Journal of Asset Management

, Volume 15, Issue 1, pp 24–47 | Cite as

An integrated risk-budgeting approach for multi-strategy equity portfolios

  • Raul Leote de Carvalho
  • Xiao Lu
  • Pierre Moulin
Original Article


The authors propose a robust optimisation approach to construct realistic constrained multi-strategy portfolios that starts with the identification of different sources of excess returns and the risk-budgeting exercise to optimally combine them. They show how systematic factor strategies can be combined with judgemental strategies and how bottom-up-based strategies for stock picking can be combined with top-down sector or country allocation strategies. The approach is fully transparent for both unconstrained and constrained portfolios. In particular, it is shown that constrained portfolios retain the exposures to systematic risks factors in the unconstrained target solution as much as possible, and that specific risk takes the toll of portfolio constraints. A realistic back-tested example combining four different well-known factor strategies – value, momentum, low risk and size – demonstrates the robustness and transparency of the approach. The advantages of the approach over the alternative process based on selecting and investing in a mix of different index funds implementing off-the-shelf active strategies is highlighted. The authors find their approach particularly suited for institutional investors interested in fully controlling the active risk budget allocation to factor strategies in their portfolios while fully understanding the final allocation in their constrained portfolios.


multi-factor models factor investing quantitative funds portfolio optimisation smart beta Black–Litterman model 


