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Can Time-Varying Copulas Improve the Mean-Variance Portfolio?

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Handbook of Financial Econometrics and Statistics

Abstract

Research in structuring asset return dependence has become an indispensable element of wealth management, particularly after the experience of the recent financial crises. In this paper, we evaluate whether constructing a portfolio using time-varying copulas yields superior returns under various weight updating strategies. Specifically, minimum-risk portfolios are constructed based on various copulas and the Pearson correlation, and a 250-day rolling window technique is adopted to derive a sequence of time-varied dependencies for each dependence model. Using daily data of the G7 countries, our empirical findings suggest that portfolios using time-varying copulas, particularly the Clayton dependence, outperform those constructed using Pearson correlations. The above results still hold under different weight updating strategies and portfolio rebalancing frequencies.

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Notes

  1. 1.

    See Chan et al. (1999), Dowd (2005), Patton (2006a), Engle and Sheppardy (2008), Chollete et al. (2009), Bauer and Vorkink (2011).

  2. 2.

    For detailed derivations, please refer to Cherubini et al. (2004), Demarta and McNeil (2005), Embrechts et al. (2003), Embrechts et al. (2005), Franke et al. (2008), Nelson (2006), and Patton (2009).

  3. 3.

    Short selling usually involves other service fees, which vary depending on the creditability of the investors. Because the focus of this study is on the effect of the dependence structure on portfolio performance, we assume that short selling is not allowed to simplify the comparison.

  4. 4.

    For example, we use return data from t 1 to t 250 to calculate the optimal portfolio weights with dependencies estimated from the copulas and the Pearson correlation. The optimal portfolio weights are applied to the return data at t 251 to calculate the realized portfolio returns.

  5. 5.

    For detailed derivations and computer codes, please refer to Ledoit and Wolf (2008).

  6. 6.

    Ledoit and Wolf (2008) suggested that 5,000 iterations guarantee a sufficient sample. We adopt a higher standard of 10,000 iterations to strengthen our testing results.

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Author information

Authors and Affiliations

  1. Department of Finance, Western Connecticut State University, Danbury, CT, 06810, USA

    Chin-Wen Huang

  2. Department of Accounting and Finance, York College, The City University of New York, 94-20 Guy R Brewer Blvd, Jamaica, NY, 11451, USA

    Chun-Pin Hsu

  3. Department of Finance and Law College of Business Administration, Central Michigan University, Mount Pleasant, MI, USA

    Wan-Jiun Paul Chiou

Authors
  1. Chin-Wen Huang
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  2. Chun-Pin Hsu
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  3. Wan-Jiun Paul Chiou
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Corresponding author

Correspondence to Chun-Pin Hsu .

Editor information

Editors and Affiliations

  1. Department of Finance and Economics, Rutgers Business School, Rutgers, The State University of New Jersey, Piscataway, New Jersey, USA

    Cheng-Few Lee

  2. Center for PBBEF Research, North Brunswick, New Jersey, USA

    John C. Lee

Appendix 1

Appendix 1

Appendix 1 illustrates the dependence of the G7 countries from different dependence models. Note that to ease the comparison between dependencies, we transform Gumbel dependencies by (1 − δ). Therefore, the range for the Clayton and the Gumbel copulas is between 0 and 1, with 0 meaning no dependence and 1 standing for perfect dependence. The range for the Gaussian copula, the Student’s t-copula, and the Pearson correlation is −1 to 1, with 0 meaning no dependence and 1 or −1 standing for complete dependence.

