Tuesday, 2 July 2013

Research Reveals that Complexity Influences Stock Returns


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.