Larry Swedroe unpacks an illustration supporting factor diversification for portfolio efficiency.

The holy grail of investing is the search for investment strategies that can deliver higher expected returns without increased risk, or the same expected return with reduced risk.

In our 2014 book, “Reducing the Risk of Black Swans,” my co-author Kevin Grogan and I showed how, for 20 years, our firm, Buckingham Strategic Wealth, has been using what we refer to as the science of investing (evidence from peer-reviewed academic journals) to help investors build more efficient portfolios—portfolios that not only have delivered higher risk-adjusted returns, but have significantly reduced the negative impact of rare events known as “black swans.”

The “secret sauce” was adding exposure to factors (such as size and value) that provided a unique/independent source of excess return. In addition, these factors should be persistent across long periods of time, pervasive across the globe and asset classes, robust to various definitions, implementable (meaning they survive transaction costs), and have logical risk- or behavioral-based explanations for why we should expect the premium to continue.

By adding exposure to factors that not only provide higher expected returns but also uncorrelated returns, investors can lower their portfolio’s exposure to market beta and increase their exposure to safe bonds.

In other words, they can lower their allocation to equities because the equities they hold have higher expected returns. As the following example shows, the result has been, at least historically, more efficient portfolios.

35 Years Of Data

Due to data limitations, we’ll examine the 35-year period from 1982 through 2016. We will look at two portfolios, A and B. Portfolio A has a typical allocation of 60% S&P 500 Index/40% five-year Treasury notes. Portfolio B will hold 25% stocks and 75% five-year Treasury notes.

With U.S. stocks representing roughly half of the global equity market capitalization, we will split the equity allocation equally between U.S. small value stocks (using the Fama-French U.S. Small Value Index) and international small value stocks (using the Dimensional International Small Cap Value Index).


As you can see, while Portfolio A produced an annualized return 0.6 percentage points higher than Portfolio B (10.3% versus 9.7%), it did so while experiencing volatility 3.1 percentage points greater (10.3% versus 7.2%). In relative terms, Portfolio A’s annualized return was only 6% greater than Portfolio B’s, while the volatility it experienced was 43% greater.

In addition, Portfolio B had fewer events in the “tails” of the return distribution (said another way, it had both fewer extremely good and fewer extremely bad return years). While Portfolio A had 11 years with returns greater than 15%, Portfolio B had nine. And while Portfolio A had just a single year with a loss of greater than 15%, Portfolio B never experienced a loss that large.

Moving the hurdle to years with 20% gains/losses, we see that Portfolio A had seven years with returns greater than that level, and no years with losses of that size, while Portfolio B had just two years of gains that large. Moving the hurdle to the 25% level, both Portfolio A and Portfolio B had two years with returns in excess of that amount and no years with losses that great.

The best single year for Portfolio A was 1995, when it returned 29.3%. The best single year for Portfolio B was 1985, when it returned 28.0%. Note that while Portfolio B has just 25% in equities, its best year was almost as good as the best year for Portfolio A, which has 60% in equities. On the other hand, Portfolio A’s worst single year was 2008, when it lost 17.0%. The worst single year for Portfolio B was 1994, when it lost just 1.2%.

What’s more, while Portfolio A experienced five years of negative returns, Portfolio B experienced just three. Portfolio B was not only the more efficient portfolio, it offered much greater downside protection. Thus, Portfolio B should be greatly preferred by risk-averse investors, especially those in the withdrawal phase of their investment careers, when the order of returns increases in importance.

Support For Factor Diversification

Louis Scott and Stefano Cavaglia, authors of the study “A Wealth Management Perspective on Factor Premia and the Value of Downside Protection,” published in the Spring 2017 issue of the Journal of Portfolio Management, provide support for the benefits of factor diversification.

The focus of their study, which examined four factors (value, size, momentum and quality), was to determine if factor diversification improved terminal wealth, and if it improved the odds of retirees in the withdrawal phase not outliving their portfolios.

The following table, which did not come from the study, shows the annual correlation of returns of the four factors in U.S. equities for the period 1964 through 2016. Observe the negative correlations of the value, momentum and quality factors to market beta. Even the size factor does not have a high correlation to market beta. These low/negative correlations should provide the dual benefits of diversification and downside protection.


To test their hypothesis, Scott and Cavaglia considered a baseline investment strategy comprising a passive, fully invested exposure to global equities over a 20-year horizon. They then examined the effect of adding an overlay of factor premiums on the distribution of terminal wealth. They used utility functions to quantify the hedging benefits of factor premiums to the baseline investment strategy. Their data set covers the period November 1990 through December 2012.

