Un-diversifying during crises: Is it a good idea?
- 24 Downloads
High levels of correlation among financial assets and extreme losses are typical during crises. In such situations, investing in few assets might be a better choice than holding diversified portfolios. We show that constraining the sparse \(\ell _q\)-norm of portfolio weights automatically controls diversification and selects portfolios with a small number of active weights and low risk, in presence of high correlation and volatility. We highlight the diversification relationships between the minimum variance portfolio, risk budgeting strategies and diversification-constrained portfolios. Finally, we show empirically that the \(\ell _q\)-strategy can successfully cope with bear markets by shrinking portfolio weights and total amount of shorting.
KeywordsDiversification Regularization methods Minimum variance Sparsity
Mathematics Subject Classification91G10 91G70 91-08
We would like to thank the two anonymous referees and the Associate Editor for providing us with constructive and detailed comments that have improved the quality of our paper. Sandra Paterlini gratefully acknowledges financial support from ICT COST Action IC1408 “Computationally-intensive methods for the robust analysis of non-standard data”.
- Benoit S, Colletaz G, Hurlin C, Perignon C (2013) A theoretical and empirical comparison of systemic risk measures. HEC Paris Research Paper (FIN-2014-1030)Google Scholar
- Bodie Z, Kane A, Marcus A (1999) Investments, 4th edn. Irwin/McGraw-Hill, BostonGoogle Scholar
- Bruder B, Roncalli T (2012) Managing risk exposures using the risk budgeting approach. Working paperGoogle Scholar
- Buffett W (1979) Chairman’s Letter. http://www.berkshirehathaway.com/letters/1979.html
- Carrasco M, Noumon N (2012) Optimal portfolio selection using regularization. Working paper, University of MontrealGoogle Scholar
- Chen C, Li X, Tolman C, Wang S, Ye Y (2013) Sparse portfolio selection via quasi-norm regularization, preprint. arXiv:1312.6350
- Grinold RC, Kahn R (1999) Active portfolio management, 2nd edn. McGraw-Hill, New YorkGoogle Scholar
- Markowitz H (1952) Portfolio selection. J Finance 7:77–91Google Scholar
- Murphy KP (2012) Machine learning: a probabilistic perspective. MIT Press, CambridgeGoogle Scholar
- Weston J, Elisseeff A, Schölkopf B (2003) Use of the zero-norm with linear models and kernel methods. J Mach Learn Res 3:1439–1461Google Scholar