About Factor Synergies – Part 2 of 2

• The correlation of different factors with each other is sometimes clearly negative.
• Due to these dependencies, overriding effects can arise in the multi-factor context.
• In addition to the holistic control of all factor effects, the level of the impact is also decisive in order to avoid the dominance of individual factors.
   

Dependencies of different factors

In the last Equity Insights article we showed that factor portfolios based on a simple sorting methodology usually suffer from unde­sirable side effects. The reason for this is that dependency struc­tures between factors are not taken into account. In the case of a combination of the factors value and size, this had a particular effect on factor characteristics outside the desired ones. Since value and size are positively correlated with each other, a high exposure can be achieved in the multi-factor portfolio, at least with regard to these two factors, through a simple sorting.

But what happens when several factors are to be combined in a multi-factor portfolio, some of which being negatively correlated with each other? This article takes a closer look at the portfolio construction of a multi-factor portfolio: value, size, quality (profitability & leverage) and momentum.

Table 1 provides a comprehensive overview of the correlations of all factors. While there is a slight positive correlation between the factors value and size, which in this case favours a combination of both factors, the situation is different with regard to the other factors. Both value and size are negatively correlated with the factors profitability, leverage and momentum. This is well known and economically intuitive. Stocks with high momentum, for ex­ample, are usually no longer value stocks. This interaction leads to high inefficiencies in the portfolio mix of factor indices, as Figure 1 shows.

Fig. 1: Factor-loading of four factor indices (value, size, quality, momentum) equal weighted

Neutralising effects in a multi-factor context

Figure 1 shows the relative factor profile of a multi-factor portfo­lio consisting of four equally weighted indices. These indices are often the basis for billion-dollar ETFs and follow a relatively simple sorting methodology.

In addition to undesirable factor, country and sector effects, there is another implication of this index mix. Due to the correlations between the factors shown above, the resulting multi-factor port­folio only has a positive, albeit manageable, impact on the factors value and size. The factors profitability, leverage and momentum, despite being taken into account by the corresponding factor indices, do not have any noteworthy characteristics due to the negative correlation.

Tab. 1: Correlations of selected factors

Assenagon Equity Framework

As shown in the previous article, a multi-factor portfolio, which does not exhibit any undesirable side effects relative to the underlying universe can be constructed through an optimisation process. However, there are two possibilities for the design of the corresponding objective function:

1. Maximisation of the sought-after factor profile in total
2. Maximisation of the desired factor profile in total under the condition that there is an equal weigth with regard to all factors.

Figure 2 shows the resulting factor portfolio in the case of maximising the sum of exposures. Compared to the uncontrolled portfolio of four indices, the holistic approach shows a clear multi-factor profile: All factors have a clearly positive value, with the size factor again achieving the highest value and thus be­coming very dominant. In other words, by controlling all relevant factors, cancellation effects are prevented. However, the market structure does lead to a strong dominance of individual factors, such as size in this case. As Figure 3 shows, this effect is also very significant over time. Thus, even in a controlled multi-factor portfolio, the factor size would always be a very dominant factor given the market structure, while value, for example, hardly shows any significant expression over a long period of time.

Fig. 2: Factor-loading comparison
 

At first glance, this seems unintuitive, as the exposures of value and size are generally positively correlated. However, value in particular shows a clearly negative correlation with momentum and quality (profitability & leverage), which results in cancelling effects in the multi-factor context. This effect is to be avoided by always achieving equally high values in all the factors.

Fig. 3: Factor loadings over time when maximising the sum of all expressions

For the investor

Generally, it becomes apparent that a holistic portfolio construc­tion, i.e. the explicit consideration of the dependency structures, is indispensable when considering the entire market structure, in order to avoid cancellation effects and the dominance of individ­ual factors. As Figure 2 shows, an optimisation approach yields significant added value by exploiting correlation effects between factor characteristics in order to achieve a high value for all the desired factors.

PS: In the next issue you can read about the implications of the current high index concentration for the market structure.