Abstract
In this chapter, we consider a new framework for understanding risk-based portfolios (global minimum variance (GMV), equally weighted (EW), equal risk contribution (ERC) and most diversified portfolio (MDP)). This framework is similar to the constrained minimum variance model of Jurczenko et al., but with another definition of the diversification constraint. The corresponding optimization problem can then be solved using the cyclical coordinate descent (CCD) algorithm. This allows us to extend the results of Cazalet et al. and to better understand the trade-off relationships between volatility reduction, tracking error and risk diversification. In particular, we show that the smart beta portfolios differ because they implicitly target different levels of volatility reduction. We also develop new smart beta strategies by managing the level of volatility reduction and show that they present appealing properties compared to the traditional risk-based portfolios.
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