The Impact of Constraints on Minimum-Variance Portfolios

Optimized minimum-variance strategies tend to have low liquidity; high turnover; high tracking error; and concentrated stock, sector, and country positions. Minimum-variance index providers typically mitigate these implementation problems by imposing constraints. The authors construct minimum-variance portfolios for the United States, global developed markets, and emerging markets and apply commonly used constraints to determine their effect on simulated portfolio characteristics, performance, and trading costs. The constraints they test succeed in improving investability but shift portfolio characteristics toward those of the capitalization-weighted benchmark. In particular, each additional constraint increases volatility. Nonetheless, minimum-variance strategies are a valid choice for risk-averse investors.The summary was prepared by Mark K. Bhasin, CFA, Basis Investment Group LLC.What’s Inside?The authors focused on the implementation challenges related to optimization-based low-volatility strategies. Index providers typically address these implementation challenges by applying various constraints in the portfolio construction process. These constraints include minimum weight, maximum weight, capacity, sector concentration, regional concentration, and turnover. The authors provided insight into the effect of these constraints on the portfolio characteristics, performance, and trading costs of low-volatility strategies. Their main findings are that constraints help improve investability but lead to greater-than-minimal volatility and shift portfolio characteristics toward those of the capitalization-weighted (cap-weighted) benchmark.How Is This Research Useful to Practitioners?This research provides investors with a clearer understanding of the potential outcome from the investment vehicles available in the marketplace, which may allow them to make better investment decisions. By studying the individual and combined effect of constraints typically used by major index providers, the authors help investors understand the trade-off between investability and performance when implementing low-volatility strategies. This research may also enable investors to create customized approaches that suit their needs better than index providers’ solutions.In addition, the fact that the authors demonstrated that their findings are fairly consistent across international markets makes this research appealing to global active investors.How Did the Authors Conduct This Research?The simulations and tests were performed separately for three markets: the United States, developed markets (including the United States), and emerging markets. The authors obtained historical stock return data from CRSP for the United States (1967–2014) and Datastream for international markets (1987–2014). To ensure investability, the starting universe in January of each year consisted of the 1,000 stocks with the largest market capitalizations as of the prior year-end. For each market, the authors constructed a long-only minimum-variance portfolio with an optimization routine under various constraints at the beginning of each January and held it for one year, which allowed them to obtain several simulated return series. They also constructed cap-weighted portfolios from the same starting universes to assess the effect of the various constraints on the structure of the minimum-variance portfolios.The constraints imposed on the hypothetical minimum-variance portfolios included minimum weight, maximum weight, capacity, sector concentration, regional concentration, and turnover. The authors tested the combined effect of these constraints on the investability, sectoral, and regional allocations, as well as the performance and risk attribution of the minimum-variance portfolios. The results show that the constraints generally lower turnover and increase investability. In analyzing performance and risk, the authors explored the effect of constraints on the strategies’ market sensitivities to other risk factors, including size, value, and momentum. The results show that the constraints push the characteristics and performance of minimum-variance portfolios toward the corresponding market portfolios. The authors concluded that the fully constrained minimum-variance portfolio is a sensible alternative to the cap-weighted benchmark because it offers higher risk-adjusted returns in all three markets.The authors also studied the standalone effect of each constraint. They observed that the turnover constraint plays an effective role in reducing trading costs, that the capacity and turnover constraints are crucial for improving liquidity, and that there is a trade-off between liquidity and volatility.In addition, the authors performed several tests to evaluate the robustness of minimum-variance strategies in the presence of constraints, including shortening the historical period in which the covariance matrix is based, reducing the number of eligible stocks, and rebalancing more than once a year.Abstractor’s ViewpointThe simulated minimum-variance portfolios produce higher Sharpe ratios than the corresponding cap-weighted benchmarks. Thus, this research seems to confirm that risk-adjusted returns can be improved by creating minimum-variance portfolios. However, investors should be aware of the trade-offs between investability and performance when implementing low-volatility strategies and understand the effect of constraints on the portfolio characteristics, performance, and trading costs.Editor’s note: The authors may have a commercial interest in the topics discussed in this article.Editor’s note: This article was reviewed and accepted by Executive Editor Robert Litterman.