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.






Similar content being viewed by others
References
Agarwal, V., & Naik, N. Y. (2000). Multi-period performance persistence analysis of hedge funds. Journal of Financial and Quantitative Analysis, 35(3), 327–342.
Agarwal, V., & Naik, N. Y. (2004). Risks and portfolio decisions involving hedge funds. Review of Financial Studies, 17(1), 63–98.
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.
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.
BarclayHedge. (2016). Hedge fund industry-assets under management, 2016. http://www.barclayhedge.com/research/indices/ghs/mum/HF_Money_Under_Management.html.
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.
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.
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.
Ennis, R. M., & Sebastian, M. D. (2003). A critical look at the case for hedge funds. Journal of Portfolio Management, 29(4), 103–112.
Fan, J., & Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of American Statistical Association, 96, 1348–1360.
Fastrich, B., Paterlini, S., & Winker, P. (2014). Cardinality versus q-norm constraints for index tracking. Quantitative Finance, 14(11), 2019–2032.
Fastrich, B., Paterlini, S., & Winker, P. (2015). Constructing optimal sparse portfolios using regularization methods. Computational Management Science, 12(3), 417–434.
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.
Fung, W., & Hsieh, D. A. (2002). Asset-based style factors for hedge funds. Financial Analysts Journal, 58(5), 16–27.
Fung, W., & Hsieh, D. A. (2007). Will hedge funds regress towards index-like products? Journal of Investment Management, 5(2), 46–65.
Fung, W., & Hsieh, D. A. (2009). Measurement biases in hedge fund performance data: An update. Financial Analysts Journal, 65(3), 1–3.
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.
Giamouridis, D., & Paterlini, S. (2010). Regular(ized) hedge funds clones. Journal of Financial Research, 33(3), 223–247.
Gotoh, J., & Takeda, A. (2011). On the role of norm constraints in portfolio selection. Computational Management Science, 5, 1–31.
Hasanhodzic, J., & Lo, A. W. (2007). Can hedge-fund returns be replicated?: The linear case. Journal of Investment Management, 5(2), 5–45.
Jaeger, L. (2007). Can hedge fund returns be replicated inexpensively? CFA Institute Conference Proceedings Quarterly, 24(3), 28–40.
Jaeger, L. (2008). Alternative beta strategies and hedge fund replication. Chichester: Wiley.
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.
Jagannathan, R., & Ma, T. (2003). Risk reduction in large portfolios: Why imposing the wrong constraints helps. Journal of Finance, 58, 1651–1684.
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.
Liang, B. (2000). Hedge funds: The living and the dead. Journal of Financial and Quantitative Analysis, 35(3), 309–326.
Murphy, K . P. (2012). Machine learning: A probabilistic perspective. Cambridge: The MIT Press.
Patton, A. J., & Ramadorai, T. (2013). On the high-frequency dynamics of hedge fund risk exposures. Journal of Finance, 68(2), 597–635.
Roncalli, T. (2014). Introduction to risk parity and budgeting. Financial mathematics series. London: Chapman & Hall/CRC.
Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6(2), 461–464.
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.
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.
Weber, and V., Peres, F. (2013). Hedge fund replication: Putting the pieces together. Journal of Investment Strategies, 3(1), 61–119.
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.
World Bank. (2015). Gross domestic product, March 2015. http://data.worldbank.org/indicator/NY.GDP.MKTP.CD.
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
Authors and Affiliations
Corresponding author
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
About this article
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
Published:
Issue date:
DOI: https://doi.org/10.1007/s10479-016-2371-5
