Skip to main content
SpringerLink
Log in

Cardinality-constrained portfolio optimization with short selling and risk-neutral interest rate

  • Published:
Decisions in Economics and Finance Aims and scope Submit manuscript

Abstract

Short selling strategy leads to a portfolio with significantly better risk-return structure compared to the standard approach. Moreover, investors can use risk-neutral interest rate to increase the return of the portfolio. In this paper, we study the cardinality-constrained mean–variance portfolio optimization model with and without short selling and risk-neutral interest rate. First, to avoid negative investment in stocks with no short selling position, the non-negativeness of the product of each stock’s return to the proportion of investment on it is added to the model as a constraint. Then, we further present an improved model, where instead of determining the term of the short rebate according to the proportion of the total funds invested, it is determined according to the return. Finally, all models are compared using the data set of the S&P 500 index, Communication Service.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alexander, G.J.: Short selling and efficient sets. J. Finance 48(4), 1497–1506 (1993)

    Google Scholar 

  • Alexander, G.J.: Efficient sets, short-selling, and estimation risk. J. Portf. Manag. 21(2), 64 (1995)

    Google Scholar 

  • Armananzas, R., Lozano, J.A.: A multiobjective approach to the portfolio optimization problem. In: 2005 IEEE Congress on Evolutionary Computation, vol. 2, pp. 1388–1395. IEEE (2005)

  • Bertsimas, D., Shioda, R.: Algorithm for cardinality-constrained quadratic optimization. Comput. Optim. Appl. 43(1), 1–22 (2009)

    Google Scholar 

  • Bielecki, T.R., Jang, I.: Portfolio optimization with a defaultable security. Asia Pac. Financ. Mark. 13(2), 113–127 (2006)

    Google Scholar 

  • Birge, J.R., Zhang, R.Q.: Risk-neutral option pricing methods for adjusting constrained cash flows. Eng. Econ. 44(1), 36–49 (1999)

    Google Scholar 

  • Chang, T.J., Meade, N., Beasley, J.E., Sharaiha, Y.M.: Heuristics for cardinality constrained portfolio optimisation. Comput. Oper. Res. 27(13), 1271–1302 (2000)

    Google Scholar 

  • Crama, Y., Schyns, M.: Simulated annealing for complex portfolio selection problems. Eur. J. Oper. Res. 150(3), 546–571 (2003)

    Google Scholar 

  • Cura, T.: Particle swarm optimization approach to portfolio optimization. Nonlinear Anal. Real World Appl. 10(4), 2396–2406 (2009)

    Google Scholar 

  • Dai, Z., Wen, F.: A generalized approach to sparse and stable portfolio optimization problem. J. Ind. Manag. Optim. 14(4), 1651–1666 (2018a)

    Google Scholar 

  • Dai, Z., Wen, F.: Some improved sparse and stable portfolio optimization problems. Finance Res. Lett. 27, 46–52 (2018b)

    Google Scholar 

  • Di Gaspero, L., di Tollo, G., Roli, A., Schaerf, A.: Local search for constrained financial portfolio selection problems with short sellings. In: International Conference on Learning and Intelligent Optimization, pp. 450–453. Springer (2011)

  • Elton, E.J., Gruber, M.J., Brown, S.J., Goetzmann, W.N.: Modern Portfolio Theory and Investment Analysis. Wiley, New York (2009)

    Google Scholar 

  • Fernández, A., Gómez, S.: Portfolio selection using neural networks. Comput. Oper. Res. 34(4), 1177–1191 (2007)

    Google Scholar 

  • Frost, P.A., Savarino, J.E.: For better performance: constrain portfolio weights. J. Portf. Manage. 15(1), 29 (1988)

    Google Scholar 

  • Gao, J., Li, D.: Optimal cardinality constrained portfolio selection. Oper. Res. 61(3), 745–761 (2013)

    Google Scholar 

  • Gilli, M., Maringer, D., Schumann, E.: Numerical Methods and Optimization in Finance. Academic Press, Cambridge (2011)

    Google Scholar 

  • Grant, M., Boyd, S., Ye, Y.: Cvx: Matlab software for disciplined convex programming, version 2.0 beta (2013)

  • Gyorfi, L., Ottucsak, G., Walk, H.: Machine Learning for Financial Engineering (Advances in Computer Science and Engineering: Texts). Imperial College Press, London (2011)

    Google Scholar 

  • Jacobs, B.I., Levy, K.N., Markowitz, H.M.: Portfolio optimization with factors, scenarios, and realistic short positions. Oper. Res. 53(4), 586–599 (2005)

    Google Scholar 

  • Jacobs, B.I., Levy, K.N., Markowitz, H.M.: Trimability and fast optimization of long-short portfolios. Financ. Anal. J. 62(2), 36–46 (2006)

    Google Scholar 

  • Jagannathan, R., Ma, T.: Risk reduction in large portfolios: why imposing the wrong constraints helps. J. Finance 58(4), 1651–1683 (2003)

    Google Scholar 

  • Jobst, N.J., Horniman, M.D., Lucas, C.A., Mitra, G., et al.: Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints. Quant. Finance 1(5), 489–501 (2001)

    Google Scholar 

  • Kawaller, I.G.: A note: debunking the myth of the risk-free return. J. Futures Mark. 7(3), 327–331 (1987)

