International diversification with market indexes.

Hanna, Michael E. ; McCormack, Joseph P. ; Perdue, Grady 等

ABSTRACT

This study examines the development of the optimum investment portfolio utilizing the major stock market index from each of the Group of Seven (G-7) industrialized countries. Results of the study based on data from the 1990s, demonstrate that international diversification may not provide the risk reduction benefits so often reported in the literature and university texts.

INTRODUCTION

International investing is widely recognized as a means to enhance the diversification of portfolios. Investing internationally should reduce the risk (volatility of returns) associated with a portfolio of securities, and, might also increase returns. Much academic research has focused on the risk reduction advantages of international diversification resulting from the theoretical ability of an investor to reduce risk (both systematic and unsystematic) with little or no negative impact on return (modern portfolio theory). The accomplishment of this objective has developed into one of the major goals of portfolio management.

The conventional wisdom in investment strategy encourages investors to diversify internationally to take advantage of the fact that there is less than perfect positive correlation between the financial markets in the United States and the financial markets in other countries. As a result losses in the domestic market may be offset by gains in foreign financial markets which have a low correlation to the financial markets in the U.S. In other words investors hope international investments do well when the U.S. components of the portfolio do not. But do U.S. investors really receive the significant risk reductions they are seeking when they follow the advice to invest internationally? When an investor adds an international asset class to a portfolio's asset allocation, is there really a meaningful reduction in risk or is there an improvement in return?

REVIEW OF THE LITERATURE

Across the last quarter of a century, the academic literature has expounded on the merits of international investing as a component of an overall investment strategy. Solnik (1974) argues the "primary motivation in holding a portfolio of stocks is to reduce risk," and he demonstrates that the systematic risk in a portfolio can be lowered with the use of international diversification. Solnik concludes that "an internationally well-diversified portfolio would be ... half as risky as a portfolio of U.S. stocks..."

Solnik has not been alone in arguing that international investing reduces risk. According to Black and Litterman (1991), the efficient frontier of portfolios shows less risk for each level of return when international investments are included in the opportunity set. Their conclusion is that international investing does reduce the level of risk beyond investing solely in a United States portfolio. Alternatively, Michaud, Bergstrom, Frashure, and Wolahan (1996) focus on both return and risk and conclude, "international diversification increases return per unit of risk relative to a comparable U.S.-only portfolio."

While many studies have historically argued for international diversification, dissenting views have occasionally emerged. Speidell and Sappenfield (1992) express concern that as economies and global events tie together a shrinking world, the benefits of international diversification between major markets may be fading away. They see evidence that the market indexes for the major world economies are becoming increasingly correlated. Sinquefield (1996) comes to a conclusion similar to Speidell and Sappenfield and suggests that actively managed emerging market portfolios may provide greater potential for diversification than does investment in developed markets. He questions if it is even still correct to use the Europe Australia Far East index (EAFE) and other major indexes to diversify an S&P 500 portfolio. Aiello and Chieffe (1999) find that international index funds fail to deliver a high level of diversification. Similarly, Most (1999) indicates that it is difficult to find the desired diversification benefits in developed international markets.

Erb, Harvey and Viskanta (1994) find that correlation coefficients appear to increase between equity markets during recessions (just when investors would want low correlation coefficients). Shawnky, Kuenzel and Mikhail (1997) report that correlation coefficients between markets appear to increase during periods of increased market volatility. Although Solnik, Boucrelle, and Le Fur (SBL) (1996) find that long-term correlations between markets have not risen significantly, they do find that the financial markets exhibit "correlation increases in periods of high market volatility." Michaud, Bergstrom, Frashure, and Wolahan (1996), like SBL, find that the major market indexes have not experienced increased correlation coefficients.

Melton (1996) shows that pension funds in other countries routinely have greater international allocations than U.S. pension funds do. But, Gorman (1998) shows that U.S. pension plans are moving in the direction of including international investments in their asset allocations. Thus, the proponents of international investing, for its diversification benefits, have swayed many pension fund managers in other countries and appear to be swaying U.S. pension fund managers. Yet, the question still remains "How should international investment be handled?"

