Tracking hedge funds returns using sparse clones

Abstract

Whether hedge fund returns could be attributed to systematic risk exposures rather than managerial skills is an interesting debate among academics and practitioners. Academic literature suggests that hedge fund performance is mostly determined by alternative betas, which justifies the construction of investable hedge fund clones or replicators. Practitioners often claim that management skills are instrumental for successful performance. In this paper, we study the risk exposure of different hedge fund indices to a set of liquid asset class factors by means of style analysis. We extend the classical style analysis framework by including a penalty that allows to retain only relevant factors, dealing effectively with collinearity, and to capture the out-of-sample properties of hedge fund indices by closely mimicking their returns. In particular, we introduce a Log-penalty and discuss its statistical properties, showing then that Log-clones are able to closely track the returns of hedge fund indices with a smaller number of factors and lower turnover than the clones built from state-of-art methods.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

References

  1. Agarwal, V., & Naik, N. Y. (2000). Multi-period performance persistence analysis of hedge funds. Journal of Financial and Quantitative Analysis, 35(3), 327–342.

    Article  Google Scholar 

  2. Agarwal, V., & Naik, N. Y. (2004). Risks and portfolio decisions involving hedge funds. Review of Financial Studies, 17(1), 63–98.

    Article  Google Scholar 

  3. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In B. N. Petrox, F. Caski F. (Eds.), Proceedings of the second international symposium on information theory (pp. 267–281). Budapest: Akademiai Kiado.

  4. Amenc, N., Géhin, W. M., & Meyfredi, J.-C. (2008). Passive hedge fund replication: A critical assessment of existing techniques. Journal of Alternative Investments, 11(2), 69–83.

    Article  Google Scholar 

  5. BarclayHedge. (2016). Hedge fund industry-assets under management, 2016. http://www.barclayhedge.com/research/indices/ghs/mum/HF_Money_Under_Management.html.

  6. Brodie, J., Daubechies, I., De Mol, C., Giannone, D., & Loris, I. (2009). Sparse and stable Markowitz portfolios. Proceedings of the National Academy of Science, 106(30), 12267–12272.

    Article  Google Scholar 

  7. Brown, S. J., Goetzmann, W. N., & Ibbotson, R. G. (1999). Offshore hedge funds: Survival and performance, 1989–1995. Journal of Business, 72(1), 91–117.

    Article  Google Scholar 

  8. De Miguel, V., Garlappi, L., Nogales, F. J., & Uppal, R. (2009). A generalized approach to portfolio optimization: Improving performance by constraining portfolio norm. Management Science, 55, 798–812.

    Article  Google Scholar 

  9. Ennis, R. M., & Sebastian, M. D. (2003). A critical look at the case for hedge funds. Journal of Portfolio Management, 29(4), 103–112.

    Article  Google Scholar 

  10. Fan, J., & Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of American Statistical Association, 96, 1348–1360.

    Article  Google Scholar 

  11. Fastrich, B., Paterlini, S., & Winker, P. (2014). Cardinality versus q-norm constraints for index tracking. Quantitative Finance, 14(11), 2019–2032.

    Article  Google Scholar 

  12. Fastrich, B., Paterlini, S., & Winker, P. (2015). Constructing optimal sparse portfolios using regularization methods. Computational Management Science, 12(3), 417–434.

    Article  Google Scholar 

  13. Fung, W., & Hsieh, D. A. (1997). Empirical characteristics of dynamic trading strategies: The case of hedge funds. Review of Financial Studies, 10(2), 275–302.

    Article  Google Scholar 

  14. Fung, W., & Hsieh, D. A. (2002). Asset-based style factors for hedge funds. Financial Analysts Journal, 58(5), 16–27.

    Article  Google Scholar 

  15. Fung, W., & Hsieh, D. A. (2007). Will hedge funds regress towards index-like products? Journal of Investment Management, 5(2), 46–65.

    Google Scholar 

  16. Fung, W., & Hsieh, D. A. (2009). Measurement biases in hedge fund performance data: An update. Financial Analysts Journal, 65(3), 1–3.

