There seems to be something like a distant relationship between low volatility and the quality investment approach, but nothing more: this was the verdict of the first two parts of this series of articles, where we subjected the two investment strategies to a descriptive (Part 1) and qualitative (Part 2) comparison. However, the value portfolio also examined seems to have almost nothing in common with the two approaches mentioned above. In this article, we will use statistical indicators to analyze whether the findings so far also stand up to quantitative evaluation. For this purpose, the sensitivities of the three factor portfolios to the Fama-French factors known in the financial literature are determined.[1]

##### Explanatory power times five

The three portfolios examined all rely on factors that empirically demonstrate better risk/return characteristics than the market index over the long term. The selection of these factors is no coincidence. Theory and practice have been dealing with the question of which systematic factors explain the excess return of investments for decades. From a multitude of answers, different convictions regarding the best investment strategy have emerged. Eugene Fama and Kenneth French's "five-factor model", an updated version of their famous "three-factor model" from 1993, provides a sound comparison of the return composition of the three investment approaches shown here.[2] While Fama and French in the 3-factor model still assume that the return on a share can essentially be explained by the "market risk", the "size of the company" (size) and the "valuation" (value), the two renowned scientists have expanded their universe of yield-driving factors in the 5-factor model by the - not undisputed [3] - dimensions "profitability" and "investment activity". While the market risk factor reflects the risk premium of a market portfolio diversified across the entire equity market compared to a risk-free investment, the size factor takes into account the fact that shares with low market capitalization (so-called small caps) have historically achieved a higher return than large-capitalized securities (so-called blue chips). In contrast, the value factor is based on the observation that shares with a low price/book ratio (P/B) yield a higher average return than shares with a high P/B ratio. The two newly added factors target different aspects of "quality". While the profitability factor is based on an increased return on equities with good operating profitability, the investment factor assumes that high investment activity, measured as a strongly growing balance sheet total, leads to declining profitability and increases risk.[4] The "five-factor model" is of interest to us because it measures how strongly an investment strategy is exposed to the major return drivers identified by Fama and French. Accordingly, the five-factor model is well suited to locate the differences and similarities between the investment returns of the three portfolios we examined.

##### Volatility is a part of it

Since we examine a value, a quality and a low volatility portfolio, it makes sense to include a volatility factor in the statistical analysis in addition to the five-factor model, which already includes value and quality. The volatility factor is based on the empirical effect known as the "low volatility puzzle", according to which securities with low volatility often perform better in the long term than those with high volatility. In line with Fama-French's methodology, we construct the volatility factor as a long-short portfolio, with equities with historically low volatility receiving a positive weight (long) and equities with high volatility a negative weight (short).

When explaining the returns of the three portfolios using the Fama French factors and the additional volatility factor, clear patterns can be seen (see table and chart). As expected, the portfolios have, in addition to the market factor, the highest exposure to the factor that should be included in it according to the construction criteria. Thus, the value portfolio is mainly driven by the value factor, the quality portfolio by profitability and the low-volatility portfolio by the volatility factor.