**Multi-Smart Beta Allocation: Toward A New Source Of Value Added In Investment Management**

While in practice, investors may select among various ways of combining smart-factor indexes in order to account for their investment beliefs, objectives and constraints, the cases of an equal-weighted allocation, and a (relative) equal-risk contribution allocation to four smart-factor indexes seeking exposure to the main consensual factors (notably value, momentum, low volatility and size) provide evidence that the benefits of multifactor allocations are sizable. In particular, exposure to various factors whose premia behave differently over time and across market conditions provides for smoother outperformance. Moreover, natural crossing benefits reduce turnover of multifactor mandates relative to separate single-factor mandates. Investors and asset managers may thus be well advised to further explore the potential of multifactor allocations in a variety of investment contexts.

**Endnotes**

- See Chambers, Dimson and Ilmanen [2012] for more details about the "Norway model" and Koedijk, Slager and Stork [2014] on how to address practical challenges that institutional investors face to integrate factor investing in their investment process.
- Diversified multistrategy weighting is an equal-weighted combination of the following five weighting schemes: maximum deconcentration, diversified risk weighted, maximum decorrelation, efficient minimum volatility and efficient maximum Sharpe ratio (see Gonzalez and Thabault [2013]).
- To make a popular analogy, one can think of the diversified multistrategy approach as exploiting an effect similar to Surowiecki [2004]'s wisdom-of-crowds effect by taking into account the "collective opinion" of a group of strategies rather than relying on a single strategy.
- Maillard et al. [2010] discuss a weighting scheme that equalises each asset's contribution to absolute risk, i.e., portfolio volatility. It is straightforward to extend their approach by applying it to relative returns with respect to a cap-weighted reference index. In this case, the objective is to equalise the contribution of each constituent to the overall relative risk (tracking error) with respect to the chosen reference index.
- The NBER defines a recession as "a significant decline in economic activity spread across the economy, lasting more than a few months, normally visible in real GDP, real income, employment, industrial production, and wholesale-retail sales." See: http://www.nber.org/cycles/cyclesmain.html.
- The days to trade (DTT) measure is computed for all stocks at each rebalancing in the last 10 years (40 quarters). Based on the estimated DTT for all constituents of a given index, we can derive an estimate of the required DTT for the index itself, by using, for example, extreme quantiles of the DTT distribution over time and constituents, such as the 95th percentile that we report.

**References**

- Amenc, N., F. Goltz, A. Lodh and L. Martellini. "Diversifying the Diversifiers and Tracking the Tracking Error: Outperforming Cap-Weighted Indices with Limited Risk of Underperformance," Journal of Portfolio Management, vol. 38, No. 3 (2012a), pp. 72–88.
- Amenc, N., F. Goltz and A. Lodh. "Choose Your Betas: Benchmarking Alternative Equity Index Strategies," Journal of Portfolio Management, vol. 39, No. 1 (2012b), pp 88-111.
- Amenc, N., F. Goltz and L. Martellini. "Smart Beta 2.0," EDHEC-Risk Institute Position Paper (2013).
- Amenc, N., R. Deguest, F. Goltz, A. Lodh and L. Martellini, "Towards Smart Equity Factor Indices: Harvesting Risk Premia without Taking Unrewarded Risks," EDHEC-Risk Institute, Working Paper (2014a).
- Amenc, N., F. Goltz, A. Lodh and L. Martellini, "Investing in Multi Smart Beta Portfolios: Reconciling Risk Factor Allocation and Smart Beta Allocation," EDHEC-Risk Institute, Working Paper (2014b).
- Ang, A., W. Goetzmann and S. Schaefer, "Evaluation of Active Management of the Norwegian Government Pension Fund – Global," (2009).
- Asness, C., "Changing Equity Risk Premia and Changing Betas over the Business Cycle and January," University of Chicago Working Paper (1992).
- Chambers, D., E. Dimson and A. Ilmanen. "The Norway Model," Journal of Portfolio Management, vol. 38, No. 2 (2012) pp. 67-81.
- Cohen, R.B., C. Polk and T. Vuolteenaho. "The Value Spread," Journal of Finance, vol. 58, No. 2 (2003), pp. 609-642.
- Faber, M. T. "A Quantitative Approach to Tactical Asset Allocation," Journal of Wealth Management, vol. 9, No. 4 (2007), pp. 69-79.
- Ferson, W.E. and M. Qian. "Conditional Performance Evaluation, Revisited," working paper, Boston College (2004).
- Gonzalez, N. and A. Thabault. "Overview of Diversification Strategies," ERI Scientific Beta White Paper (2013).
- Harvey, C. R., "Time-Varying Conditional Covariances in Tests of Asset Pricing Models," Journal of Financial Economics, vol. 24 (1989), pp. 289-317.
- Ilmanen, A. and J. Kizer, "The Death of Diversification has been Greatly Exaggerated," Journal of Portfolio Management, vol. 38 (2012), pp. 15-27.
- Kan, R. and G. Zhou. "Optimal Portfolio Choice with Parameter Uncertainty," Journal of Financial and Quantitative Analysis, vol. 42, No. 3 (2007), pp. 621-656.
- Khandani, A. and A. Lo, "What Happened to the Quants in August 2007?" Journal of Investment Management, vol. 5 (2007), pp. 29-78.
- Koedijk, K., A. Slager and P. Stork. "Factor Investing in Practice: A Trustees' Guide to Implementation," Available on SSRN (2014).
- Levy, R.A. "Beta Coefficients as Predictors of Returns," Financial Analysts Journal, vol. 30, No. 1 (1974), pp. 61-69.
- Maillard, S., T. Roncalli and J. Teiletche. "The Properties of Equally Weighted Risk Contributions Portfolios," Journal of Portfolio Management, vol. 36, No. 4 (2010), pp. 60-70.
- Surowiecki, J. "The Wisdom of Crowds: Why the Many are Smarter than the Few and How Collective Wisdom Shapes Business, Economies, Societies, and Nations," New York: Doubleday (2004).
- Turner, C., R. Starz and C. Nelson. "A Markov Model of Heteroskedasticity, Risk, and Learning in the Stock Market," Journal of Financial Economics, vol. 25 (1989), pp. 3-22.
- Van Gelderen, E. and J. Huij, "Academic Knowledge Dissemination in the Mutual Fund Industry: Can Mutual Funds Successfully Adopt Factor Investing Strategies?"
- Available on SSRN (2013).