Abstract
It has been frequently observed that US markets leads other developed markets in Europe or Asia, and that at times the leader becomes the follower. Within a market, or even across different markets, some assets’ returns are observed to behave like other assets’ returns, or completely opposite, and thus may serve as pairs for a trading strategy or portfolio selection.
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Notes
- 1.
\(\text {sgn}(z)\) is either \(-1\), \(0\) or \(1\), if \(z<0\), \( z=0\) or \(z>0\), respectively.
- 2.
For \(y_t = f(x_t)\) and \(n\) observations, the residual sum of squares is \(RSS = \sum _{t=1}^n(y_t - f(x_t))^2.\)
- 3.
Friedman, M., & Schwartz, A. J. (1963). Money and business cycles. The Review of Economics and Statistics, 45, 32–64.
- 4.
To learn the need of this causality relation see Dwyer, G. P., Locke, P., & Yu, W. (1996). Index arbitrage and nonlinear dynamics between the S&P 500 futures and cash. Review of Financial Studies, 9, 301–332.
- 5.
Joe Ward (1963) considered cluster analysis as an analysis of variance problem, and consequently he considers as point-distance the squared Euclidean norm, and his objective function to minimize (the inter-cluster distance) when merging two clusters is the the sum of squared deviations or errors. This results in the formula given for \(\widehat{d}\).
- 6.
The tickers for these stocks are: ABE, ABG, ACS, ACX, ANA, BBVA, BKT, BME, BTO, CRI, ELE, ENG, FCC, FER, GAM, GAS, GRF, IBE, IBLA, IBR, IDR, ITX, MAP, MTS, OHL, POP, REP, SAB, SAN, SYV, TEF, TL5, TRE, REE. The table Ibex0809 can be downloaded from the web page of the book, http://computationalfinance.lsi.upc.edu.
- 7.
recall Ward’s method that treats clustering as a problem of variance.
- 8.
An interesting subject of research is to determined this partition.
- 9.
This strategy attempts to capture the spread between two correlated stocks as they reverse to the mean price. It consists on taking long and short positions on the pair of stocks as they move together, changing positions at the mean (Vidyamurthy 2004).
- 10.
By a leaf of a heap we understand a node with no ingoing edges. By updating the keys of the leaves only we significantly reduce computation time since we do not need to traverse all the heap. Also the information about the key value of inner nodes is irrelevant for our purposes. For further details on heaps see Cormen et al. (1990).
- 11.
The finding of the heaviest paths in this example confirmed a popular observation, known by many local brokers (at least as of 2010), that the banks BBVA and SAN conform the most stable cluster through any period of time, and further we see that this duo tends to participate in the largest clusters of IBEX components at different periods of time; hence being both together a driving force of the Spanish market.
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Arratia, A. (2014). Correlations, Causalities and Similarities. In: Computational Finance. Atlantis Studies in Computational Finance and Financial Engineering, vol 1. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-070-6_3
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DOI: https://doi.org/10.2991/978-94-6239-070-6_3
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