Constraining Optimized Portfolios: Handle with Care

We recently wrote a series of papers that examined the impact of constraints on optimized portfolios. The original paper focused on US-based Momentum strategies, and the current trilogy looks at Momentum, Value and Low Volatility strategies from a global developed market perspective. In addition to expanding the universe beyond the US and changing some of the parameters from the initial US-based tests, the new series of papers added Axioma’s Constraint Attribution capability to the analysis, on top of a detailed risk and performance breakdown, to get an even more detailed perspective. The papers can be found here.

For the studies, we ran backtests using the FTSE Developed index as the benchmark and investment universe, targeting 2.5% tracking error while maximizing (minimizing) exposure to Axioma’s Medium-Term Momentum, Value and (Volatility) factors.  Portfolios were long-only and fully invested. We created three versions of each factor portfolio: Unconstrained, which did not add any additional constraints, Lightly Constrained, which was meant to reflect typical institutional constraints (e.g. 2% active country and sector weights, 0.2 exposures to style factors other than the targeted one), and Constrained, which did not allow any active country, sector or other factor bets.  We did not include any asset-level, turnover, liquidity, or other constraints. The results for Value and Momentum were similar to those we found in the US version, but Low Volatility exhibited some different risk and performance characteristics.

Some of our findings across the strategies and test factors are as follows:

  • Constraints tend to concentrate risk and shift exposure away from the desired factor and toward specific risk.

  • In Momentum and Value, we show better absolute performance when there were fewer constraints, but for portfolios that tilt on Low Volatility, the performance advantage of fewer constraints was not clear.

  • Constraint attribution highlighted which constraints had the biggest impact on performance, and led to some surprises.  For example, the no-shorting constraint actually helped the performance of the Momentum portfolio for a few years, suggesting that the factor return worked better on the long side, counter to our expectations.

  • In most cases, the budget (no-leverage) constraint (which is tied to the no-shorting constraint in that without shorting one also cannot lever the portfolio) had the biggest impact.

  • Individual style constraints also had quite a big impact on performance, although some were positive and some negative, so they tended to cancel each other out.  Most notably, constraining Size exposure (when most portfolios wanted to have a small-cap bias) was usually the biggest drag on performance from a single factor.

  • After budget (no leverage) and no shorting constraints took their toll there was not much return left for the Low Volatility strategy over the full test period.  Although Low Volatility did deliver positive active returns when markets were down a lot, the advantage of this kind of strategy was unclear when markets were up, as it outperformed in some and underperformed in others.

  • The one advantage of constraints was that they served to better keep ex-post tracking error in line with ex-ante expectations, but that often came at a performance — and information ratio — disadvantage.

Below we show some sample charts:

Source: FTSE Russell, Axioma

In summary, as constraints move the portfolio away from the desired factor, that risk vacuum may be filled with specific risk, which is not what the factor-based manager intends. Most institutional portfolios add additional constraints, such as limits on liquidity and trading, on top of the few we illustrated, which are likely to drive even bigger differences in returns. The impact of those constraints can be analyzed in constraint attribution as well, but even a more-simple analysis can help managers and their clients better understand what happens when constraints are imposed.

Melissa R. Brown, CFA

As Managing Director of Applied Research, Melissa Brown generates unique insights into risk trends by consolidating and analyzing the vast amount of data on market and portfolio risk maintained by Axioma. Brown’s perspectives help both clients and prospects to better understand and adapt to the constantly changing risk environment.