METHODOLOGY

The study reported here analyzes the risk and return implications for a hypothetical United States investor who chooses to diversify his portfolio's asset allocation with an international equity component. The study utilizes the primary equity market indexes of the U.S. and the other G-7 countries to construct an efficient frontier of portfolios. Those other six nations were Canada, the United Kingdom, France, Germany, Italy, and Japan. Data to describe each of the seven markets is based on monthly prices and exchange rates during the 1990s. The data is used to determine or create the efficient frontier of portfolios for an U.S.-based investor who sought to combine the S&P 500 index with an investment in one or more of the market indexes from the other G-7 industrialized nations.

Using data that have been adjusted for exchange rates, geometric mean returns and standard deviations are computed from the monthly return data for each of the seven indexes. These computed values provide a basic risk-return comparison of the seven markets. Correlation coefficients are also calculated to ascertain the relationship between each foreign market index and the S&P 500. The dollar-adjusted variables are then utilized in the analysis to determine the efficient frontier.

Seeking the minimum standard deviation portfolio for each of a variety of return levels develops an efficient frontier. As an additional portfolio, the minimum standard deviation portfolio is also ascertained. For each new portfolio constructed in this process, the portfolio return, standard deviation, and coefficient of variation are reported.

DATA

The particular market indexes under study in this research are the S&P 500, the Toronto Stock Exchange (TSE) 300 Composite Index, the Financial Times Index of London, the Paris CAC 40, the Frankfurt DAX, the Milan MlBtel, and the Tokyo Nikkei 225. This study utilizes the 121 months of monthly equity market data from January 1990, through January 2000. Monthly observations for the S&P 500 and the six foreign indexes are obtained from the first joint trading day of each month, as reported in The Wall Street Journal. Exchange rate data are also collected for the same trading day as the stock index observations, and are used to convert market return data to United States dollar equivalent returns.

While the data used in this study were monthly data, the results have been converted to an annualized basis for readability.

FINDINGS

The geometric mean return and standard deviation of returns for each of the seven markets are presented in Table 1. As observed in the table, the U.S. index clearly dominates the other indexes in this table. The U.S. market enjoys the highest geometric mean rate of return, and is also the most stable (i.e., has the smallest standard deviation of returns) across this ten-year (121-month) period. The data show the Frankfurt DAX has the closest comparable dollar-adjusted rate of return, but this index has a standard deviation of returns that is over half again larger than that of the S&P 500. The standard deviation of returns for the Toronto 300 was the second smallest one in this period, but the dollar-adjusted rate of return in the Canadian market index was only slightly above one-third of that experienced by the S&P 500. The S&P 500 index also had the lowest coefficient of variation for this period of study. This indicates that it has the lowest amount of risk relative to return.

Adjusted to U.S. dollars, the implications of investing $10,000 in each of these markets is illustrated in Figure 1. As is clear from this figure, an investor investing in either the S&P 500 or Frankfurt DAX would have more than tripled these invested funds across this ten-year (121-month) period. Investing in the London index would have produced nearly identical results with investing in the Paris index as the funds in each more than doubled during this period. At the lower extreme, almost a third of the funds invested in the Tokyo index would have been lost.

Table 2 reports the correlation coefficients between returns in each of the seven markets. All correlation coefficients are positive, indicating a clearly positive relationship between the returns over this period in the seven financial markets. Correlation to the United States market is highest with the Toronto exchange and lowest with the Tokyo and Milan indexes. All other things being equal, we would expect the low correlation coefficients to indicate that the Tokyo and Milan indexes would be the best indexes for diversification purposes for an U.S. investor.

Utilizing the data from these seven markets, potential minimum variance portfolios were developed for several possible rates of return. This was accomplished by including all seven indexes in the hypothetical portfolio, and then minimizing the standard deviation of the portfolio. Minimization of the standard deviation of the portfolio was performed subject to two constraints. First the portfolio must earn the highest rate of return. Second the weighting of the indexes must sum to one and no index could be allowed to have negative weighting.

In modern portfolio theory one ascertains the desired rate of return and utilizes it as one of the constraints in seeking the optimum portfolio. Therefore the choice of a desired rate of return becomes a key component in optimizing the portfolio. As one moves down the relevant portion of the efficient frontier, there is an expected trade-off between return and risk. Each successive portfolio on the frontier represents both lower returns and lower levels of risk.

Table 3 presents the returns, standard deviations, and coefficients of variation for several possible combinations of the United States S&P 500 and other market indexes. Figure 2 is a graphical representation of this table. These portfolios are the minimum volatility portfolios for each rate of return listed in the table. The weight of the United States component varies in each portfolio from a 100 percent United States component to only 63 percent, with the weight of each of the other indexes also being varied as required.

[FIGURE 2 OMITTED]

While there is an efficient frontier present in Figure 2, it is quite short. The portfolio with the highest return consisted of only the S&P 500 Index and had an average rate of return of 14.79 percent and a standard deviation of 12.10 percent. The minimum variance portfolio had an average rate of return of 13.70 percent and a standard deviation of 11.79 percent. Thus, the range of returns was only 1.07 percent and the range of standard deviations was only 0.31 percent. This historical efficient frontier was indeed very short.

In this study the U.S. market index had the highest return, so the inclusion of any other index lowers the overall portfolio return. The high return on the S&P 500 combined with its low volatility during this period are major reasons why the minimum variance portfolio has an 80 percent weighting in the U.S. market index (See Table 3).

Using the coefficient of variation to compare the risk-return trade-off between the U.S.-only portfolio and the minimum risk portfolio, one observes that the U.S.-only portfolio has a coefficient of variation of 0.818 while the minimum variance portfolio has a coefficient of variation of 0.861. This indicates that the U.S.-only portfolio represented a better risk-return trade-off versus the minimum variance portfolio. Contrary to what is normally expected, investing in the minimum risk portfolio gave the investor very little reduction in risk and did so at a relatively large reduction in return. Furthermore, international diversification would entail greater investment and management costs. The U.S. investor had almost nothing to gain across the decade of the nineties through diversification by investing in the major market indexes.

CONCLUSIONS

In theory an investor's portfolio may benefit by being invested in the U.S. market and another market that is less than perfectly correlated with the U.S. market. Diversification typically reduces risk significantly at the cost of a small reduction in return. However, during the decade of the 1990s, U.S. investors were not rewarded for international diversification. They would have experienced small reductions in risk coupled with large reductions in return. Data across this time period using the market indexes for the United States and its G-7 partners fail to support the usefulness of international diversification.

If the goal of the investor's investment strategy is risk minimization and offsetting domestic market losses, then the investor facing an asset allocation decision must consider the historical market patterns discussed here. The cases which are examined in this study show international diversification (based on major market indexes) over these ten years (121 months) would not have been as potent a tool for U.S. investors as has been suggested in much of the academic research and by many investment advisors. The risk reduction benefits of diversification were simply not evident. Given this recent historical experience, the investor must ask if there is sufficient reason (in terms of risk reduction) to pursue international diversification. Going forward there is clearly little in the data from the 1990s to argue for using the indexes from other industrialized countries to diversify an U.S.-based portfolio. It may be that inclusion of the indexes can only be done if subjective judgment tells the investor that things will be different in the future.

The results of this study might be sample specific. The complete data set of the decade from 1990 through 2000 is used in describing the relationship between the United States and the remaining G-7 markets. However, it may be difficult to extrapolate the findings of this research to any other markets, specific stocks in these markets, or to other time periods. Nevertheless, investors typically obtain reasonable expectations of the potential benefits of international diversification by studying historical relationships and the results in this study should provide input that allows investors to make a more informed investment decision.

REFERENCES

Aiello, S. & Chieffe, N. (1999). International Index Funds and the Investment Portfolio. Financial Services Review, 8 (1), 27-35.

Bailey, W. & Lim, J. (1992). Evaluating the Diversification Benefits of the New Country Funds. The Journal of Portfolio Management, 8 (3), 74-80.

Black, F. & Litterman, R. (1991). Global Portfolio Optimization. Financial Analysts Journal, 48 (5), 28-43.

Erb, C.B., Harvey, C.R. & Viskanta, T.E. (1994). Forecasting International Equity Correlations, Financial Analysts Journal, 50 (6), 39-45.

Gorman, S.A. (1998). The International Equity Commitment, The Research Foundation of the Institute of Chartered Financial Analysts, Charlottesville, VA.

Melton, P. (1996). The Investor's Guide to Going Global with Equities, Pitman Publishing, London.

Michaud, R.O., Bergstrom, G.L., Frashure, R.D. & Wolahan, B.K. (1996). Twenty Years of International Equity Investing: Still a route to higher returns and lower risks? The Journal of Portfolio Management, 23 (1), 9-22.

Most, B.W. (1999). The Challenges of International Investing Are Getting Tougher. Journal of Financial Planning, February, 38-40, 42-46.

Shawnky, H.A., Kuenzel, R. & Mikhail, A.D. (1997). International Portfolio Diversification: A Synthesis and Update, Journal of International Financial Markets, Institutions and Money, 7, 303-327.

Sinquefield, R.A. (1996). Where Are the Gains from International Diversification? Financial Analysts Journal, 52 (1), 8-14.

Solnik, B.H. (1974). Why Not Diversify Internationally Rather than Domestically? Financial Analysts Journal, 30 (4), 48-54.

Solnik, B., Boucrelle, C. & Le Fur, Y. (1996). International Market Correlation and Volatility. Financial Analysts Journal, 52 (5), 17-34.

Speidell, L.S. & Sappenfield, R. (1992). Global Diversification in a Shrinking World. The Journal of Portfolio Management, 19 (1), 57-67.

Wahab, M. & Khandwala, A. (1993). Why Not Diversify Internationally with ADRS? The Journal of Portfolio Management, 19 (2), 75-82.

Michael E. Hanna, University of Houston--Clear Lake

Joseph P. McCormack, University of Houston--Clear Lake

Grady Perdue, University of Houston--Clear Lake

TABLE 1
Rates of return, standard deviations, and coefficients of variation
All values stated as percentages

Market Annual Geometric Standard Deviation Coefficient of
 Mean Return of Returns Variation

S&P 500 14.79 12.10 0.82
Toronto 5.08 16.37 3.22
London 10.55 21.43 2.03
Paris 9.85 19.16 1.95
Frankfurt 12.36 18.45 1.49
Milan 5.72 28.93 5.06
Tokyo -3.63 29.43 -8.11

TABLE 2
Correlation coefficients between indexes

 S&P 500 Toronto London Paris Frank. Milan Tokyo

S&P 500 1
Toronto 0.6866 1
London 0.4023 0.3777 1
Paris 0.5762 0.4524 0.4320 1
Frank. 0.5274 0.4739 0.3632 0.7264 1
Milan 0.2783 0.3311 0.3140 0.3580 0.3872 1
Tokyo 0.3501 0.2983 0.2876 0.3674 0.2618 0.2526 1

TABLE 3
Efficient Frontier Portfolios
All values stated as percentages

 Portfolios

Annual Annual Coefficient
Return Standard of
 Deviation Variation

14.79 12.10 0.818
14.5 11.91 0.821
14.0 11.80 0.843
13.7 11.79 0.861
13.5 11.80 0.874
13.0 11.81 0.908
12.5 11.85 0.948
12.0 11.90 1.071

Weight of each index in frontier portfolios

 S&P Toronto London Paris Frankfurt Milan Tokyo
 500

 100.0 0 0 0 0 0 0
 87.3 0 6.1 0 6.6 0 0
 80.4 0.9 7.9 0 7.2 3.3 0.4
 79.6 1.1 8.0 0 7.2 3.4 0.8
 76.2 4.0 7.9 0 6.9 3.4 1.6
 71.9 7.3 7.8 0 6.6 3.6 2.8
 67.8 10.6 7.7 0 6.1 3.9 3.9
 63.4 13.9 7.6 0 6.1 4.0 5.1

Figure 1

Today's value of $10,000 invested 10 year ago

 Market

S&P 500 39.7
Toronto 16.4
London 27.3
Paris 25.6
Frankfurt 32.1
Milan 17.4
Tokyo 6.9

Note. Table made from bar graph.