Document Type : Research Article


1 University of Guilan

2 Qatar University


The use of variance as a risk measure is limited by its non-coherent

nature. On the other hand, standard deviation has been demonstrated as a

coherent and effective measure of market volatility. This paper suggests the

use of standard deviation in portfolio optimization problems with cardinality

constraints and short selling, specifically in the mean-conditional value-at risk

framework. It is shown that, subject to certain conditions, this approach leads

to lower standard deviation. Empirical results obtained from experiments on

the SP index data set from 2016-2021 using various numbers of stocks and

confidence levels indicate that the proposed model outperforms existing models

in terms of Sharpe ratios.


[1] Artzner, P., Delbaen, F., Eber, J.M., Heath, D, Coherent measures of risk, Math. Finance., 9 (1999), pp. 203–228.
[2] Chang, K., Young, M., Liu, C., and Chung, H, Behavioral stock portfolio optimization
through short-selling, Int. j. model. optim., 8(2018), pp. 125–130.
[3] Dai, Z., Wen, F, A generalized approach to sparse and stable portfolio optimization problem,
J. Ind. Manag. Optim., 14 (2018), 1651.
[4] Elahi, Y., Abd Aziz, M.I, Mean-variance-cvar model of multiportfolio optimization via
linear weighted sum method, Math. Probl. Eng., 2014 (2014).
[5] Goodwin, T.H, The information ratio, Financ. Anal. J., 54 (1998), pp. 34–43.
[6] Grant, M., Boyd, S., Ye, Y, Cvx: Matlab software for disciplined convex programming,
version 2.0 beta (2013).
[7] Hamdi, A., Khodamoradi, T., Salahi, M, A penalty decomposition algorithm for the extended mean-variance-cvar portfolio optimization problem, Discrete Math. Algorithms Appl.,
[8] Khodamoradi, T., Salahi, M, Extended mean-conditional value-at-risk portfolio optimization with PADM and conditional scenario reduction technique, Comput. Stat., (2022), pp.
[9] Khodamoradi, T., Salahi, M., Najafi, A.R, A note on CCMV portfolio optimization
model with short selling and risk-neutral interest rate, Stat. Optim. Inf. Comput., 8 (2020),
pp. 740–748.
[10] Khodamoradi, T., Salahi, M., Najafi, A.R, Cardinality-constrained portfolio optimization
with short selling and risk-neutral interest rate, Decis. Econ. Finance., (2021), pp. 1–18,
[11] Khodamoradi, T., Salahi, M., Najafi, A.R, Multi-intervals robust mean-conditional valueat-risk portfolio optimization with conditional scenario reduction technique, Int. J. Appl.
Decis., (2022), pp. 1–18
[12] Kim, J.H., Lee, Y., Kim, W.C., Fabozzi, F.J, Mean–variance optimization for asset allocation, J. Portf. Manag., 47 (2021), pp. 24–40.
[13] Kobayashi, K., Takano, Y., Nakata, K, Bilevel cutting-plane algorithm for cardinalityconstrained mean-cvar portfolio optimization, J Glob Optim., 81 (2021), pp. 493–528.
[14] Konno, H., Waki, H., Yuuki, A, Portfolio optimization under lower partial risk measures,
Asia-Pac. Financial Mark. , 9 (2002), pp. 127–140.
[15] Lo, A.W, The statistics of sharpe ratios Financ. Anal. J., 58 (2002), pp. 36–52.
[16] Pineda, S., Conejo, A, Scenario reduction for risk-averse electricity trading, IET Gener.
Transm. Distrib., 4 (2010), pp. 694–705.
[17] Rockafellar, R.T., Uryasev, S, Optimization of conditional value-at-risk, J. Risk., 2
(2000), pp. 21–42
[18] Roman, D., Darby-Dowman, K., Mitra, G., Mean-risk models using two risk measures: a
multi-objective approach, Quant Finance., 7 (2007), pp. 443–458.
[19] Shi, Y., Zhao, X., Yan, X, Optimal asset allocation for a mean-variance-cvar insurer under
regulatory constraints, Am. j. ind. bus. manag., 9 (2019), 1568.