    Article  Google Scholar 

  17. Gasso, G., Rakotomamonjy, A., & Canu, S. (2009). Recovering sparse signals with a certain family of nonconvex penalties and DC programming. IEEE Transactions on Signal Processing, 57(12), 4686–4698.

    Article  Google Scholar 

  18. Giamouridis, D., & Paterlini, S. (2010). Regular(ized) hedge funds clones. Journal of Financial Research, 33(3), 223–247.

    Article  Google Scholar 

  19. Gotoh, J., & Takeda, A. (2011). On the role of norm constraints in portfolio selection. Computational Management Science, 5, 1–31.

    Google Scholar 

  20. Hasanhodzic, J., & Lo, A. W. (2007). Can hedge-fund returns be replicated?: The linear case. Journal of Investment Management, 5(2), 5–45.

    Google Scholar 

  21. Jaeger, L. (2007). Can hedge fund returns be replicated inexpensively? CFA Institute Conference Proceedings Quarterly, 24(3), 28–40.

    Article  Google Scholar 

  22. Jaeger, L. (2008). Alternative beta strategies and hedge fund replication. Chichester: Wiley.

    Google Scholar 

  23. Jaeger, L., & Wagner, C. (2005). Factor modeling and benchmarking of hedge funds: Can passive investments in hedge fund strategies deliver? Journal of Alternative Investments, 8(3), 9–36.

    Article  Google Scholar 

  24. Jagannathan, R., & Ma, T. (2003). Risk reduction in large portfolios: Why imposing the wrong constraints helps. Journal of Finance, 58, 1651–1684.

    Article  Google Scholar 

  25. Kolm, P. N., Tütüncü, R., & Fabozzi, F. J. (2014). 60 years following Harry Markowitz’s contribution to portfolio theory and operations research. European Journal of Operational Research, 234(2), 343–582.

    Article  Google Scholar 

  26. Liang, B. (2000). Hedge funds: The living and the dead. Journal of Financial and Quantitative Analysis, 35(3), 309–326.

    Article  Google Scholar 

  27. Murphy, K . P. (2012). Machine learning: A probabilistic perspective. Cambridge: The MIT Press.

    Google Scholar 

  28. Patton, A. J., & Ramadorai, T. (2013). On the high-frequency dynamics of hedge fund risk exposures. Journal of Finance, 68(2), 597–635.

    Article  Google Scholar 

  29. Roncalli, T. (2014). Introduction to risk parity and budgeting. Financial mathematics series. London: Chapman & Hall/CRC.

    Google Scholar 

  30. Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6(2), 461–464.

    Article  Google Scholar 

  31. Sharpe, W. F. (1992). Asset allocation: Management style and performance measurement. Journal of Portfolio Management, 18(2), 7–19. Reprinted with permission from The Journal of Portfolio Management, Winter.

  32. Takeda, A., Niranjan, M., Gotoh, J., & Kawahara, Y. (2013). Simultaneous pursuit of out-of-sample performance and sparsity in index tracking portfolios. Computational Management Science, 10(1), 21–49.

    Article  Google Scholar 

  33. Weber, and V., Peres, F. (2013). Hedge fund replication: Putting the pieces together. Journal of Investment Strategies, 3(1), 61–119.

  34. Weston, J., Elisseeff, A., & Schoelkopf, B. (2003). Use of the zero-norm with linear models and Kernel methods. Journal of Machine Learning Research, 3, 1439–1461.

    Google Scholar 

  35. World Bank. (2015). Gross domestic product, March 2015. http://data.worldbank.org/indicator/NY.GDP.MKTP.CD.

Download references

Acknowledgements

We would like to thank the two anonymous referees and the Associate Editor for providing us with constructive comments that have improved the quality of our paper. Sandra Paterlini acknowledges financial support from CRoNos COST Action IC1408.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Sandra Paterlini.

Additional information

The opinions expressed in this article are those of the authors and do not necessarily reflect the views Prime Capital AG.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Giuzio, M., Eichhorn-Schott, K., Paterlini, S. et al. Tracking hedge funds returns using sparse clones. Ann Oper Res 266, 349–371 (2018). https://doi.org/10.1007/s10479-016-2371-5

Download citation

Keywords

  • Style analysis
  • Hedge fund replication
  • Log-penalty regression
  • LASSO
  • Alternative betas