Open Access

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

Artor Nuhiu
Artor Nuhiu
, 
Florin Aliu
Florin Aliu
 and 
Bedri Peci
Bedri Peci
   | Mar 31, 2022
International Journal of Management and Economics's Cover Image
About this article
Previous Article
Next Article
Cite
Article Category: Empirical Paper
Published Online: Mar 31, 2022
Page range: 3 - 16
Received: Sep 17, 2020
Accepted: Mar 16, 2022
DOI: https://doi.org/10.2478/ijme-2022-0001
Keywords
© 2022 Artor Nuhiu et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1

Risk diversification of different portfolios. Source: Authors’ calculations based on the Thomson Reuters Eikon database.
Risk diversification of different portfolios. Source: Authors’ calculations based on the Thomson Reuters Eikon database.

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
eISSN:
2543-5361
Language:
English
Publication timeframe:
4 times per year
Journal Subjects:
Business and Economics, Political Economics, Economic Theory, Systems and Structures, Business Management, Management Accounting, Financial Controlling, Cost Calculation, Investment
Journal RSS Feed