There are many factors that can influence the cross
section of stock returns. Among them, the state-of-the-art ones are
size, book-to-market ratio and momentum. Recently performed research
indicates that complexity may become a new factor that can influence
stock returns. Our results show that among five plausible measures,
three measures (size, complexity and momentum) stand out as the factors
that can influence stock returns. Using data from 2009 to 2013, we find
that increases in complexity have negative relationship with stock
returns. We also find the complexity-based trading strategy can provide
more stable returns than size-based and momentum-based strategies. These
findings might be exploited in developing innovative trading
strategies.

Due to the high uncertainty in the prediction of
equity returns, we don’t intend to explain the equity return by one or a
combination of several variables. Instead, we’d like to see which
variables can help provide information in the understanding of the
cross-sectional difference in common stock returns. Based on the three
criteria, we can establish a thorough evaluation of the importance and
effectiveness of different risk factors in the specific time period. We use components of the S&P 100 index for one single period to perform the test.

Test 1

Five risk factors (size, book-to-market ratio,
momentum, complexity and resilience) are compared via their correlation
with stock return. Two measures (book-to-market ratio and resilience)
have almost no correlation with stock returns. Size and complexity have
negative relationship with stock return while momentum has positive
correlation. The ranking of the relative importance of the three
nontrivial risk factors are size, complexity and momentum.

Table 1: Correlation between risk factors and stock return

Test 2

Next, we evaluate different risk factors via
multiple regression. We fit several multiple linear regression models to
the data and choose the one with the highest adjusted R-square value.
In the regression with all factors, only three factors (size, complexity
and momentum) have the absolue value of the t statistic larger than 1.
This suggests to attempt regression with these three risk factors. The
multiple regression with these three factors is the best model according
to the comparison of the adjusted r-square value. The relative
importance of the three factors according to the ranking of the absolute
value of the t statistic in the three factor regression model is size,
momentum and complexity.

Table 2: t-statistic in the multiple regression including three risk factors

Test 3

Finally, we compare the five factors based on the
performance of factor-based strategy. In constructing the portfolio we
divide all stocks into two subgroups with same number of stocks based on
the ranking of the risk factor. Then we calculate the difference
between the return of the group with large values in the risk factor and
the return of the group with small values in the risk factor. To
decide the weighting of each stock in the subgroup, we choose the naive
1/N portfolio strategy. This strategy is validated by DeMiguel, Garlappi
and Uppal(2009). They find that among 14 models examined, no one
performs consistently better than 1/N rule. We can rank these factors
based on the difference between the two factor-based subgroup. The
ranking result is momentum, complexity, resilience, size and
book-to-market ratio.

Based on these three tests, we can see that size,
complexity and momentum stand out in this period. We would like to
explore better the interaction of different factors. We divide the
components into different subgroups. Then within each subgroup we
compare the average return for different subgroups based on different
risk factors. If we only consider average return, momentum factor
performs best. If we consider both average return and standard
deviation, then the complexity factor performs best.

Table 3: Summary of performance of size-based strategy

Excessive complexity implies fragility. This may be
the reason that complexity has a negative relationship with equity
returns. In this study, we find that besides two well-known measures
(size and momentum) complexity provides significant information related
to stock returns. The study opens up new perspectives in terms of
developing new trading strategies, in particular a complexity-based
approach to trading.

Submitted by Di Chen, student at the Ecole Polytechnic Fédéral de Lausanne and intern at Ontonix.

See example of portfolio. Measure the complexity of your portfolio here.

www.ontonix.com

Submitted by Di Chen, student at the Ecole Polytechnic Fédéral de Lausanne and intern at Ontonix.

See example of portfolio. Measure the complexity of your portfolio here.

www.ontonix.com