To add or to multiply - How do I combine factors in a portfolio?

By: Rob Bush | March 29, 2017

In this blog we briefly address a few of the differences in the methods through which multifactor exposures can actually be achieved in practice.

Broadly speaking, there are two options commonly used in the industry – additive (or “composite”) approaches and multiplicative (or “tilt”) approaches. Additive approaches have the virtue of being very simple to understand. An investor just takes a single factor strategy and then blends it with another single factor strategy. So, for example, if interested in having exposure to both Value and Momentum, they could allocate half of their assets to each (or, all of their assets to a product that evenly blends the two approaches).

However, because of the fairly uncorrelated nature of many factors, which we discussed in a separate blog, this approach runs the risk of diluting factor exposure. It might include stocks that have Value but not Momentum, as well as stocks that have Momentum but not Value.

An alternative approach is to overweight stocks that tend to exhibit both Value and Momentum (and indeed as many other factors included in the strategy). Though slightly more complicated, this approach has the advantage of more concentrated factor exposures. Figures One and Two below illustrate this more clearly.

On the y-axis, both charts show the same metric - a score out of 5 for each of the stocks in the Russell 1000 across five factors: value, size, momentum, quality, and low volatility. So, it’s clear that the “worst” stock scored around 0.50 out of 5, and the “best” stock scored around 4 out of 5.

On the x-axis, both charts also show the same metric – the over, or under, weighting of each stock, relative to its starting market capitalization in the Russell 1000 (so a three on the x-axis, for example, would mean that a stock that had a weight of 0.10% in the Russell 1000 now has a weight of 0.30%).

So how do the charts differ? Well, only in the methodology applied when combining the factor scores. In Figure One, an additive, or "composite" approach has been used. Each of the stocks receives an average of its weightings in each single factor index (which is then rescaled to add up to 100%).

However, in Figure Two, a multiplicative, or "tilt-tilt" approach has been used. Each stock is multiplied by each of its factor scores across the five factors (then re-scaled to add to 100%).

Notice the very powerful result of this straightforward difference in methodology. The additive approach, as one would expect, certainly overweights stocks that score more highly across the five factors. It also underweights those that score below the median (2.5) - but it does so in a relatively conservative manner. Its biggest overweight is 2.2 times the starting market capitalization weight. So, on the stock that it favors the most, the additive approach is prepared to go from, say, 0.10% to 0.22%.

Contrast that to the multiplicative approach. On the exact same stock - the one that has the best combined five factor score - a tilt approach is prepared to overweight by 26.6 times. So it would take that same initial 0.10% starting weight and move it to 2.6%, a position that is around twelve times the size of the additive approach.

And note that this is broadly true of high-scoring stocks in general. As their scores increase, a multiplicative approach starts to become increasingly aggressive in its conviction (which explains the sharp shift to the right in the plot). Of course, this conviction probably comes at the cost of a higher tracking error, given that the weightings are moving further from market cap on average. And so, as with all investing, one needs to consider that trade-off. Ultimately though, this "conviction level" is a key difference between these methodologies, and investors must decide which they prefer. (After all, an alpha of 2% and a tracking error of 2% gives the same ratio as an Alpha of 5% and a tracking error of 5%, but they are clearly very different investments).

However, we would argue that, if a stock is being evaluated according to it scores on five factors that have demonstrated their ability to generate alpha in the long run, then the far more concentrated approach of the tilt methodology may be preferable to long term holders.

Source: FTSE Russell as of June 27, 2016 rebalance. This chart represents the relative over- or under-weights (compared to the market cap starting universe that a “tilt-tilt” or multiplicative approach puts on stocks with different factor scores).

Source: FTSE Russell as of June 27, 2016 rebalance. This chart represents the relative over- or under-weights (compared to the market cap starting universe that a “composite,” or averaging approach puts on stocks with different factor scores).

The Bottom Line
There are many ways of combining factor exposures within a portfolio. Be sure to understand the process fully, and know the relative pros and cons of your chosen methodology.

Rob Bush
ETF Strategist
For general inquiries:
(844) 851-4255


When combining factor exposures within a portfolio,understand the process;
know the relative pros and cons of your chosen methodology.

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