# Time-Dependent Black–Litterman

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## Abstract

The Black–Litterman method is widely used in the investment management industry to incorporate views in investment portfolios. The method applies when views are expressed as expected returns over the horizon for which allocation decisions are made, i.e., the investment horizon. In practice, however, the investor’s views are typically formulated for the near future while the investor’s investment horizon is much longer. To incorporate such views, we introduce the time-dependent Black–Litterman method and show that, in a time-dependent setting, a distinction should be made between unconditional and conditional views. Furthermore, we demonstrate its use for buy and hold investors. In an example, we show that the investor’s views have a plausible impact on resulting allocation decisions.

## Keywords

Black–Litterman Kalman filter Asset allocation Views## Notes

### Acknowledgements

We would like to thank our colleagues Kai Ming Lee, Marc Francke, Alex Boer and Patrick Tuijp for their useful feedback on the paper.

## References

- Basak, S. and Chabakauri, G. (2010) Dynamic mean-Variance asset allocation.
*The Review of Financial Studies*23(8): 2970–3016.CrossRefGoogle Scholar - Black, F. and Litterman, R. (1992) Global portfolio optimization.
*Financial Analysts Journal*48(5): 28–43.CrossRefGoogle Scholar - Campbell, J. and Viceira, L. (1999) Consumption and portfolio decisions when expected returns are time varying.
*The Quarterly Journal of Economics*114(2): 433–495.CrossRefGoogle Scholar - Campbell, J. and Viceira, L. (2002)
*Strategic asset allocation: portfolio choice for long-term investors*. Oxford: Oxford University Press.Google Scholar - Campbell, J. and Viceira, L. (2005a) The term structure of the risk-return trade-off. NBER working paper 11119.Google Scholar
- Campbell, J. and Viceira, L. (2005b) The term structure of the risk-return trade-off.
*Financial Analysts Journal*61(1): 34–44.Google Scholar - Cheung, W. (2010) The Black–Litterman model explained.
*Journal of Asset Management*11(4): 229–243.CrossRefGoogle Scholar - Davis, M. and Lleo, S. (2013) Black–Litterman in continuous time: the case for filtering.
*Quantitative Finance Letters*1(1): 30–35.CrossRefGoogle Scholar - Fabozzi, F.J., Focardi, S.M. and Kolm, P.N. (2006) Incorporating trading strategies in the Black–Litterman framework.
*The Journal of Trading*1(2): 28–37.CrossRefGoogle Scholar - Fusai, G. and Meucci, A. (2003) Assessing views.
*Risk*16(3): 18–21.Google Scholar - Geweke, J. (1978) The dynamic factor analysis of economic time series models. SSRI workshop series, Social Systems Research Institute, University of Wisconsin-Madison.Google Scholar
- He, G. and Litterman, R. (1999) The intuition behind Black–Litterman model portfolios. Goldman Sachs asset management working paper.Google Scholar
- Idzorek T (2007) A step-by-step guide to the Black–Litterman model: incorporating user specified confidence levels. In: S. Satchell (ed.)
*Forecasting Expected Returns in the Financial Markets*, Oxford: Academic Press, pp. 17–38.Google Scholar - IMF (2009) World economic outlook. http://www.imf.org/external/pubs/ft/weo/2009/01/weodata/index.aspx. https://www.imf.org/external/pubs/ft/weo/2009/01/index.htm.
- Jones, R., Lim, T. and Zangari, P.J. (2007) The Black–Litterman model for structured equity portfolios.
*Journal of Portfolio Management*33(2): 24.CrossRefGoogle Scholar - Kalman, R.E. (1960) A new approach to linear filtering and prediction problems.
*Journal of Fluids Engineering*82(1): 35–45.Google Scholar - Maggiar, A. (2009) Active fixed-income portfolio management using the Black–Litterman model. MSc thesis, Imperial College.Google Scholar
- Mankert, C. (2006) The Black–Litterman model: mathematical and behavioral finance approaches towards its use in practice. PhD thesis, University dissertation from Stockholm: KTH.Google Scholar
- Mankert, C. (2010) The Black–Litterman model: towards its use in practice. PhD thesis, University dissertation from Stockholm: KTH.Google Scholar
- Mankert, C. and Seiler, M.J. (2011) Mathematical derivations and practical implications for the use of the Black–Litterman model.
*Journal of Real Estate Portfolio Management*17(2): 139–159.Google Scholar - Mazzoni, T. (2015) Nonlinear portfolio views: an efficient extension to the Black–Litterman approach.
*Journal of Business Economics*85(6): 693–717.CrossRefGoogle Scholar - Meucci, A. (2008) Fully exible views: theory and practice.
*Risk*21(10): 97–102.Google Scholar - Meucci, A. (2009) Enhancing the Black–Litterman and related approaches: views and stress-test on risk factors.
*Journal of Asset Management*10(2): 89–96.CrossRefGoogle Scholar - O’Toole, R. (2013) The Black–Litterman model: a risk budgeting perspective.
*Journal of Asset Management*14(1): 2–13.CrossRefGoogle Scholar - Sargent, T. and Sims, C. (1977) Business cycle modeling without pretending to have too much a priori economic theory. In: C.A. Sims (ed.)
*New Methods of Business Cycle Research*, Minneapolis: Federal Reserve Bank of Minneapolis.Google Scholar - Satchell, S. and Scowcroft, A. (2000) A demystification of the Black–Litterman model: managing quantitative and traditional portfolio construction.
*Journal of Asset Management*1(2): 138–150.CrossRefGoogle Scholar - Stock, J.H. and Watson, M.W. (2002) Macroeconomic forecasting using diffusion indexes.
*Journal of Business & Economic Statistics*20(2): 147–162.CrossRefGoogle Scholar - Stock, J.H. and Watson, M.W. (2011) Dynamic factor models. In:
*Oxford Handbook of Economic Forecasting*, Oxford University Press, pp. 35–59.Google Scholar - Stock, J.H. and Watson, M.W. (2012a) Disentangling the channels of the 2007–2009 recession. Brookings Papers on Economic Activity Spring 2012.Google Scholar
- Stock, J.H. and Watson, M.W. (2012b) Generalized shrinkage methods for forecasting using many predictors.
*Journal of Business & Economic Statistics*30(4): 481–493.Google Scholar - Van der Schans, M. and Steehouwer, H. (2015) Views, factor models and optimal asset allocation.
*Procedia Economics and Finance*29: 122–134.CrossRefGoogle Scholar - Walters, J. (2014) The Black–Litterman model in detail. SSRN working paper.Google Scholar