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Combining Alphas via Bounded Regression

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  • Zura Kakushadze

    (Quantigic® Solutions LLC, 1127 High Ridge Road #135, Stamford, CT 06905, USA
    Business School & School of Physics, Free University of Tbilisi, 240, David Agmashenebeli Alley, Tbilisi 0159, Georgia)

Abstract

We give an explicit algorithm and source code for combining alpha streams via bounded regression. In practical applications, typically, there is insufficient history to compute a sample covariance matrix (SCM) for a large number of alphas. To compute alpha allocation weights, one then resorts to (weighted) regression over SCM principal components. Regression often produces alpha weights with insufficient diversification and/or skewed distribution against, e.g., turnover. This can be rectified by imposing bounds on alpha weights within the regression procedure. Bounded regression can also be applied to stock and other asset portfolio construction. We discuss illustrative examples.

Suggested Citation

  • Zura Kakushadze, 2015. "Combining Alphas via Bounded Regression," Risks, MDPI, vol. 3(4), pages 1-17, November.
  • Handle: RePEc:gam:jrisks:v:3:y:2015:i:4:p:474-490:d:58313
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    References listed on IDEAS

    as
    1. Adcock, C. J. & Meade, N., 1994. "A simple algorithm to incorporate transactions costs in quadratic optimisation," European Journal of Operational Research, Elsevier, vol. 79(1), pages 85-94, November.
    2. Dylan Possamai & H. Mete Soner & Nizar Touzi, 2012. "Homogenization and asymptotics for small transaction costs: the multidimensional case," Papers 1212.6275, arXiv.org, revised Jan 2013.
    3. Abel Cadenillas & Stanley R. Pliska, 1999. "Optimal trading of a security when there are taxes and transaction costs," Finance and Stochastics, Springer, vol. 3(2), pages 137-165.
    4. Costa, O. L. V. & Paiva, A. C., 2002. "Robust portfolio selection using linear-matrix inequalities," Journal of Economic Dynamics and Control, Elsevier, vol. 26(6), pages 889-909, June.
    5. Franklin R. Edwards & Jimmy Liew, 1999. "Managed commodity funds," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 19(4), pages 377-411, June.
    6. Li, Huanan & Wei, Yi-Ming, 2015. "Is it possible for China to reduce its total CO2 emissions?," Energy, Elsevier, vol. 83(C), pages 438-446.
    7. Fung, William & Hsieh, David A., 1999. "A primer on hedge funds," Journal of Empirical Finance, Elsevier, vol. 6(3), pages 309-331, September.
    8. Fung, William & Hsieh, David A., 2000. "Performance Characteristics of Hedge Funds and Commodity Funds: Natural vs. Spurious Biases," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 35(3), pages 291-307, September.
    9. Zura Kakushadze, 2015. "A Spectral Model of Turnover Reduction," Econometrics, MDPI, vol. 3(3), pages 1-13, July.
    10. Miguel Lobo & Maryam Fazel & Stephen Boyd, 2007. "Portfolio optimization with linear and fixed transaction costs," Annals of Operations Research, Springer, vol. 152(1), pages 341-365, July.
    11. Andre F. Perold, 1984. "Large-Scale Portfolio Optimization," Management Science, INFORMS, vol. 30(10), pages 1143-1160, October.
    12. Jacek Gondzio & Roy Kouwenberg, 2001. "High-Performance Computing for Asset-Liability Management," Operations Research, INFORMS, vol. 49(6), pages 879-891, December.
    13. Zura Kakushadze & Jim Kyung-Soo Liew, 2014. "Is It Possible to OD on Alpha?," Papers 1404.0746, arXiv.org, revised Nov 2018.
    14. Karel Janeček & Steven Shreve, 2004. "Asymptotic analysis for optimal investment and consumption with transaction costs," Finance and Stochastics, Springer, vol. 8(2), pages 181-206, May.
    15. Liang, Bing, 2000. "Hedge Funds: The Living and the Dead," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 35(3), pages 309-326, September.
    16. H. Mete Soner & Nizar Touzi, 2012. "Homogenization and asymptotics for small transaction costs," Papers 1202.6131, arXiv.org, revised Jun 2013.
    17. Zura Kakushadze, 2014. "A Spectral Model of Turnover Reduction," Papers 1404.5050, arXiv.org, revised Nov 2015.
    18. Dimitris Bertsimas & Christopher Darnell & Robert Soucy, 1999. "Portfolio Construction Through Mixed-Integer Programming at Grantham, Mayo, Van Otterloo and Company," Interfaces, INFORMS, vol. 29(1), pages 49-66, February.
    19. Jakša Cvitanić & Ioannis Karatzas, 1996. "Hedging And Portfolio Optimization Under Transaction Costs: A Martingale Approach12," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 133-165, April.
    20. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    21. Esteban Moro & Javier Vicente & Luis G. Moyano & Austin Gerig & J. Doyne Farmer & Gabriella Vaglica & Fabrizio Lillo & Rosario N. Mantegna, 2009. "Market impact and trading profile of large trading orders in stock markets," Papers 0908.0202, arXiv.org.
    22. Agarwal, Vikas & Naik, Narayan Y., 2000. "Multi-Period Performance Persistence Analysis of Hedge Funds," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 35(3), pages 327-342, September.
    23. Zura Kakushadze, 2014. "Factor Models for Alpha Streams," Papers 1406.3396, arXiv.org, revised Oct 2014.
    24. Dumas, Bernard & Luciano, Elisa, 1991. "An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs," Journal of Finance, American Finance Association, vol. 46(2), pages 577-595, June.
    25. Fung, William & Hsieh, David A, 2001. "The Risk in Hedge Fund Strategies: Theory and Evidence from Trend Followers," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 313-341.
    26. Hans Kellerer & Renata Mansini & M. Speranza, 2000. "Selecting Portfolios with Fixed Costs and Minimum Transaction Lots," Annals of Operations Research, Springer, vol. 99(1), pages 287-304, December.
    27. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    28. Magill, Michael J. P. & Constantinides, George M., 1976. "Portfolio selection with transactions costs," Journal of Economic Theory, Elsevier, vol. 13(2), pages 245-263, October.
    29. Zura Kakushadze, 2014. "Combining Alpha Streams with Costs," Papers 1405.4716, arXiv.org, revised Jan 2015.
    30. Zura Kakushadze, 2014. "4-Factor Model for Overnight Returns," Papers 1410.5513, arXiv.org, revised Jun 2015.
    31. Thomas Schneeweis & Richard Spurgin & David McCarthy, 1996. "Survivor bias in commodity trading advisor performance," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 16(7), pages 757-772, October.
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    Cited by:

    1. Zura Kakushadze & Willie Yu, 2017. "How to combine a billion alphas," Journal of Asset Management, Palgrave Macmillan, vol. 18(1), pages 64-80, January.
    2. Zura Kakushadze, 2015. "Heterotic Risk Models," Papers 1508.04883, arXiv.org, revised Jan 2016.
    3. Zura Kakushadze, 2020. "Quant Bust 2020," Papers 2006.05632, arXiv.org.

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