(November 15, 2012) – Let’s be realistic: Many asset owners are not free to build their equity portfolios any way they want to.
Still, while investors have myriad individual restrictions—from short-selling or investing in tobacco companies—they all have a common goal: alpha.
With that in mind, three quants from BNP Paribas set out to create and test various approaches for constructing equity portfolios around constraints, and model the alpha each returned. Raul Leote de Carvalho (head of quantities strategies), Pierre Moulin (head of financial engineering), and Xiao Lu (quantitative analyst) recently published their findings in a whitepaper, titled “Multi-Alpha Equity Portfolios: An Integrated Risk Budgeting Approach for Robust Constrained Portfolios.”
The authors conclude that moderate restrictions do not, in general, reduce a portfolio’s exposure to systematic risk. This is both good news and bad news. Constraints on portfolio construction do not shield funds from certain risks as they’re intended to. But, constructed thoughtfully, a constrained portfolio can capture similar levels of alpha to its free-investing counterparts.
They built a number of model portfolios with various constraints, in isolation and combination:
1) A long-only constraint, which makes it impossible to sell-short stocks.
2) Liquidity constraints, which is particularly relevant for larger investors who may find it difficult to invest at all in some stocks Stock exclusion list constraints, where investing in some stocks is not authorized due to, for instance, environmental, social and governance (ESG) investing mandates.
3) Restricted access to derivatives instruments, in particular over-the-counter derivatives In one model portfolio of global equities, the authors run scenario analyses using three different risk-budgeting strategies, including mean variance, maximum diversification, and equal-risk weighting.
Moulin, de Carvalho, and Lu tested each of these individually-risk budgeted portfolios at three different levels of restrictions: none; long-only plus liquidity constraints; and long-only, liquidity constrains, plus a capped number of total stocks.
The best performer was in fact the most constrained portfolio, constructed through a mean-variance risk budget. When back-tested against historical data, the portfolio returned 5.9% above the MSCI World Index.
“We show that constrained portfolios built from the stock implied returns of the unconstrained allocation retain much the same exposures to systematic risk factors than the unconstrained portfolio,” Moulin, de Carvalho, and Lu explain in their whitepaper. “The constrained portfolio remains very close to the unconstrained target portfolio when constraints are not too binding. When constraints are too binding, the risk-adjusted returns of the constrained portfolio can be too low to justify taking active risk.”
Read the entire paper here.