Quantitative Monographs 29 August 2018Summary
There are two common approaches to building a multi-factor portfolio. You can
either build multiple, stand-alone, smart beta factor portfolios and then invest
some of your money in each of those portfolios, or you can create a composite
smart beta score and build a portfolio based on that composite factor. These are
commonly known as the mixed approach and the integrated approach
respectively.
The figure below illustrates this concept with long only portfolios that use two
factors. The two charts show scatterplots of our factor values (it is the same data
for both charts). In each case, the shaded area indicates the stocks that we would
hold under each approach.
Figure 1: Mixed approachFigure 2: Integrated approach
Source:UBS Quantitative Research, illustrative example
For the mixed portfolio (on the left) you hold the top ranked names by each factor,
taking a double weight in stock names that are top ranked by both factors. Note
that with this approach you will hold stocks even if they look unattractive by one
factor, provided they look attractive by the other.
For the integrated portfolio (on the right) you only hold stocks which look at least
fairly attractive by both factors. Note that with this approach you will reject any
stocks that look unattractive by either factor.
Some academic research has suggested that the integrated approach obtains
superior performance and risk adjusted returns than the mixed approach. In our
Sept 2016 Academic Research Monitor, Combining Smart Beta Factors, we found
that the integrated approach had a better information ratio for a value-momentum
portfolio in three of the five regions considered. In this paper, we compare the
performance difference in greater depth.
We examine a very large number of pairs of backtests. Each pair uses the same set
of smart beta factors, the same portfolio construction method and the same
region, but one uses the mixed approach and the other the integrated approach.
We then compare their risk adjusted performances.
What are the two main
approaches
Which approach gets better
performance
Quantitative Monographs 29 August 2018Analysing each pair independently we find that, for the great majority of pairs of
backtests, there is no significant difference in risk adjusted performance, but of the
pairs that do show a significant difference, the result is much more likely to favour
the integrated approach over the mixed approach.
We use a hierarchical Bayesian technique to model the problem in order to
overcome problems with multiple testing. This gives us a similar result. The
outcome of no-difference cannot be rejected in any of the cases we consider,
but the majority of the posterior distribution lies towards the integrated side.
We also note that the integrated approach is more likely to be significantly better if
you are combining a larger number of smart beta factors, or if you are looking at
long-only rather than long-short portfolios.
This result seems to be partially driven by low volatility – as an example, we split
the two-factor, long-only analysis below into two – including and excluding low
vol; and for the case where we do not include low volatility, we find that the
distribution of the differences in information ratios centres on zero.
Figure 3: Two factors – information ratio differences dependent on volatility
Source:UBS
Some (weak) evidence suggests
integrated gets better
performance
Particularly with long-only
portfolios that combine a large
number of smart beta factors.
For backtests that do not include
low vol, the mixed and integrated
approaches have very similar
performance
Quantitative Monographs 29 August 2018Advantages and disadvantages
Both approaches have some benefits that are worth considering when making a
choice between the two techniques.
Advantages of integrated approach
By construction, the mixed portfolio cannot have a higher return than any of the
individual factor portfolios that make it up. In contrast, the integrated portfolio can
outperform all of the stand-alone factor portfolios.
The mixed approach buys stocks that look attractive on any factor, which means
that, unless your factors are all strongly positively correlated, it will buy stocks that
one or more of your factors find unattractive, because there is at least one factor
that rates the stock highly. That seems counter-intuitive.
Disadvantages of integrated approach
The integrated approach will almost certainly result in a more concentrated
portfolio than the mixed approach. This is easiest to understand by considering a
top quintile portfolio construction method. For the integrated portfolio, you build a
composite score and then buy the top quintile of the market, so if the market has
1,000 names, you will own 200. For the mixed portfolio, you build individual factor
portfolios, each of which has 200 names, and then take weights in those
portfolios. With two factors, the number of stocks that you hold is therefore 200 x
2 minus the number of stocks that fall in both portfolios. Unless the top quintiles
of the two factors perfectly coincide, that will be more than 200 names.
With the mixed approach, it is straightforward to decompose your return into the
return from each individual style. With the integrated approach, it is more complex
and may require a risk model. This makes it harder to interpret your results.
For some factors, notably momentum and low risk, time varying leverage greatly
improves the performance or risk profile of the factor portfolio:
- For momentum, high market volatility is associated with dramatic
drawdowns to the style. By reducing exposure to the style when volatility
is high, investors may be able to avoid the worst of these drawdowns and
improve their performance.1
- For investors who are benchmarked against an index (the majority of
today's investors), low beta stocks can seem unattractive because they
lead to a large tracking error. The ability to lever this portfolio up is
important to making low beta an attractive strategy for benchmarked
investors.
For the mixed approach, incorporating this leverage into the portfolio construction
is straightforward. You simply change the weight assigned to the portfolio with
leverage. For the integrated approach, this is more complicated. You can change
the weight assigned to that particular factor in the composite score, but,
depending on the relationship between momentum / risk and the other styles, this
may not have the intended effect. For example, your portfolio may still exhibit a
beta significantly below one.
1 Please see the Appendix for discussion of a possible work-around in this case.
The mixed portfolio cannot
outperform individual factor
portfolios
Integrated avoids stocks that any
factor has a negative view on
Integrated approach leads to
more concentrated portfolios
Harder to decompose factor
returns
No natural interpretation of
leveraging individual factors with
integrated approach。