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Portfolio selection based on Extended Gini Shortfall risk measures

  • Lhoucine Ben Hssain ORCID logo EMAIL logo , Mohammed Berkhouch ORCID logo and Ghizlane Lakhnati ORCID logo
Published/Copyright: October 5, 2023
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Abstract

In this paper, we conducted a comprehensive examination of the Extended Gini Shortfall (EGS) as a flexible risk measure for portfolio selection, employing various approaches. The EGS measure possesses desirable properties, such as coherence, risk and variability measurement, and risk aversion. Additionally, we introduced the Reward Risk Ratio induced from EGS and explored its associated properties. Our main focus centered on a convex optimization problem, where the objective was to minimize portfolio risk while adhering to reward and budget constraints. We demonstrated the effectiveness of the obtained theoretical results through a practical application.

MSC 2010: 91G70; 91G10; 47N10

A Before Covid-19

Table 6

Correlation between stocks before Covid-19.

MSFT AAPL AMZN NFLX FB TSLA WMT GOOGL VZ IBM
MSFT 1.000 0.629 0.733 0.580 0.537 0.325 0.272 0.729 0.182 0.482
AAPL 0.629 1.000 0.602 0.459 0.464 0.314 0.222 0.601 0.065 0.391
AMZN 0.733 0.602 1.000 0.623 0.593 0.305 0.217 0.687 0.046 0.373
NFLX 0.580 0.459 0.623 1.000 0.460 0.306 0.160 0.558 0.048 0.299
FB 0.537 0.464 0.593 0.460 1.000 0.254 0.132 0.610 0.047 0.253
TSLA 0.325 0.314 0.305 0.306 0.254 1.000 0.143 0.292 0.061 0.199
WMT 0.272 0.222 0.217 0.160 0.132 0.143 1.000 0.199 0.284 0.275
GOOGL 0.729 0.601 0.687 0.558 0.610 0.292 0.199 1.000 0.095 0.419
VZ 0.182 0.065 0.046 0.048 0.047 0.061 0.284 0.095 1.000 0.242
IBM 0.482 0.391 0.373 0.299 0.253 0.199 0.275 0.419 0.242 1.000
Table 7

Descriptive statistics of stocks before Covid-19.

MSFT AAPL AMZN NFLX FB TSLA WMT GOOGL VZ IBM
𝜎 0.0137 0.0156 0.0172 0.0233 0.0186 0.0306 0.0121 0.0145 0.0112 0.0130
Mean 0.00129 0.00124 0.0011 0.00117 0.0007 0.00075 0.00085 0.0007 0.0003 −0.00012
Min −0.0558 −0.1049 −0.0814 −0.1083 −0.2102 −0.1496 −0.1073 −0.0779 −0.0479 −0.0793
Max 0.0729 0.0680 0.1241 0.1270 0.10270 0.1627 0.1034 0.0918 0.0739 0.0849
Skew −0.0375 −0.4997 0.1662 0.0256 −1.9722 0.1059 0.3243 −0.3015 −0.0506 −0.3185
Kurt 3.7288 5.1659 6.5953 3.2477 24.648 4.9720 19.642 5.0146 4.2105 8.8486

B During Covid-19

Table 8

Correlation between stocks during Covid-19.

MSFT AAPL AMZN NFLX FB TSLA WMT GOOGL VZ IBM
MSFT 1.000 0.808 0.697 0.568 0.705 0.490 0.518 0.825 0.466 0.509
AAPL 0.808 1.000 0.675 0.522 0.701 0.479 0.476 0.704 0.396 0.458
AMZN 0.697 0.675 1.000 0.612 0.637 0.431 0.367 0.654 0.269 0.308
NFLX 0.568 0.522 0.612 1.000 0.538 0.38 0.369 0.510 0.225 0.190
FB 0.705 0.701 0.637 0.538 1.000 0.389 0.358 0.743 0.342 0.389
TSLA 0.490 0.479 0.431 0.380 0.389 1.000 0.165 0.413 0.084 0.224
WMT 0.518 0.476 0.367 0.369 0.358 0.165 1.000 0.415 0.513 0.363
GOOGL 0.825 0.704 0.654 0.510 0.743 0.413 0.415 1.000 0.447 0.508
VZ 0.466 0.396 0.269 0.225 0.342 0.084 0.513 0.447 1.000 0.594
IBM 0.509 0.458 0.308 0.19 0.389 0.224 0.363 0.508 0.594 1.000
Table 9

Descriptive statistics of stocks during Covid-19.

MSFT AAPL AMZN NFLX FB TSLA WMT GOOGL VZ IBM
𝜎 0.0216 0.0235 0.0202 0.0249 0.0242 0.0466 0.0157 0.0202 0.0126 0.0210
Mean 0.0015 0.0018 0.0012 0.0012 0.0010 0.0049 0.0003 0.0015 −0.00013 0.00016
Min −0.1594 −0.1370 −0.0825 −0.11809 −0.1530 −0.2365 −0.0950 −0.1236 −0.0684 −0.1375
Max 0.1329 0.1131 0.0763 0.1557 0.0974 0.1814 0.1107 0.0883 0.0696 0.1070
Skew −0.4636 −0.2805 −0.0338 0.2214 −0.3884 −0.3181 0.7753 −0.377 0.5953 −0.9468
Kurt 10.3165 5.5327 2.2052 5.3735 4.7758 4.0342 12.1188 5.3392 7.5634 8.6554

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Received: 2022-12-27
Revised: 2023-08-01
Accepted: 2023-08-16
Published Online: 2023-10-05
Published in Print: 2024-01-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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