A sound “portfolio optimization strategy” is one that takes into consideration how its assets are behaving in the bad times, those that represent the left-side tail of the bell curve.

This is not all that novel an idea, but* Maria Kartsakli and Felix Schlumpf,* Zurich Insurance Company executives, give it their own spin. They begin by looking at the Fama-French factors (risk, size, value) and asking how those factors perform in the worst 10 scenarios.

The “worst scenarios” are those for whom the lowest number is obtained by subtracting the risk-free rate from the market return, available in US data. Measured in years (from absolute worst to the least bad of the 10) the worst scenarios are: 1931, 2008, 1974, 1937, 1930, 1973, 2002, 1929, 1981, 2000.

Measured by month, the worst scenarios are: Sept. 1931, March 1938, Oct. 1987, May 1940, May 1932, Oct. 1929, April 1932, Oct. 2008, June 1930 and Aug. 1998.

**Two Sorts of Regression Analysis**

As a matter of history, Fama-French-style factor strategies have long been associated with mutual funds, but in recent years, as Kartsakli and Schlumpf observe, exchange-traded funds have begun indexing these factors, making them available to passive investors.

More to their point, they observe that the factors do pretty well when stress-tested against these worst-case scenarios. Even in the months September 1931, March 1938, and October 1987, the size and momentum factors show positive average values.

From such observations, Kartsakli and Schlumpf move to regression analysis. In the beginning they stick with what they call “traditional regression” analysis. That is: they plot the leading factors in the scholarly literature against the market excess return, then fit a quadratic function to produce a low R-squared trend. They conclude quite generally that factor returns “remain high and positive for the 10 worst cases of the market.”

But their emphasis is on performance through crisis, so they proceed to quantile regression, where the 10th quantile is the lowest quantile in a dataset that keeps 10% of the data below and 90% of the data above it. For their data in this test they use the Fidelity High Dividend ETF, the Fidelity Dividend ETF for rising rates, the Fidelity Momentum Factor ETF, the Fidelity Low Volatility Factor ETF and the Fidelity Value Factor ETF. Also in the mix: the Fidelity High Quality Factor and the SPDR S&P 500 ETF. Respectively, these are abbreviated as FDVV, FDRR, FDMO, FDLO, FVAL, FQAL, and SPY.

**The Mainstream is Right**

So, what happens in the lowest returns of these indices (that 10th quantile)?

Kartsakli and Schlumpf’s analysis confirms the value of mainstream factor analysis. They show that “the factors have … explanatory power and in addition to that their positive sign provides evidence for their diversification benefits in the lowest tail. More specific, in the case of FDLO three of five Fama-French factors together with MOM are positive and significant. For the FDRR three of the five hold a positive statistically significant relationship.”

This is a perspective with obvious consequences for portfolio maximization. In the words of these authors, they suggest a portfolio strategy that “takes into consideration how its assets are behaving in [the] bad times of the market economy,” and they believe that the mainstream factors are of great value in this process.

**A Word More About Each Author**

Kartsakli is also a co-author of “Have Commodities Become a Financial Asset?” an article she wrote two years ago with Zeno Adams, of the University of St. Gallen, chronicling the way commodities have migrated from being physical assets to becoming financial assets and how that gradual transformation explains the “variation in commodity returns and volatility today.”

Schlumpf is the co-author of an article back in 2012 that applied factor analysis to real estate. That was written with Genene Tessera, also of Zurich Insurance. Schlumpf contended that direct investment in real estate has low interest rate sensitivity, and a high correlation to both equities and credit exposure.