dorsal/arxiv
View SchemaTopological Properties of the Minimal Spanning Tree in Korean and American Stock Markets
| Authors | Cheoljun Eom, Gabjin Oh, Seunghwan Kim |
|---|---|
| Categories | |
| ArXiv ID | physics/0612068 |
| URL | https://arxiv.org/abs/physics/0612068 |
| DOI | 10.3938/jkps.51.1432 |
Abstract
We investigate a factor that can affect the number of links of a specific stock in a network between stocks created by the minimal spanning tree (MST) method, by using individual stock data listed on the S&P500 and KOSPI. Among the common factors mentioned in the arbitrage pricing model (APM), widely acknowledged in the financial field, a representative market index is established as a possible factor. We found that the correlation distribution, $\rho_{ij}$, of 400 stocks taken from the S&P500 index shows a very similar with that of the Korean stock market and those deviate from the correlation distribution of time series removed a nonlinearity by the surrogate method. We also shows that the degree distribution of the MSTs for both stock markets follows a power-law distribution with the exponent $\zeta \sim$ 2.1, while the degree distribution of the time series eliminated a nonlinearity follows an exponential distribution with the exponent, $\delta \sim 0.77$. Furthermore the correlation, $\rho_{iM}$, between the degree k of individual stock, $i$, and the market index, $M$, follows a power-law distribution, $<\rho_{iM}(k) > \sim k^{\gamma}$, with the exponent $\gamma_{\textrm{S&P500}} \approx 0.16$ and $\gamma_{\textrm{KOSPI}} \approx 0.14$, respectively. Thus, regardless of the markets, the indivisual stocks closely related to the common factor in the market, the market index, are likely to be located around the center of the network between stocks, while those weakly related to the market index are likely to be placed in the outside.
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"abstract": "We investigate a factor that can affect the number of links of a specific\nstock in a network between stocks created by the minimal spanning tree (MST)\nmethod, by using individual stock data listed on the S\u0026P500 and KOSPI. Among\nthe common factors mentioned in the arbitrage pricing model (APM), widely\nacknowledged in the financial field, a representative market index is\nestablished as a possible factor. We found that the correlation distribution,\n$\\rho_{ij}$, of 400 stocks taken from the S\u0026P500 index shows a very similar\nwith that of the Korean stock market and those deviate from the correlation\ndistribution of time series removed a nonlinearity by the surrogate method. We\nalso shows that the degree distribution of the MSTs for both stock markets\nfollows a power-law distribution with the exponent $\\zeta \\sim$ 2.1, while the\ndegree distribution of the time series eliminated a nonlinearity follows an\nexponential distribution with the exponent, $\\delta \\sim 0.77$. Furthermore the\ncorrelation, $\\rho_{iM}$, between the degree k of individual stock, $i$, and\nthe market index, $M$, follows a power-law distribution, $\u003c\\rho_{iM}(k) \u003e \\sim\nk^{\\gamma}$, with the exponent $\\gamma_{\\textrm{S\u0026P500}} \\approx 0.16$ and\n$\\gamma_{\\textrm{KOSPI}} \\approx 0.14$, respectively. Thus, regardless of the\nmarkets, the indivisual stocks closely related to the common factor in the\nmarket, the market index, are likely to be located around the center of the\nnetwork between stocks, while those weakly related to the market index are\nlikely to be placed in the outside.",
"arxiv_id": "physics/0612068",
"authors": [
"Cheoljun Eom",
"Gabjin Oh",
"Seunghwan Kim"
],
"categories": [
"physics.data-an",
"physics.comp-ph",
"q-fin.ST"
],
"doi": "10.3938/jkps.51.1432",
"title": "Topological Properties of the Minimal Spanning Tree in Korean and American Stock Markets",
"url": "https://arxiv.org/abs/physics/0612068"
},
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