A New Look on Financial Markets Co-Movement through Cooperative Dynamics in Many-Body Physics

Abstract

One of the main contributions of the Capital Assets Pricing Model (CAPM) to portfolio theory was to explain the correlation between assets through its relationship with the market index. According to this approach, the market index is expected to explain the co-movement between two different stocks to a great extent. In this paper, we try to verify this hypothesis using a sample of 3.000 stocks of the USA market (attending to liquidity, capitalization, and free float criteria) by using some functions inspired by cooperative dynamics in physical particle systems. We will show that all of the co-movement among the stocks is completely explained by the market, even without considering the market beta of the stocks.

Keywords: capital assets pricing model; collective motion; econophysics; finance; stock market.

Figure 1

Co-movement with $C_1$ function. A value of 1 means that there is no co-movement, while values of less than 1 mean that the stocks tend to move in the same direction.

Figure 2

Co-movement with $C_2$ function. A value of 0 means that there is no co-movement, while values greater than 0 mean that the stocks tend to move in the same direction.

Figure 3

Co-movement with $C_3$ function. A value of 0 means that there is no co-movement, while values that are greater than 0 mean that the stocks tend to move in the same direction.

Figure 4

Co-movement ($C_{3t}\left(20\right)$) of the whole market from 2003 to 2011. Blue line is the daily co-movement, while black line is a moving average of the blue line with a time window of 60 trading days.

Figure 5

Co-movement ($C_{3t}\left(20\right)$) of the whole market from 2012 to 2020. Blue line is the daily co-movement, while black line is a moving average of the blue line with a time window of 60 trading days.

Figure 6

Co-movement ($C_{3t}\left(20\right)$) of the whole market from 2003 to 2011 with the market removed. Blue line is the daily co-movement, while black line is a moving average of the blue line with a time window of 60 trading days.

Figure 7

Co-movement ($C_{3t}\left(20\right)$) of the whole market from 2012 to 2020 with the market removed. Blue line is the daily co-movement, while black line is a moving average of the blue line with a time window of 60 trading days.

Scheme 1

Co-movement ($C_{3t}\left(20\right)$) of the whole market during 2003–2011 (left) and 2012–2020 (right) with the market removed. Blue line is the daily co-movement, while black line is a moving average of the blue line with a time window of 60 trading days. The representation of the market is, from top to bottom: ew, cap, SPY, IWM. The horizontal line represent the average co-movement ($C_3\left(20\right)$) along the full period.

Scheme 2

Co-movement ($C_{3t}\left(20\right)$) of the whole market during 2003–2011 (left) and 2012–2020 (right) with the market removed when considering the beta of each stock. The blue line is the daily co-movement, while black line is a moving average of the blue line with a time window of 60 trading days. The representation of the market is, from top to bottom: ew, cap, SPY, IWM. The horizontal line represent the average co-movement ($C_3\left(20\right)$) along the full period.