When Factors Don't Span Their Basis Portfolios

Factoring characteristics into returns: A clinical study on the SMB and HML portfolio construction methods

“…5 These issues are important because better constructed factors can improve asset pricing tests and might lead to the acceptance of a model that would otherwise be rejected because of poor measurement. We also contribute to another important recent finding in this field made by Grinblatt and Saxena (2019), who show that mimicking risk factors can be improved by using optimal weights of basis portfolios rather than traditional equal weighting of the long and short positions. The authors do not compare ways of constructing these underlying "basis portfolios" or challenge their configuration.…”

“…For this reason, we think that the two methods (Dependent-Symmetric-Name (DSN) and the Grinblatt and Saxena method) are not directly comparable or in competition. However, testing the joint combination of the approaches of Grinblatt and Saxena (2019) and ours could potentially lead to empirical factors closer to the true mean-variance efficient factors. This research would indeed combine the merits of the two different approaches.…”

Risk optimizations on basis portfolios: The role of sorting

“…Table II recalls the analytic forms of the risk-based allocations that serve as a practical base in our empirical analysis; namely, minimum variance (MV), maximum diversification (MD), and risk parity (RP). Following Ao et al (2018), Ardia et al (2018), Grinblatt and Saxena (2018), and Roncalli and Weisang (2016) among others, these risk-based allocations are rebalanced on a monthly basis.…”

“…We show that the performance of these portfolios is highly sensitive to its underlying assets or building blocks. Directly related to our research, Grinblatt and Saxena (2018) established a statistical technique to create a mean-variance efficient (MVE) portfolio starting from a set of characteristics-or style portfolios. This portfolio is shown to span the opportunity set formed from a 3-factor model (Fama & French, 1993).…”

“…For 7 out of 9 risk-based optimizations, the dependent opportunity set offers significantly higher total diversification returns (DR EW ) than the independent sort. Consistent with Grinblatt and Saxena (2018), risk-return improvement can be achieved by allocating basis portfolios with optimization techniques, which departure from the traditional equal-weight allocation. However, our results uncover that it is only valid when advanced sorting methods are used to construct the basis portfolios.…”