Price correlation 을 이용한 경제네트워크 구성과 clustering 가능성

Seung-Woo Son email: sonswoo@kaist.ac.kr

Complex System and Statistical Physics Lab., Dept. Physics, KAIST, Taejeon 305-701, Korea

2003. 12. 13. SERI

Correlation ?

Price correlation vs. Return correlation

T/N ratio ( T: trading day, N: number of companies )

– random matrix theorem – should be significantly larger than one

Correlation matrix vs. Distance matrix )1(2 ,, jiji cd

Price correlation

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.00.000

0.001

0.002

0.003

0.004

Dis

trib

utio

n

Correlation Value

1991 - 2003 ( 468 companies, 3431 trading days )

Log return correlation

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.00.000

0.001

0.002

0.003

0.004

Dis

trib

utio

n

Correlation Value

1991 - 2003 ( 468 companies, 3431 trading days )

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.00.000

0.002

0.004

0.006

0.008

Dis

trib

utio

n

Correlation value

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.00.000

0.002

0.004

0.006

0.008

Dis

trib

utio

n

Correlation value

1980 - 2003 ( 228 companies, 6648 trading days )

Price log return

Correlation between two correlations

1991 - 2003 ( 468 companies, 3431 trading days )

1 10 100

1

10

100

Dis

trib

utio

n

degree

MST - Price correlation

1991 - 2003 ( 468 companies, 3431 trading days )

1 10 100

1

10

100

~ 2.076

Dis

trib

utio

n o

f d

eg

ree

degree (k)

MST - Return correlation

1991 - 2003 ( 468 companies, 3431 trading days )

Time moving of return correlation

Period -1982~2000

NYSE105 comp.

Black Monday( 1987 )

Dong-Hee Kim

1982~1986, IBM k=24

1983~1987, GE k=34

1985~1989, GE k=27

1986~1990, GE k=25

1993~1997, MER k=16

1996~2000, GE k=23

Percolation approach &Girvan-Newman cluster method

After sorting Cij in descending order, add a link between i and j following that order. When all nodes make a giant cluster, stop the attachment.

It means the links with values Cij > C * (percolation threshold) are valid and connected.

1.Building giant cluster by percolation approach

2.Break into several cluster by Girvan-Newman cluster method

1991 - 2003 ( 468 companies, 3431 trading days )

Percolate net (all node connected condition) 468 nodes, 85376 links (78.13% of fully connected) bad case!!

- meaningless degree distribution

1991 - 2003 ( 468 companies, 3431 trading days )

Hierarchical tree – clustering

average link method– 두 cluster 사이에 평균 거리 순으로 연결

complete link method– 두 cluster 사이에 가장 먼 거리 순으로…

single link method– 두 cluster 사이에 가장 가까운 거리 순으로…

single link method 는 MST 방법과 일치

average link method

Young-Ho Eom

1991 - 2003 ( 468 companies, 3431 trading days )

complete link method

Young-Ho Eom

1991 - 2003 ( 468 companies, 3431 trading days )

single link method

Young-Ho Eom

1991 - 2003 ( 468 companies, 3431 trading days )

Conclusion

한국증시 KOSPI

Detailed list of used data