Characterizing Stock Market Behavior Correlations in Complex Networks Daniel Lopez CS – 765 Fall 2017

Brief Overview Review of Problem Methodology Bipartite Graphs and Projections Temporal shifts in correlation Expected Results and Comparisons

Review Stock tickers are represented as nodes in the graphs, and the edges between them represent similarities between graphs.

Goal and Motivation What is the best way to define that correlation such that similar stocks are more linked together? How can we characterize temporal causality behavior in this way? To maximize portfolio diversity (for loss resiliency), you want stocks that have a large average path length. I want to generalize this to any set of multiple stochastic time series value whose behavior you want to quantify.

Methodology

Bipartite Graph First, let’s represent a set of portfolios that buy and sell stocks in a resulting bipartite graph. Each portfolio randomly buys and sells stock at different intervals with the only condition that whichever action they take, it’s applied to ALL stocks.

Bipartite Graph When these portfolios buy their stock, they will buy whatever is $100 of it (for normalization purposes). Behavioral characterization should tend to give more positively correlated trends values closer to 1 and more negatively correlated trends closer to -1

Bipartite Graph with Time Shifts To consider causality between portfolios after some time shift, we have a copy of the portfolios which according to their unique variable, the phase shift 𝛿, will focus on a particular portfolio. For a set of portfolios with a time-shift, their results would provide a temporal shift in the weight of the projections, showing temporal causality. Time step: 1 2 3 4 5 6 7 8 Action Buy Single Buy the Rest Sell Single Sell Rest

Bipartite Graph with Time Shifts We will be varying the time shift, and having a set of portfolios that focus on each stock respectively. Notice the dashed line which implies that it will perform the action on these stocks later in time.

Equation for correlation Let 𝑓 𝑝 𝑖 =∑ ln 𝑠∈S 𝑠(𝑡+𝑑) 𝑠(𝑡) , which stands for the return for portfolio pi who bought at time t and sold at time t+d. Consider a correlation matrix, where the values are defined as 𝑒 𝑖𝑗 = 𝑝∈𝑃 2(𝑓 𝑝 𝑖 +𝑓( 𝑝 𝑗 )) 𝑓 𝑝 𝑖 +|𝑓 𝑝 𝑗 | −1 Denominator normalizes to 0 and 1, multiplying by 2, and subtracting 1 puts in range [-1,1]

How To Interpret Results

Comparing Results Since we are varying deltas and stock focuses, we will produce graphs that show different metrics of the one mode projection. PageRank or Density -> Influence of Stock Clustering -> High stock similarity behavior Path Length -> Strength of Influence Centrality -> Most important stocks We will be comparing using Pearson Correlation for these values, and see which better captures different characteristics. Denominator normalizes to 0 and 1, multiplying by 2, and subtracting 1 puts in range [-1,1]

Minimum Spanning Tree There are papers were the countries themselves are considered nodes and the financial transactions between economic systems are considered for edges.

Future Work We could use other economical stock properties than just the price of the stock; maybe the DEMA, TEMA, T3 metrics as data points. Instead of performing actions randomly for a different amount of time, the actions could be periodic and pattern based.

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Thank you for listening Q&A Any questions?