You have made the decision to target the size, value, and profitability premiums in equities, which is great, but it is only a great starting point. There are many questions to consider when incorporating these premiums into real-world asset allocations. How to allocate across premiums and regions? Is it better to get exposure to the premiums through a combination of single factor portfolios, a market-satellite combination, or an integrated solution? What type of weighting scheme should you use? We address these questions in a series of recent papers.

In “Assessing the Relative Magnitude of Premiums” we evaluate whether the size, value, and profitability premiums differ in magnitude across regions. Using various statistical tests, our study shows no reliable differences in the expected premiums, either individually or jointly, across US, developed ex US, and emerging markets. We then examine whether the premiums vary across dimensions: Is the size premium reliably different from the value premium? Is the value premium reliably different from the profitability premium? The tests do not show reliable differences across premiums within any region or globally. Therefore, while it may be sensible to adjust your allocation across premiums and regions to meet your investment goals and constraints, think twice before favoring one premium over another or one region over another based on the magnitude of the expected profitability premiums.

Once the overall allocation is determined, what portfolios should you use to get to the desired exposures? You have at least a few options: combining the market portfolio with single factor portfolios, combining the market portfolio with a satellite multifactor portfolio, or using an integrated core portfolio that simultaneously targets the size, value, and profitability premiums across the entire market. We compare these approaches in “Pursuing Multiple Premiums: Combination vs. Integration.” Our results show that the integrated core approach can better account for the interactions among multiple premiums and lead to more reliable outperformance, better risk control, and lower costs. These benefits can be critical to an efficient pursuit of multiple premiums and cannot be replicated through combination approaches.

Another important decision you face is how to weigh individual stocks in systematic portfolios. Our paper “Weighting for the Right One: Weighting Scheme Design for Systematic Equity Portfolios” compares eight frequently used weighting schemes and highlights the aspects of weighting scheme design that deserve your attention. Perhaps most importantly, you want to see a close link between security weights and market prices. Ignoring prices, as in the cases of equal weighting, rank weighting, z-score weighting, and inverse volatility weighting, can result in uncontrolled overweights in the smallest names, which in turn can lead to significant underweights in the biggest names. More concretely, you might end up overweighting some small cap names by 50 or even 100 times their market cap weights while holding the largest stocks, like Apple, at a few basis points. While such extreme deviations from market weights can produce shining performance on paper, the performance is unlikely to survive the excessive turnover and trading costs in the real world. Using a price-based weighting scheme can effectively mitigate these issues, but there is more to designing a robust weighting scheme. Among the various price-based weighting schemes, our analysis identifies the integrated core approach as the most effective at integrating multiple premiums, managing risks and costs, and accounting for different investor objectives and practical considerations.

So it is great that you have decided to target the size, value, and profitability premiums in your equity allocation. The next, and equally important, decision is to choose the right way to go about it. After all, factors by themselves are not investment strategies. As Nobel laureate Myron Scholes once said, “Ideas alone are cheap—implementation is what really counts.”


Basis point: One basis point equals 0.01%.

Equal weighting: A weighting scheme that holds all firms at the same weight.

Inverse volatility weighting: A weighting scheme that weights firms in proportion to the inverse of their return volatility.

Market-satellite combination: An approach to pursuing multiple premiums by combining the market portfolio with a single strategy that focuses on the intersection of stocks with high expected returns across multiple premiums.

Price-based weighting: Weighting schemes that maintain the link between security weights and market prices.

Profitability premium: The return difference between stocks of companies with high profitability vs. those with low profitability.

Rank weighting: A weighting scheme that weights firms in proportion to their ranks based on sorts on their market capitalization, relative price, and profitability.

Single factor portfolio: A strategy focused on one single premium.

Size premium: The return difference between small capitalization stocks and large capitalization stocks.

Value premium: The return difference between stocks with low relative prices (value) and stocks with high relative prices (growth).

Z-score weighting: A weighting scheme that weights firms based on their market capitalization, relative price, and profitability z-scores. Z-score is calculated as a characteristic’s raw value minus its cross-sectional average, divided by its cross-sectional standard deviation.


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