTSEMIB + MDAX + IBEX35	0.81	3.43	0.36	4	0.63	148
Portfolio (BCEF)	FTSE100 + CAC40 + FTSEMIB + MDAX	0.61	3.01	0.27	4	4.74	225
Portfolio (BCEG)	FTSE100 + CAC40 + FTSEMIB + IBEX35	0.55	2.57	0.27	4	3.74	210
Portfolio (BCFG)	FTSE100 + CAC40 + MDAX + IBEX35	0.58	3.07	0.27	4	0.59	218
Portfolio (BEFG)	FTSE100 + FTSE MIB + MDAX + IBEX35	0.49	2.63	0.26	4	4.01	217
Portfolio (CEFG)	CAC40 + FTSEMIB + MDAX + IBEX35	0.75	3.26	0.39	4	3.74	158
Portfolio (ABCEF)	DAX + FTSE100 + CAC40 + FTSEMIB + MDAX	0.72	3.28	0.29	5	4.41	255
Portfolio (ABCEG)	DAX + FTSE100 + CAC40 + FTSE MIB + IBEX35	0.65	2.92	0.29	5	3.53	240
Portfolio (ABCFG)	DAX + FTSE100 + CAC40 + MDAX + IBEX35	0.69	3.35	0.29	5	4.24	248
Portfolio (ABEFG)	DAX + FTSE100 + FTSEMIB + MDAX + IBEX35	0.59	2.97	0.28	5	3.77	247
Portfolio (ACEFG)	DAX + CAC40 + FTSEMIB + MDAX + IBEX35	0.92	3.60	0.38	5	0.57	188
Portfolio (BCEFG)	FTSE100 + CAC40 + FTSEMIB + MDAX + IBEX35	0.56	2.89	0.27	5	0.66	257

Risk elements of the individual stock indexes

Portfolios	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018
std-FTSE100	1.15	1.43	0.98	0.82	0.91	1.03	1.11	1.20	1.77	1.68	1.44
std-CAC40	3.32	5.72	4.31	2.91	3.92	3.35	3.75	3.22	4.89	4.60	5.80
std-DAX	4.23	7.91	4.69	3.79	4.71	3.87	4.59	3.64	6.94	5.39	5.14
std-IBEX35	2.08	3.61	1.53	1.27	1.58	2.91	1.39	1.15	1.60	1.49	1.79
std-FTSEMIB	1.28	2.66	1.71	1.01	1.58	0.86	1.25	0.99	1.32	1.33	1.60
std-MDAX	3.66	6.14	3.85	3.38	4.24	2.93	3.80	3.44	5.15	4.41	5.58
rij-FTSE100	0.21	0.62	0.66	0.41	0.24	0.43	0.32	0.19	0.33	0.15	0.12
rij-CAC40	0.30	0.73	0.80	0.31	0.61	0.36	0.55	0.22	0.50	0.29	0.42
rij-DAX	0.30	0.75	0.76	0.37	0.58	0.46	0.48	0.23	0.43	0.17	0.34
rij-MDAX	0.25	0.64	0.75	0.62	0.42	0.26	0.36	0.16	0.35	0.20	0.31
rij-IBEX35	0.10	0.70	0.68	0.37	0.47	0.43	0.51	0.25	0.29	0.22	0.34
rij-FTSEMIB	0.22	0.78	0.78	0.23	0.67	0.36	0.56	0.25	0.54	0.15	0.31
comb-FTSE100	3,741	4,005	4,095	4,095	4,095	4,186	4,371	4,656	4,753	4,851	4,950
comb-CAC40	666	703	703	703	703	703	703	703	703	741	780
comb-DAX	406	406	406	406	406	406	406	435	435	435	435
comb-MDAX	435	496	496	496	561	595	666	780	861	990	1081
comb-IBEX35	276	300	300	300	325	406	406	406	435	496	496
comb-FTSEMIB	351	406	406	465	465	496	496	561	630	666	741

List of sample countries’ stock index, the currency used, and the period covered

Country	Index	Portfolio designation	No. of companies	Currency	Period
Germany	DAX – Equity Index	Portfolio A	30	Euro	2008–2018
	MDAX – Equity Index	Portfolio F	60	Euro	2008–2018
England	FTSE 100 – Equity Index	Portfolio B	100	Euro	2008–2018
France	CAC 40 – Equity Index	Portfolio C	40	Euro	2008–2018
Italy	FTSE MIB – Equity Index	Portfolio E	40	Euro	2008–2018
Spain	IBEX 35 – Equity Index	Portfolio G	35	Euro	2008–2018