  1. Andy, C.W.C., Titman, S. and Wei, K.C.J. (2010) Individualism and momentum around the world. Journal of Finance 65 (1): 361–392.CrossRefGoogle Scholar
  2. Avramov, D., Chordia, T., Jostova, G. and Philipov, A. (2013) Anomalies and financial distress. Journal of Financial Economics 108 (1): 139–150.CrossRefGoogle Scholar
  3. Banz, R.W. (1981) The relationship between return and market value of common stocks. Journal of Financial Economics 9 (1): 3–18.CrossRefGoogle Scholar
  4. Basu, S. (1977) Investment performance of common stocks in relation to their price-earnings ratios: A test of the efficient market hypothesis. Journal of Finance 32 (3): 663–682.CrossRefGoogle Scholar
  5. Black, F. and Litterman, R. (1992) Global portfolio optimization. Financial Analysts Journal 48 (5): 28–43.CrossRefGoogle Scholar
  6. Blitz, D. (2012) Strategic allocation to premiums in the equity market. The Journal of Index Investing 2 (4): 42–49.CrossRefGoogle Scholar
  7. Blitz, D.C. and Swinkels, L.A.P. (2008) Fundamental indexation: An active value strategy in disguise. Journal of Asset Management 9 (4): 264–269.CrossRefGoogle Scholar
  8. Bloomfield, R.J., Tayler, W.B. and Zhou, F.H. (2009) Momentum, reversal, and uninformed traders in laboratory markets. Journal of Finance 64 (6): 2535–2558.CrossRefGoogle Scholar
  9. Capaul, C. (1999) Asset-pricing anomalies in global industry indexes. Financial Analysis Journal 55 (4): 17–37.CrossRefGoogle Scholar
  10. Chambers, D., Dimson, E. and Ilmanen, A. (2012) The norway model. Journal of Portfolio Management 38 (2): 67–80.CrossRefGoogle Scholar
  11. Choueifaty, Y. and Coignard, Y. (2008) Towards maximum diversification. Journal of Portfolio Management 34 (4): 40–51.CrossRefGoogle Scholar
  12. de Carvalho, R.L., Lu, X. and Moulin, P. (2012) Demystifying equity risk-based strategies: A simple alpha plus beta description. Journal of Portfolio Management 38 (3): 56–70.CrossRefGoogle Scholar
  13. Desrosiers, S., L’Her, J.-F. and Plante, J.-F. (2004) Style management in equity country allocation. Financial Analysts Journal 60 (6): 40–53.CrossRefGoogle Scholar
  14. Doeswijk, R.Q. (2008) The optimism cycle: Sell in May. De Economist 156 (2): 175–200.CrossRefGoogle Scholar
  15. Edmans, A. (2011) Does the stock market fully value intangibles? Employee satisfaction and equity prices. Journal of Financial Economics 101 (3): 621–640.CrossRefGoogle Scholar
  16. Fama, E.F. and French, K.R. (2009) Dissecting anomalies. Journal of Finance 63 (4): 1653–1678.CrossRefGoogle Scholar
  17. Fama, E.F. and French, K.R. (2012) Size, value, and momentum in international stock returns. Journal of Financial Economics 105 (3): 457–472.CrossRefGoogle Scholar
  18. Gergaud, O. and Ziemba, W.T. (2012) Great investors: Their methods, results, and evalutation. Journal of Portfolio Management 38 (4): 128–147.Google Scholar
  19. Givoly, D. and Lakonishok, J. (1979) The information content of financial analysts’ forecasts of earnings: Some evidence on semi-strong efficiency. Journal of Accounting and Economics 1 (3): 165–186.CrossRefGoogle Scholar
  20. Haugen, R.A. and Baker, N. (1996) Commonality in the determinants of expected stock returns. Journal of Financial Economics 41 (3): 401–439.CrossRefGoogle Scholar
  21. Haugen, R.A. and Heins, A.J. (1972) On the Evidence Supporting the Existence of Risk Premiums in the Capital Markets, Wisconsin University, Working paper.Google Scholar
  22. He, G. and Litterman, R. (1999) The Intuition Behind Black-Litterman Model Portfolios. US: Goldman Sachs Investment Management Series.Google Scholar
  23. Jegadeesh, N. (1990) Evidence of predictable behavior of security returns. Journal of Finance 45 (3): 881–898.CrossRefGoogle Scholar
  24. Jensen, M. (1968) The performance of mutual funds in the period 1945–1964. Journal of Finance 23 (2): 389–416.CrossRefGoogle Scholar
  25. Kritzman, M. (2006) Are optimizers error maximizers? Journal of Portfolio Management 32 (4): 66–69.CrossRefGoogle Scholar
  26. Lam, F.Y.E.C. and Wei, K.C.J. (2011) Limits to arbitrage and the asset growth anomaly. Journal of Financial Economics 102 (1): 127–149.CrossRefGoogle Scholar
  27. Lehmann, B.N. (1990) Fads, martingales, and market efficiency. Quarterly Journal of Economics 105 (1): 1–28.CrossRefGoogle Scholar
  28. Ogliaro, F., Rice, R.K., Becker, S. and de Carvalho, R.L. (2012) Explicit coupling of informative prior and likelihood functions in a Bayesian multivariate framework and application to a new non-orthogonal formulation of the Black–Litterman model. Journal of Asset Management 13 (2): 128–140.CrossRefGoogle Scholar
  29. Moskowitz, T.J. and Grinblatt, M. (1999) Do industries explain momentum? Journal of Finance 54 (4): 1249–1290.CrossRefGoogle Scholar
  30. Novy-Marx, R. (2012) Is momentum really momentum? Journal of Financial Economics 103 (3): 429–453.CrossRefGoogle Scholar
  31. Novy-Marx, R. (2013) The other side of value: The gross profitability premium. Journal of Financial Economics 108 (1): 1–28.CrossRefGoogle Scholar
  32. Perchet, R. and de Carvalho, R.L. (2014) Constant Volatility Framework for Factor Investing, France, Paris: BNP Paribas Investment Partners.Google Scholar
  33. Perchet, R., de Carvalho, R.L., Heckel, T. and Moulin, P. (2014) Inter-temporal risk parity: A constant volatility framework for equities and other asset classes. SSRN Working Paper, 10 January,, accessed 28 January 2014.
  34. Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L., Guhr, T. and Stanley, H. (2002) A Random matrix approach to cross-correlations in financial data. Physical Review E 65 (6): 1–18.CrossRefGoogle Scholar
  35. Sloan, R.G. (1996) Do stock prices fully reflect information in accruals and cash flows about future earnings? The Accounting Review 71 (3): 289–315.Google Scholar
  36. Scherer, B. (2004) Portfolio Construction and Risk Budgeting. 2nd edn. London: Riskwaters Books.Google Scholar

Copyright information

© Palgrave Macmillan, a division of Macmillan Publishers Ltd 2014

Authors and Affiliations

  1. 1.BNP Paribas Investment Partners, 14 rue BergèreParisFrance

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