(Non-) linear factor dependencies in multi-asset portfolios

Multi-Asset funds invest in multiple asset classes, such as stocks, bonds, credits, currencies and commodities. The combination of various strategies applied to different asset classes brings typical challenges for the fine-tuning and risk management of these funds. Robeco has several multi-asset funds and continues to grow in this area. Through this internship we want to improve and extend our understanding of efficient factor harvesting and effective portfolio construction.

Our multi-asset portfolios are based on a factor matrix. Each cell of this matrix represents a specific strategy style (such as trend, value, carry and quality) implemented within one of the asset classes. Each strategy is defined by a set of signals from which the positions in the underlying markets are derived. When combining factors into the multi-asset portfolio, we hope to benefit from risk reduction from diversification. The degree of portfolio diversification depends on how the underlying factor returns interact. These factor interactions take place at the signal level, the asset level, and the factor level. The modelling of these interactions and their use in fine-tuning the risk-return characteristics of the factor portfolio is the main research question of this internship.

At the signal level, the question is how strategy signals interact. In the internship, we want you to explore non-linear set-ups, in which for example positions are taken only after a specific signal threshold has been exceeded. An example is mean-reversion, that we expect to be strongest after larger negative returns. And we want you to investigate non-linear interactions between signals, by analyzing and comparing the performance from positive and negative signal combinations.
For example, trend and value signals tend to be negatively correlated in a global sense (after a negative trend, an asset can become cheap), but different trend-value signal combinations can produce very different performances. Such patterns could be captured by non-linear models, in which the interaction between signals is modeled by means of cross-terms (cf. regression models in which the interaction between explanatory variables is represented by their product).
Also, some signals may change frequently over time, whereas others are more sticky. Combining strategies with short and long horizons provides horizon diversification and this is yet another way to diversify risk. But how can we estimate the effective horizons of strategies and exploit this information ?

Additionally, we want to measure asset and factor correlations. The conventional way to do this is to consider the full range of historical returns and calculate the global correlation matrix. However, correlations are not persistent over time and we are therefore interested in the potential value-added of dynamic correlation modeling. In addition to global correlations, we wish to measure correlations in times of market stress. Under extreme market conditions, correlations can switch sign or spike. But how can you best estimate these tail (or quantile) correlations, especially when historical data may be sparse ? And do these measures add sufficiently to outweigh their increased complexity ?

The main research question of this internship is how signals and factors interact, and how we can use this information to improve our factor and portfolio construction process. In the description above we already mentioned some related questions, but we expect your active contribution in exploring the (academic) literature and formulating relevant research questions. You will have regular contact with the quant allocation portfolio managers, who can give practical feedback on the results found.

Are you interested?
Let us know your motivation and send it together with your top-3 favorite internship topics, your CV and list of grades to
Previous projects


DiBartolomeo D. & S. Warrick, 2001, “Estimating Nonlinear Effects of Management Styles in the US Equity Market.” Download from

Lempérière, Y., C. Deremble, T. T. Nguyen, P. Seager, M. Potters & J. P. Bouchaud, 2016, “Risk premia: Asymmetric Tail Risks and Excess Returns.” Quantitative Finance 17/1, pp.1–14

Levin, A.U., 1996, “Stock Selection via Nonlinear Multi-Factor Models.” Download from

Phoa, W., 2015, “Extreme Correlations and optimizing for Stress.” The Journal of Portfolio Management 41/2, pp.71-75

Polbennikov, S., A. Desclee & J. Hyman, 2010, “Horizon Diversification: Reducing Risk in a Portfolio of Active Strategies.” The Journal of Portfolio Management 36/2, pp.26-38

Wang, P. & L. Kochard, 2011, “Using a Z-score Approach to Combine Value and Momentum in Tactical Asset Allocation.” Available at SSRN: