New criterion on portfolio selection based on trimmed clusters of stock market

Abstract

Decades have passed since the financial market began to receive attention from academia. Financial Economics became a solid branch of Economics, and statistical tools and Econometrics were exhaustively employed to analyze the financial data from every possible directions. A framework proposed using mathematical models was a catalyst for expansion of the market. Analytical tools from other fields such as Signal Processing and Physics discovered phenomena ubiquitous in financial data and established the stylized facts. Though these studies did deepen the understanding of the financial market, they werent sufficient to prevent financial crises. Institutional investors and policy makers helplessly watched the market tumbles and the academia was unable to provide a clear answer and often held responsible for crises. An apparent conclusion was that the financial market is far from being fully grasped, and further study is necessary. Recently, Network theory gained popularity as a tool to interpret the financial market structure. Analytical methods found in this field such as hierarchical tree and Minimum Spanning Tree were effective to visualize relative positions and interaction between assets. A network analysis begins with a similarity/dissimilarity measure to represent the system of objects. Statistical correlation between assets were extensively studied and accepted as a good quantity to measure the similarity/dissimilarity of assets. Another approach to utilize a dissimilarity measure is data mining. Data mining methods are particularly useful to process large amount of data in an exploratory research. Given that the financial market is yet to be explained such approach might provide an insight which was overlooked before. Therefore, clustering analysis, one of the most well-known data mining methods, was applied to the financial market. In this study, correlation coefficients between stocks were measured and transformed using a distance function. A well-established distance function preserves the topology of the original correlation matrix. It is a good metric to see the stocks as they were. Clustering analysis was then performed on dissimilarity matrices, which are correlation matrices transformed by a distance function. Clustering analysis is designed to put similar objects together in a cluster. Though not in a quantitative way as the clustering analysis, the investors and market participants already have a framework to group similar firms together. The categorization of firms using industrial sector such as the one given by MSCIs Global Industry Classification Standard is accepted as the standard approach to group firms together. Investors would compare the firms in the same sector and add the most promising ones to their stock portfolio. One of the objectives of this study is to test whether the quantitative methods agree with the traditional classification by sectors. Firms were grouped by their correlations in stock returns and the members of the cluster were individually identified by their industrial sector. When a small data set of largest 30 firms by market capitalization in Korea were used to create a dendrogram, firms in the same sector were often found next to each other on the tree which suggests they are close to each other. There were few exceptions and the overall structure of trees varies for different correlation coefficients but a large part of the data would agree with the classification by the sector. However, when a clustering analysis was performed on a larger data set of 200 firms in Korea, most clusters were made of firms from different sectors and clusters rarely had more than 75% covered by a single sector which implies even within a sector, there is no clear dominant pattern which the members of the sector follow. A portfolio of stocks were constructed based on the clustering analysis. A hypothesis was that if the clustering analysis was able to capture the market structure, the portfolio created based on this information should outperform benchmarks such as the market index. The largest 200 firms by market capitalization in Korea were used to for the analysis, and portfolios of 10, 20, and 30 stocks were built and their performance was recorded. Stocks were chosen randomly from each clusters and the average performances of 1000 such portfolios were compared to the benchmarks. Since the stocks were chosen randomly, another benchmark, a portfolio of stocks randomly chosen from the entire data set was created. The purpose of the random portfolio is to determine whether there is a statistical difference in choosing stocks from portfolio or choosing in a completely random fashion. All clustering portfolios were able to outperform the market index but many failed to beat the random portfolio in terms of return-to-risk ratio. One of the possible explanation was found that the clustering analysis was able to identify a group of underperforming stocks and by choosing equal number of stocks from each clusters, the clustering portfolio had a relatively larger number of underperforming stocks. For an investor, the purpose of creating a stock portfolio is not to analyze the market structure but to buy diverse stocks with varying risk profiles thereby generating positive excess returns with an acceptable level of downside risk. Therefore, a trading simulation was performed to see if the clustering portfolios can be used to serve this purpose. Correlations of stocks were estimated using the historical data before a portfolio was launched, and then the portfolios were constructed in the same manner as the previous section. The portfolios were launched after the period of correlation estimation, so no information regarding the period of investment was incorporated in the portfolios. Although the clustering portfolios did outperform the market index, none of them were able to beat the random portfolio. A marked underperformance of clustering portfolios was detected for most of the portfolios. Detailed analyses of each portfolios and their clusters revealed that there were clusters of underperforming stocks and the portfolios had a disproportionately large number of underperforming stocks in their portfolio. By trimming down the underperforming clusters and thereby removing them from the portfolio construction step, the clustering portfolios were able to beat the random portfolio. The framework was formalized and using the US market, an extended portfolio management over 20 years were simulated. Clustering portfolios were constructed in 1990 and were managed until the end of 2015. Three rebalancing periods of 3 months, 6 months and 12 months were chosen and the assets were reallocating every rebalancing period to study the effect of rebalancing frequency. Three correlation estimation periods of 1 year, 3 years and 5 years were chosen and correlation coefficients were estimated over a given period to study how changing correlation estimation period would affect the performance of portfolio. Many clustering portfolios were unable to outperform the market index, and it was found that neither rebalancing period nor correlation estimation period had a linear relationship with the performance of portfolios. The cluster trimming process was formalized with rules and when a cluster with the most firms with net earnings loss over a long correlation estimation period of 3 years or 5 years was removed, the average return and return-to-risk ratio was improved. The result makes sense because firms with persistent earnings loss are likely to be struggling and adding them to portfolio is likely to be detrimental for portfolios performance. Another rule found was that when clusters with more firms with net earnings loss than firms with net earnings gain were removed, the performance of portfolios was improved significantly. The two rules were applied simultaneously and all clusters which satisfied the conditions were removed. The portfolios created without those clusters were able to outperform other clustering portfolios and the benchmark index. The purpose of this research was to analyze the market structure using clustering analysis based on correlation coefficients and propose a framework to create a stock portfolio. It was found that the classification by sector is insufficient to create a diversified portfolio. A framework to construct a portfolio based on clustering analysis was proposed and the trimming process to remove clusters of inferior stocks was introduced.