 

CA

FR

DE

IT

JP

UK

USA

Panel A: Gaussian dependence

CA

       

Max

       

Min

       

FR

       

Max

0.7064

      

Min

0.3914

      

DE

       

Max

0.6487

0.9686

     

Min

−0.2016

0.7856

     

IT

       

Max

0.6320

0.9407

0.9274

    

Min

−0.2143

−0.2303

0.7001

    

JP

       

Max

0.1814

0.2761

0.2478

0.4023

   

Min

−0.2115

−0.2238

−0.2229

0.0119

   

UK

       

Max

0.6393

0.9100

0.8665

0.8575

0.4664

  

Min

−0.1945

−0.2384

−0.2008

−0.2050

0.0329

  

USA

       

Max

0.7221

0.5031

0.5231

0.4661

0.5831

0.5671

 

Min

−0.1864

−0.2127

−0.2087

−0.2414

−0.2241

0.1997

 

Panel B: Student’s t dependence

CA

       

Max

       

Min

       

FR

       

Max

0.7509

      

Min

0.3921

      

DE

       

Max

0.4578

0.9810

     

Min

−0.1070

0.7476

     

IT

       

Max

0.4367

0.9810

0.9586

    

Min

−0.1089

0.7476

0.6937

    

JP

       

Max

0.1093

0.1679

0.1522

0.6846

   

Min

−0.1284

−0.1511

−0.1574

0.0093

   

UK

       

Max

0.4478

0.8055

0.7380

0.7316

0.7335

  

Min

−0.1094

−0.1546

−0.1359

−0.1230

0.0284

  

USA

       

Max

0.5733

0.8055

0.3457

0.3176

0.4375

0.6614

 

Min

−0.1107

−0.1546

−0.1343

−0.1360

−0.1519

0.2687

 

Panel C: Gumbel dependence

CA

       

Max

       

Min

       

FR

       

Max

0.5947

      

Min

0.3220

      

DE

       

Max

0.3744

0.9063

     

Min

0.0000

0.5928

     

IT

       

Max

0.3666

0.7286

0.8544

    

Min

0.0000

0.0000

0.5516

    

JP

       

Max

0.0961

0.1384

0.1222

0.5356

   

Min

0.0000

0.0000

0.0000

0.0200

   

UK

       

Max

0.3650

0.6946

0.6156

0.6086

0.5855

  

Min

0.0000

0.0000

0.0000

0.0000

0.0234

  

USA

       

Max

0.4340

0.2816

0.2952

0.2649

0.3261

0.5967

 

Min

0.0000

0.0000

0.0000

0.0000

0.0000

0.2493

 

Panel D: Clayton dependence

CA

       

Max

       

Min

       

FR

       

Max

0.6763

      

Min

0.2899

      

DE

       

Max

0.3585

0.9327

     

Min

0.0000

0.6696

     

IT

       

Max

0.3463

0.7635

0.9004

    

Min

0.0000

0.0000

0.6006

    

JP

       

Max

0.0038

0.0408

0.0287

0.6476

   

Min

0.0000

0.0000

0.0000

0.0000

   

UK

       

Max

0.3657

0.7193

0.6567

0.6506

0.6794

  

Min

0.0000

0.0000

0.0000

0.0000

0.0000

  

USA

       

Max

0.5248

0.2450

0.2476

0.1987

0.3472

0.6622

 

Min

0.0000

0.0000

0.0000

0.0000

0.0000

0.1982

 

Panel E: Pearson correlation

CA

       

Max

       

Min

       

FR

       

Max

0.7002

      

Min

0.3966

      

DE

       

Max

0.6944

0.9726

     

Min

0.3645

0.7890

     

IT

       

Max

0.6833

0.9596

0.9477

    

Min

0.3877

0.8204

0.6965

    

JP

       

Max

0.3549

0.4594

0.4702

0.4073

   

Min

−0.0411

0.0251

0.0170

−0.0072

   

UK

       

Max

0.7080

0.9573

0.9298

0.9181

0.4612

  

Min

0.3676

0.7791

0.6572

0.6990

0.0154

  

USA

       

Max

0.7586

0.6096

0.7443

0.5871

0.2078

0.5480

 

Min

0.3764

0.2647

0.2921

0.2481

−0.1562

0.1913

 

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Huang, CW., Hsu, CP., Chiou, WJ.P. (2015). Can Time-Varying Copulas Improve the Mean-Variance Portfolio?. In: Lee, CF., Lee, J. (eds) Handbook of Financial Econometrics and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7750-1_8

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  • DOI: https://doi.org/10.1007/978-1-4614-7750-1_8

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-7749-5

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