    Google Scholar 

  • Khodamoradi, T., Salahi, M., Najafi, A.R.: Robust CCMV model with short selling and risk-neutral interest rate. Phys. A Stat. Mech. Appl. 547, 124429 (2020)

    Google Scholar 

  • Kwan, C.C.: Optimal portfolio selection under institutional procedures for short selling. J. Bank. Finance 19(5), 871–889 (1995)

    Google Scholar 

  • Kwan, C.C.: Portfolio selection under institutional procedures for short selling: normative and market-equilibrium considerations. J. Bank. Finance 21(3), 369–391 (1997)

    Google Scholar 

  • Lai, T.L., Xing, H., Chen, Z., et al.: Mean-variance portfolio optimization when means and covariances are unknown. Ann. Appl. Stat. 5(2A), 798–823 (2011)

    Google Scholar 

  • Li, D., Ng, W.L.: Optimal dynamic portfolio selection: multiperiod mean-variance formulation. Math. Finance 10(3), 387–406 (2000)

    Google Scholar 

  • Li, D., Sun, X., Wang, J.: Optimal lot solution to cardinality constrained mean-variance formulation for portfolio selection. Math. Finance Int. J. Math. Stat. Financ. Econ. 16(1), 83–101 (2006)

    Google Scholar 

  • Lintner, J.: Security prices, risk, and maximal gains from diversification. J. Finance 20(4), 587–615 (1965)

    Google Scholar 

  • Maringer, D.: Portfolio Management with Heuristic Optimization. Springer, Berlin (2006)

    Google Scholar 

  • Maringer, D., Kellerer, H.: Optimization of cardinality constrained portfolios with a hybrid local search algorithm. OR Spectr. 25(4), 481–495 (2003)

    Google Scholar 

  • Markowitz, H.: Portfolio selection. J. Finance 7(1), 77–91 (1952)

    Google Scholar 

  • Najafi, A.A., Ghasemi, H.R.: Portfolio optimization in terms of justifiability short selling and some market practical constraints. Financ. Res. J. 14(2), 117–132 (2013)

    Google Scholar 

  • Patel, N.R., Subrahmanyam, M.G.: A simple algorithm for optimal portfolio selection with fixed transaction costs. Manag. Sci. 28(3), 303–314 (1982)

    Google Scholar 

  • Salehpoor, I.B., Molla-Alizadeh-Zavardehi, S.: A constrained portfolio selection model at considering risk-adjusted measure by using hybrid meta-heuristic algorithms. Appl. Soft Comput. 75, 233–253 (2019)

    Google Scholar 

  • Schaerf, A.: Local search techniques for constrained portfolio selection problems. Comput. Econ. 20(3), 177–190 (2002)

    Google Scholar 

  • Sedighi, M., Jahangirnia, H., Gharakhani, M.: A new efficient metaheuristic model for stock portfolio management and its performance evaluation by risk-adjusted methods. Int. J. Financ. Manag. Account. 3, 63–77 (2019)

    Google Scholar 

  • Shaw, D.X., Liu, S., Kopman, L.: Lagrangian relaxation procedure for cardinality-constrained portfolio optimization. Optim. Methods Softw. 23(3), 411–420 (2008)

    Google Scholar 

  • Soleimani, H., Golmakani, H.R., Salimi, M.H.: Markowitz-based portfolio selection with minimum transaction lots, cardinality constraints and regarding sector capitalization using genetic algorithm. Expert Syst. Appl. 36(3), 5058–5063 (2009)

    Google Scholar 

  • Weiss, G.: The long and short of short-selling. Bus. Week 10, 106–108 (1991)

    Google Scholar 

  • Xie, J., He, S., Zhang, S.: Randomized portfolio selection with constraints. Pac. J. Optim. 4(1), 89–112 (2008)

    Google Scholar 

  • Zhang, S., Wang, S., Deng, X.: Portfolio selection theory with different interest rates for borrowing and leading. J. Glob. Optim. 28(1), 67–95 (2004)

    Google Scholar 

  • Zhao, L., Palomar, D.P.: A markowitz portfolio approach to options trading. IEEE Trans. Signal Process. 66(16), 4223–4238 (2018)

    Google Scholar 

Download references

Acknowledgements

The authors would like to thank all reviewers for their useful comments and suggestions and Center of Excellence for Mathematical Modeling, Optimization and Combinatorial Computing (MMOCC), University of Guilan, for partially supporting this research.

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

    Tahereh Khodamoradi, Maziar Salahi & Ali Reza Najafi

  2. Center of Excellence for Mathematical Modeling, Optimization and Combinatorial Computing (MMOCC), University of Guilan, Rasht, Iran

    Maziar Salahi

Authors
  1. Tahereh Khodamoradi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Maziar Salahi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ali Reza Najafi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Maziar Salahi.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khodamoradi, T., Salahi, M. & Najafi, A.R. Cardinality-constrained portfolio optimization with short selling and risk-neutral interest rate. Decisions Econ Finan 44, 197–214 (2021). https://doi.org/10.1007/s10203-020-00293-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10203-020-00293-9

Keywords

Mathematics Subject Classification

JEL Classification

Search

Navigation