Assessing the diversification risk of a single equity market: evidence from the largest European stock indexes

Stock markets are an essential element of the financial system that enables the efficient allocation of funds from savers to investors. Financial investors seek out stocks that minimize the diversification risk and raise portfolio benefits. As such, the volatility of the stock markets has gained increased attention from policymakers, scholars, and the media. Markowitz [1952, 1959] established the profound framework on portfolio management, known as Modern Portfolio Theory (MPT). The theory considers that investors hold diverse risk preferences, influenced by their perceptions of the forthcoming events. Moreover, MPT stands on the efficiency assumption where investors cannot beat the market since stock prices contain all available information. To this end, constructing an optimal portfolio that outperforms market returns relies on the capacity of portfolio managers to anticipate future events. The European Commission's initiative on a single capital market in the European Union (EU) tends to reduce country differences and expand the diversity of listed firms. In 2014, chair commissioner Jean-Claude Juncker launched an action plan for a single EU capital market that would increase efficiency and harmonize trading platforms. In this context, private initiatives have been taken where the Paris Stock Exchange (CAC), Amsterdam Stock Exchange (AEX), and Brussel Stock Exchange launched the Euronext in September 2000 [Euronext, 2021]. Currently, Euronext stands as the largest capital market in Europe with a capitalization of over $5 trillion. The merger of stock markets tends to dampen transaction costs but at the same time makes financial problems more interdependent. The study by Espinosa-Méndez et al. [2020] shows that the Euronext Stock Exchange has increased interdependency and reduced diversification opportunities. The case of the Latin Integrated Market represents a situation where, in 2009, the Santiago Stock Exchange, Lima Stock Exchange, and Columbia Stock Exchange established a joint trading entity named MILA [MILA, 2021].

The creation of MILA raised the trade volume of less active exchanges but also amplified their short-and long-run integration [Mellado and Escobari, 2015; Espinosa-Méndez et al., 2017]. The concept of a single capital market with regional characteristics is also known as the Balkan Stock Exchange [SEE Link, 2021], and that of the Baltic countries is known as Nasdaq Baltic [NB, 2021]. The merger of the stock exchanges into a single one does not mitigate the risk level to all countries involved. Aliu et al. [2019] studied diversification risk benefits of the possible single equity market for the Budapest Stock Exchange (BUX), Bratislava Stock Exchange (SAX), and Warsaw Stock Exchange (WIG20). Results indicate that diversification benefits from a single equity market for BUX declines while it increases for SAX and WIG20. Integrated stock markets have reduced the prospect of portfolio optimization through international diversification.

The EU integration process made local economies interdependent with EU members. Furthermore, free capital flows, followed by trade liberalization and the introduction of a single currency, strengthened the interdependency of the European financial system. However, increased integration among components of the international equity market diminishes diversification benefits for financial investors. Such investors can now achieve international diversification even by investing only in domestic stock indexes [Berrill and Kearney, 2010; Oehler et al., 2017]. Financial globalization and deregulation have created interdependency among stock markets, which has dampened the space for diversification opportunities. The financial crisis of 2008–2009 proved that the global financial system is highly integrated, such that problems in one country quickly spill over into other countries. The concept of a single market stands as a controversial topic among scholars, policymakers, and portfolio managers. We have analyzed the risk–return tradeoff of the six largest equity indexes in Europe through standard diversification methods. However, the capacity of this study is constrained by the sample of the six largest equity indexes in Europe. The results of our work report that not all selected equity indexes benefit from the hypothetical single equity market. The diversification risk for the equity indexes FTSE100, FTSE MIB, and IBEX 35 increases as a result of joining the single equity market. However, for indexes like DAX, MDAX, and CAC40, diversification risk declines as a result of joining the single equity market.

Studies and controversial discussions on the single equity market in Europe are quite old, while they were intensified with the creation of the Eurozone. Arguments on an integrated equity market were generally oriented toward increasing trade volume for listed firms and improved operational efficiency for the participants [Dorodnykh, 2014]. On the other hand, the economy of scale as an outcome of the single market tends to diminish transaction costs by attracting international financial investors [McAndrews and Stefanadis, 2002]. Europe is generally dependent on the banking industry as the main lender to the economic activity and less on the equity and bond markets. For this and many other reasons, stock markets in Europe possess diverse levels of market efficiency. Recognizing this issue, Nielsson [2009] documents that the need for a single equity market in the EU arises from the increased competition of well-capitalized exchanges in the US and Asia. As a consequence, the integrated equity markets in the EU tend to facilitate access to finance for corporations and SMEs [Kokkoris and Olivares-Caminal, 2008]. The prospect of establishing a single equity market in the EU cannot be analyzed only in financial terms but requires a more comprehensive approach. The EU countries operate under different tax systems, monetary policies (non-Eurozone members), and economic arrangements, which aggravates the complexity of this issue. Previous studies were mainly focused on co-integration issues within European stock markets as an obstacle for cross-border diversification. This study measures the diversification risk of the major European equity indexes such as DAX, MDAX, CAC40, FTSE100, IBEX35, and FTSE MIB. Moreover, the outcome of the work provides a historical outlook on the risk perspectives related to the respective stock indexes, by considering them as individual portfolios. To the best of our knowledge, the present study is the first to measure the diversification risk of individual stock indexes using portfolio management techniques. Additionally, the results of the work demonstrate the diversification benefits of creating a common equity market in Europe. Outcomes of this work have implications for investors that tend to diversify their portfolios in the largest European equity indexes. Finally, we provide modest indications for the European policymakers on the diversification benefits of a possible common equity market. Based on the identified problem, the study tries to answer the following research questions:

RQ1: What is the diversification risk of the major European equity indexes from 2008 to 2018?

The rest of the paper is structured as follows: the second part contains a brief literature review on portfolio diversification; part three documents the methodology used; research results are presented in the fourth section; and concluding remarks and recommendations can be found in the final section.

Stock markets represent the most complex structure of the financial system, attracting constant interest from researchers. Risk linked to the stock market stems mainly from the uncertainties associated with stock price instability. The diversification of financial investments is important for risk management since it tends to reduce uncertainties linked to portfolio returns. Portfolio risk is mainly influenced by the correlation coefficient among financial securities, weights concentration, and volatility of returns. However, there is a positive tradeoff between diversification benefits and increased operational costs [Shawky and Smith, 2005]. Standard portfolio theories confirm that holding all investments in one place exposes financial investors to higher risk. Portfolio optimization should contain diverse types of financial securities, such as stocks, bonds, commodities, etc. Discussions concerning investment diversification and risk dynamics are at least a century old. Lowenfeld [1909] provided initial theoretical concepts of portfolio management and stressed the importance of diversification. Over four decades later, Markowitz [1952] confirmed that portfolio optimization is prone to correlation among financial assets, weight concentration, and standard deviations of return. Previous paradigms on portfolio creation indicate that the international spread of financial investments reduces diversification risk. Grubel [1968] confirmed that distributing financial investments beyond national equity exchanges reduces unsystematic risk. The Asian crisis of 1987 delivered the first signals that international investments are not a significant input in reducing portfolio risk. Multiple studies in the literature [Dwyer and Hafer, 1988; Eun and Shim, 1989; Bertero and Mayer, 1990] have confirmed that the stock markets of Germany, Japan, and the United States were highly interconnected during the 1987 crisis. Likewise, the 2008 financial crisis proved on a larger scale that various stock markets are highly correlated. The crisis which started in the United States quickly affected the world financial system, challenging the neoliberal theories that financial markets correct their excesses. Further studies by Morana and Beltratti [2008] and Tamakoshi and Hamori [2012] confirmed that correlation coefficients tend to increase in times of great uncertainty, like the one of 2008–2009. The equity markets in Germany, France, England, Spain, and Italy experienced an enormous downturn during 2008–2009. Similarly, the Eurozone debt crisis of 2011 dampened investor confidence, which resulted in another slump of equity markets in Europe. Government intervention was required to protect the world financial system from collapse. Karim et al. [2011] proved that the 2007 subprime loan crisis did not have a long-term effect on co-movements within stock indexes worldwide. This is confirmed by Albulescu et al. [2015], who demonstrated that in the short run, correlation among the FTSE100, DAX, and CAC40 increased during periods of high volatility. In addition, De Araújo et al. [2013] documented a strong spillover effect from the DAX and FTSE100 to the CAC40, and from the ATHEX20 to the IBEX35 and PSE20, during the meltdown period. It is well known that stock markets efficiently reflect bad news generated by national and international stock indexes. Stock markets on occasion are prone to extreme movements caused by unexpected events, e.g., the bankruptcies of Enron and World Com [De Groen, 2011] and the financial collapse of Lehman Brothers [Haas and Horen, 2012]. Globalization and the integration of financial markets have diminished the ability to reduce the unsystematic risk of a portfolio. Moreover, an increased number of synthetic financial instruments have made risk invisible and unpredictable. Portfolio managers aim to reduce unsystematic risk by distributing financial investments to various industries and sectors. On the other hand, the systematic risk that comes from market shocks is beyond a manager's ability to control.

The efficient market hypothesis claims that stock prices tend toward an equilibrium where deviations from the equilibrium are random. To this end, stock prices reflect expectations for future cash flows while the future is unknown since it is subject to unmade choices. In contrast, most of the financial markets do not satisfy the required efficiency assumption, since stock prices do not reflect the fundamental settings of the company and the national economy. Fama [1968] established the paradigm that financial markets adjust their excesses, prohibiting anyone from making long-run profits. In contrast, Shiller [2001] recognized physiological factors as additional significant elements driving stock price volatility and generating asset bubbles. Portfolio managers tend to eliminate unsystematic risk via diversification, whereas systematic risk is outside the manager's capacity to control. Moreover, they are not concerned simply with stock price volatility, but also with the correlation within financial assets, which is an important element of portfolio risk. The higher the positive correlation coefficient, the higher the portfolio risk, and vice versa [Syllignakis and Kouretas, 2011; Dajcman, 2015].

Weight concentrations in particular securities expose a portfolio to higher risk since portfolio returns rely mainly on the performance of particular securities. A clear theoretical guideline is not available for the optimal arrangement of a portfolio. Structuring an optimal portfolio stands on a complex set of elements, such as an investor's risk appetite, a manager's talent, political events, economic prospects, etc. The number of stocks stands as an additional element of the portfolio risk exposure. Portfolios with a limited number of stocks hold higher diversification risk, and the other way around. Several studies have shown that a portfolio with 10–20 stocks can achieve a higher level of diversification benefits [Klemkosky and Martin, 1975; Bloomfield et al., 1977; Bird and Tippett, 1986; Statman, 1987; Beck et al., 1996; Brands and Gallagher, 2005]. Other scholars [Jennings, 1971; Fielitz, 1974; Johnson and Shannon, 1974] have argued that a portfolio with 8–16 stocks is adequate for achieving maximum portfolio optimization. Recently, Aliu et al. [2020] have confirmed that diversification risk is completely removed on the portfolios holding more than 47 equity stocks. Still, there is no consensus among scholars concerning the number of stocks that would allow for maximum portfolio diversification. However, buying a market portfolio is considered as a way to achieve optimal diversification. In contrast to previous scholars, we have used portfolio diversification techniques to generate risk–reward tradeoffs associated with the largest stock indexes in Europe. No study (to the best of our knowledge) has measured the internal risk of the stock indexes by considering them as individual portfolios. Furthermore, our research generates historical records of the different poolings within stock indexes, making it possible for a single stock index to be created. Consequently, the study generates signals for the index funds that follow stock exchange performance as a benchmark. From a policy perspective, we analyze the possibility of creating a single equity market in Europe using diversification risk techniques. However, our work sheds light on a limited dimension of such complex problems as the creation of a single equity market in Europe.

This study uses secondary data published by the Thomson Reuters Eikon database on stock prices and trade volumes. Stock market prices and trade volumes were collected every week from January 1, 2008 to December 31, 2018 and are expressed in Euros. Diversification risk and weighted average returns are measured on the following stock indexes: FTSE100, CAC40, DAX30, MDAX, IBEX35, and FTSE MIB. The risk level was measured initially for the individual stock indexes. The same methodological process was then conducted for measuring the risk levels of the different poolings within stock indexes. Weekly stock prices and weekly trade volumes are two main inputs in measuring the diversification risks of the portfolio stock indexes. Collection of the data in the same period enabled joining the stock indexes and measuring the diversification risks of different poolings within the stock indexes (portfolios). A diversification formula was used to obtain results. Portfolio risk was determined from elements such as the correlation coefficient within stock prices (rij) and the concentration of the weight (w) based on trading volumes of the listed companies and standard deviations of return (δ). Moreover, each of these elements impacted risk levels. Table 1 below shows the list of sample countries’ stock index, the currency used and the period covered:

The following diversification formula has been used to measure the risk level of the individual stock indexes. The same diversification formula was used to measure poolings within the stock indexes of Italy, Spain, France, Germany, and England: (1) σk2=∑inkwik2σik2+2∑ink∑j<inkwikwjkσjkρijk \sigma _{\rm{k}}^2 = \sum\limits_{\rm{i}}^{{\rm{nk}}} {{\rm{w}}_{{\rm{ik}}}^2\sigma _{{\rm{ik}}}^2} + 2\sum\limits_{\rm{i}}^{{\rm{nk}}} {\sum\limits_{{\rm{j < i}}}^{{\rm{nk}}} {{{\rm{w}}_{{\rm{ik}}}}{{\rm{w}}_{{\rm{jk}}}}{\sigma _{{\rm{jk}}}}{\rho _{{\rm{ijk}}}}} } where σk2 \sigma _k^2 of the portfolio in the year k is computed on the sample of n_k companies, index i indicates a company, and j is an auxiliary index assuring that covariance is computed on distinct companies; ω represents the weight of each listed company in the stock index within the portfolio based on its trade volume; ω² represents weight in the square; σ² indicates variance of returns (stock prices of individual listed companies in the stock indexes); σ stands for the standard deviations of return (stock prices of the individual listed companies in the stock index); and φ(i,j) shows the correlation coefficient within returns (stock prices of the individual listed companies in the stock index).

The mathematical formula was implemented from the following computer programs: Python 3.6.3 (version 0.21.0), Numpy (version 1.13.3), and Jupiter Notebook (version 5.2.0). Generating the inputs of the risk level (δ²) starts with splitting the tables that contain prices and trade volumes. The following matrix was used to generate the results: (2) Uij={aijfor i<j0for i ≥j {U_{ij}} = \left\{ {\matrix{{{a_{ij}}} & {for\,i < j} \cr 0 & {for\,i\, \ge j} \cr } } \right. where a_ij indicates combinations (correlation) between companies i and j.

The process of pooling two or more stock indexes stands as follows: We present an example of pooling two stock indexes. Let A be the first stock index and B the second stock index. A_d represents dates and data (prices and trade volumes) for stock index A, and B_d represents dates and data for stock index B. Merging the two stock indexes is realized through the intersection within A_d and B_d. The new generated portfolio (A + B) creates a new stock index with existing prices and trade volumes from A_d and B_d, since prices and trade volumes are collected on the common dates for both stock indexes (they are intersected by dates). Risk and return calculations of the merged stock indexes follow the same process when calculating a particular stock index.

Stock markets are considered a fundamental component of the financial system, which facilitates the transference of funds from savers to borrowers. Stock markets do not hold a major position within the European financial system, since Europe was traditionally oriented toward banks as the main lenders for business operations and human consumption. The results of our study confirm that the stock markets of Germany, Italy, Spain, France, and England were highly influenced by the financial crisis of 2008–2009. Moreover, the DAX, MDAX, and CAC40 had the lowest diversification benefits (highest risk) during the crisis period. In contrast, the FTSE100, IBEX35, and FTSE MIB were less influenced by the crisis. The financial crisis of 2007–2008 generated a downturn in stock prices that caused the average correlation coefficient to increase. Volatility, as measured through the standard deviation of returns, increased during the crisis period. The most well-diversified index from 2008 to 2018 was the FTSE100, while the least diversified was the MDAX. The Eurozone debt crisis of 2011 produced an additional financial shock within the stock indexes of Germany, Spain, England, Italy, and France. The lowest diversification benefits (highest risk) during the European debt crisis appeared in the CAC40, followed by the DAX and MDAX. The two financial crises proved that the six stock indexes deliver fewer diversification benefits during bad times. In addition, the crisis periods were characterized by higher positive correlations and increased volatility.

This study primarily explored whether there would be diversification benefits if the six indexes operated together. In terms of volatility and diversification benefits, the DAX, MDAX, and CAC40 would have higher diversification benefits by joining a common stock index. In contrast, for the FTSE100, FTSE MIB, and IBEX35, risk and volatility would increase by joining a common stock index. The second objective of the study was to observe diversification benefits within different poolings of stock indexes. Among the portfolios with two stock indexes, maximum diversification (risk and reward) is achieved in portfolio (BG), which pools the FTSE100 and IBEX35. Possible portfolios with three stock indexes confirm that portfolio (BEG), which consists of the FTSE100, FTSEMIB, and IBEX35, delivers the highest diversification. Portfolios with four stock indexes show that when the FTSE100 pools together with the FTSEMIB, MDAX and IBEX35, maximum diversification is generated by a portfolio (BEFG). Portfolios with five stock indexes confirm that portfolio (BCEFG) delivers the lowest risk and highest rewards.

This study does not consider transaction costs and exchange rate risks when calculating weighted average returns, which is a limitation. Future research should identify diversification benefits when stock indexes of the entire EU operate together. Future research should also control transaction costs. Moreover, future research might identify which EU countries would benefit, and which would not, from a common stock index; this information could have important policy and managerial implications.