The authors used a bootstrapping technique (rather than a Monte Carlo simulation) to simulate returns in a way that preserved the autocorrelation observed in markets. They used the bootstrap simulations to generate alternative histories for the market and the four factor premiums.

They then used these histories to generate terminal wealth distributions from investing $1 across alternative investment strategies. The alternative investment strategies they considered were an investment in the global equity market, an investment in the global market complemented by an overlay in a risk premium (each factor considered independently), and an investment in the market complemented by an overlay of an equal-weighted (1/N) allocation to each factor premia.

In the case of a single factor, the overlay is $1 invested in the long side of the premium and $1 invested in the short side. In the case including all four factors, each factor has $0.25 invested in the long side and $0.25 invested in the short side. The portfolios were rebalanced monthly.

The following table shows the terminal wealth at various percentiles of performance. For example, while $1 invested in the global market grows to a median value of $4.17 after 20 years, the fifth percentile of terminal wealth shows a value of $1.06, the first percentile shows a loss of 44%, and the top percentile (the 99th) shows an increase of more than twentyfold.


Note that with the sole exception of the first percentile of the portfolio that includes the global market plus the size factor overlay, the outcomes are improved. That particular outcome is due to the procyclical nature of the size factor.

However, results are quite different when we look at the portfolio with the quality factor overlay. This should not be surprising, because quality tends to outperform in negative market environments. That said, the downside protection did not come with an offsetting reduction in terminal wealth at any percentile.

In all cases, relative to the global market portfolio, the 1/N diversified portfolio produced dramatically superior results, enhancing both downside protection and terminal wealth in good environments.

What If Factor Premiums Decline?

Given that research has shown factor premiums tend, on average, to shrink by about one-third post-publication, Scott and Cavaglia then considered what would happen if the factor premiums shrunk to half the historical levels.

As the following table shows, the portfolio of factor premiums continues to mitigate most of the unfortunate tail (the lower 5%) of the cases in which the investor’s terminal wealth is lower than at the starting point while improving terminal wealth in almost all other cases—the 1/N overlay portfolio has higher terminal wealth in all percentiles, and avoids a loss even at the first percentile.


The authors also performed an interesting test. They compared the performance of a portfolio fully invested in global equities managed by an investor with market-timing skill set at 10% (they could accurately forecast 10% of bear markets, a high hurdle given the lack of evidence supporting the view that bear markets can be forecasted) with the performance of a strategy fully invested in global equities and an overlay of equal-weighted factor premiums.

They found that the distribution of terminal wealth across all percentiles is greater for the factor premiums strategy than for the skill-based strategy. In other words, the factor premiums strategy dominates the skill-based one, creating a very high hurdle for active management in terms of ability to time markets.

Does Factor Diversification Make The Road Less Bumpy?

Scott and Cavaglia next tested to see if the factor portfolio allowed investors to “sleep better,” perhaps improving their ability to stay disciplined and avoid panicked selling. They noted that the median value of the drawdowns for a strategy fully invested in the market was 0.43 (a loss of 43%), suggesting investors will be exposed to at least one sizable, nasty event on their journey to achieving their retirement goals.

The authors found that the overlay portfolio can smooth the ride, providing smaller drawdowns at every percentile, even with the 50% haircut to the premiums applied.

Scott and Cavaglia also considered the utility of the downside protection. The research shows investors are, on average, risk-averse. Therefore, they are willing to “buy insurance” (accept lower expected returns) to protect against downside losses. Using utility functions, with varying degrees of risk aversion, they found that, in all cases, the value of downside protection provided by the factor overlay portfolio (benchmarked against the market P&L) is economically large and significant, emphasizing the factor overlay portfolio’s protection against individuals’ aversion to losses.


Scott and Cavaglia showed the distribution of terminal wealth of a market portfolio strategy can be significantly enhanced via an overlay that allocates capital equally across the four premiums they studied.

In particular, the factor exposures help to mitigate downside risk. Importantly, their simulations demonstrated that, even if the means of the premiums were halved, their drawdown mitigation properties would be preserved.

Finally, they showed that active asset allocation strategies require significant market-timing skill to outperform a passive factor-premium-based overlay strategy.

Post Script

Kevin Grogan and I are working on an update to “Reducing the Risk of Black Swans.” It will include not only more recent data and evidence from the latest research, but also a discussion of certain alternative investments with unique sources of risk and return, and how they broaden the opportunity set and allow for building even more efficient portfolios. We hope to have it published early next year.

This commentary originally appeared November 20 on

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