Key Points

  1. Implementing a low-volatility strategy entails mitigating out-of-sample estimation errors; over-concentration in sectors, regions, and names; and high transaction costs.
  2. Representative constraints succeed in making simulated minimum-variance portfolios more investable but push them in the direction of the cap-weighted benchmark.
  3. Constraints that are similarly designed to improve the investability of heuristically constructed low-volatility portfolios tend to preserve the intended portfolio characteristics.

Equity investors have endured two extreme market downturns since the turn of the century. The broad U.S. market, represented by the S&P 500 Index, fell by 44% in the aftermath of the dot-com bubble and 51% in the great recession. These devastating experiences reawakened institutional and individual investors to the downside of market volatility and, for a while, prompted great interest in low-volatility investing. Over the last six years, however, the market has been climbing; at the end of July 2015, the price level of the S&P 500 was over 200% higher than its trough in March 2009.1 Low-volatility strategies have languished, and many investors appear to be sleepwalking again—possibly toward a cliff.

While human nature conditions us to chase whatever has been working best—a strategy that we know will backfire badly for the long-term investor—we also know that inertia generally doesn’t pay off. Given the immense gains of this bull market, it may be timely to take some profits off the table, and to dampen our overall portfolio risk through exposure to the well-documented low-volatility effect.2 But, like most things that sound inviting, not all low-volatility portfolio strategies are equally attractive. It pays to understand the differences. Let’s focus first on issues surrounding the implementation of minimum-variance strategies. The same challenges arise for heuristic low-volatility portfolio construction; we consider their impact below.

The Need for Constraints

There are essentially two approaches to low-volatility investing. One of them, called minimum-variance investing, is based on quantitative optimization techniques,3  while the other employs heuristic portfolio construction rules. Some products use combinations of the two approaches, but for this purpose, we will focus on the two primary approaches.

  • The minimum-variance portfolio approach uses a numerical optimizer to select a set of non-negative stock weights such that the resulting predicted portfolio volatility is minimized.
  • A heuristic approach to low-volatility investing typically uses a common risk measure (e.g., beta or volatility) to screen out volatile companies, and assigns weights to the remaining securities by their market capitalizations or the inverse of the company-specific risk measure.

Solidly grounded in finance theory, the minimum-variance method is clearly a sound approach to constructing a low-volatility portfolio. Nonetheless, implementing this method may be more problematic than many investors realize, and the chosen solutions unavoidably affect investment results.4 The challenges relate to “implementation shortfall,” including disappointing out-of-sample performance due to estimation errors,5 extreme and unstable portfolio characteristics, and high transaction costs.6

[drizzle]In addition to applying advanced statistical techniques,7 asset managers and index providers often mitigate estimation errors—and address other minimum-variance implementation issues—by imposing constraints on the optimization process. They typically apply minimum and maximum weight constraints to avoid over-concentration in individual stocks; sector and regional weight constraints to forestall excessive allocations to any one industry group or geographical area; and turnover constraints to control trading costs.

These restrictions are successful in fixing the identified problems, and as a result, they make minimum-variance portfolios more investable. But the improvements come at a price. The constraints progressively nudge the portfolio closer to the market-cap-weighted index and, more importantly, introduce a link between the price of a stock and its weight in our portfolio. As we (and others) have demonstrated, the link between stock price and the portfolio weight has a cost; indeed, severing that link is the main source of alpha for fundamentally weighted and other non-cap-weighted strategies. As a practical matter, it appears that optimization-based minimum-variance strategies cannot be implemented without meaningful slippage.

Empirical Study

To evaluate the impact of typical constraints, we constructed three hypothetical long-only minimum variance portfolios8 from the 1,000 stocks with the highest market capitalization in our universe: a U.S. portfolio, a developed markets portfolio, and an emerging markets portfolio. The baseline minimum-variance portfolios, which were rebalanced annually over the simulation periods, incorporated minimum and maximum weight constraints on individual stock positions. Then we serially applied a capacity constraint related to the stocks’ weights in the market-cap-weighted benchmark; sector and regional concentration constraints; and a ceiling on one-way turnover. (See the Appendix for details on the constraints and regional makeup.)

In Table 1, we see that the stepwise imposition of constraints decreases turnover, increases weighted-average market capitalization (WAMC), increases the effective number of stocks,9 and decreases the aggregate weight of the top 10 names. Just as intended, the constraints limit trading and give the minimum-variance portfolios greater liquidity, higher capacity, and lower concentration.

Low-Volatility Investing

In Panel A of Table 2, we see how performance drops, risk rises, and the Sharpe ratio falters, as we apply more constraints to the simulated U.S. portfolio. Interestingly, the capacity constraint helps performance in the hypothetical developed markets (Panel B) and emerging markets (Panel C) portfolios. In all markets, tracking error against the cap-weighted benchmark decreases monotonically with each new constraint. By partially reversing the optimization, the added constraints move the portfolios away from the theoretical minimum-variance baseline toward the cap-weighted benchmark.

Low-Volatility Investing

The effect of constraints on the ratios of excess return to volatility and value added to tracking error can be seen in Figure 1. Taken together, the constraints push the U.S. minimum-variance portfolio in the direction of the cap-weighted benchmark.

Low-Volatility Investing

We also observe that the U.S. minimum-variance portfolio’s sector allocation more closely resembles that of the cap-weighted benchmark when all constraints are in effect. Figures 2a–2c display simulated three-month smoothed sector weights using Kenneth French’s 12-industry classification. In the baseline case, shown in Figure 2a, the utilities sector has a very large allocation over most of the measurement period. The fully constrained portfolio (Figure 2b) has a more balanced allocation to economic sectors, much like the cap-weighted benchmark (Figure 2c).

Low-Volatility Investing

Low-Volatility Investing

Low-Volatility Investing

So far, we have studied the optimization-based approach to low-volatility investing. We confirm that the optimization process must be constrained to assure the minimum-variance portfolio is implementable. These constraints are also necessary to obtain reasonable portfolio characteristics such as diversification and capacity. But they have a cost. The portfolio becomes more like the market, and the risk increases, with mixed effects on risk-adjusted performance over the simulation periods. Let’s now turn to the heuristic approach to low-volatility investing.

The Heuristic Approach

We conducted a similar analysis of a heuristic approach to low-volatility portfolio construction. To construct the simulated baseline heuristic portfolios, we selected the 200 stocks with the lowest volatility from fundamentally weighted indices for the U.S., developed, and emerging markets. To construct region- and sector-constrained portfolios, we selected from the fundamentally weighted indices’ constituents the 20% of stocks with the lowest volatility within each region and sector, thereby conserving the original allocations. Finally, to incorporate a turnover constraint, we limited trading to removing stocks whose volatility moves outside a pre-established band and adding previously ineligible stocks whose volatility now falls within

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