The UK investor and international diversification.

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

ABSTRACT

This study describes the development of the optimum investment portfolio for a United Kingdom-based investor who seeks to utilize the major stock market index from each of the Group of Seven (G-7) industrialized countries to diversify a domestic equity index portfolio. Results of the analysis based on data from the 1990s, indicate that substantial international diversification is essential if the UK investor's objective is to obtain an optimal portfolio.

INTRODUCTION

In modern portfolio theory international investing is widely accepted as an efficient means to diversify a portfolio. A great body of academic literature has focused on the risk reduction enjoyed by an investor who is able to reduce risk with little or no negative impact on return. Today many modern investment strategies include international investments to take advantage of the imperfect correlation between the financial markets of an investor's home market and those of other countries. The objective is to have gains in a foreign market to offset losses in the domestic market. To what extent should United Kingdom (UK) investors in the new millennium engage in international investing? This question takes on new importance in light of the growing trend towards the use of defined contribution retirement plans in the UK. Individuals who have never considered themselves as investors and who have previously relied on the state or company-administered pension schemes (as they are called in the UK), now face asset allocation decisions and the risk and return implications inherent with those decisions. Given this new situation, it is appropriate to realize that the extent a modern UK investor should engage in international investing will be related to the degree of risk reduction or return augmentation possible when that investor adds an international asset class to the portfolio's original domestic only asset allocation.

REVIEW OF THE LITERATURE

Numerous academic studies have explored the virtues of international investing as an element of an asset allocation strategy. Solnik, 1974, discusses the "primary motivation in holding a portfolio of stocks is to reduce risk," and he shows that international diversification can lower the systematic risk in a portfolio. Based on historical data a long-run allocation of 20 to 30 percent in foreign equity appears correct for an investor based in the United States, according to Clark and Tullis, 1999. Black and Litterman, 1991, conclude that international investing reduces the level of risk below that of a purely domestic portfolio. Michaud, Bergstrom, Frashure, and Wolahan, 1996, arrive at the finding that "international diversification increases return per unit of risk ..."

While many studies have historically argued for international diversification, some contrary views have occasionally emerged. Speidell and Sappenfield, (1992, and Most, 1999, 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. Of particular importance to UK investors, Beckers, 1999, shows that "European stocks are starting to behave more similarly." Aiello and Chieffe, 1999, find that international index funds fail to deliver a high level of diversification because the market indexes for the major world economies are becoming increasingly correlated. Sinquefield, 1996, 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. Sinquefield, 1996, and Eaker, Grant and Woodard, 2000, contend that actively managed emerging market portfolios may provide greater potential for diversification than investment in developed 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. Higher correlation would imply a reduction in diversification potential and thus higher portfolio risk. Although Solnik, Boucrelle, and Le Fur, 1996, find that long-term correlation 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 the previous authors, 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 questions still remain: "How should international investment be handled?" and "How much international diversification is appropriate?"

METHODOLOGY AND DATA

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

Geometric mean returns and standard deviations are computed from the monthly return data for each of the seven indexes, after the data have been adjusted for exchange rates fluctuations. 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 FTSE. The pound-adjusted variables are then utilized in the analysis to determine the efficient frontier.

The study reported here analyzes the risk and return implications for a hypothetical United Kingdom investor choosing to diversify a domestic equity index portfolio by incorporating international equity index components. The study utilizes the major equity market indexes of the UK and the other G-7 countries to construct an efficient frontier of portfolios. Those other six nations were Canada, the United States, France, Germany, Italy, and Japan. Data to describe each of the seven markets is based on monthly returns on the indexes and on monthly exchange rates during the 1990s. The data is used to determine the efficient frontier of portfolios for an UK-based investor who sought to combine the Financial Times Stock Exchange (FTSE) index with an investment in one or more of the market indexes from the other G-7 industrialized nations.

Ascertaining the minimum standard deviation portfolio for each of a variety of selected returns develops the efficient frontier. For each new portfolio constructed in this process, the portfolio return, standard deviation, and coefficient of variation are reported. The minimum volatility portfolio contained a relatively small UK component, and this may not be attractive to some UK investors. The minimum weighting of the UK component of the portfolio was initially set to zero and gradually increased and new efficient portfolios are developed.

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

FINDINGS

Presented in Table 1 are the geometric mean return and standard deviation of returns for each of the seven markets. The London FTSE produced the third best performance during this time period, and had the third best coefficient of variation. Of the European markets only Frankfurt had both a better return and a lower level of volatility. However, as is observable from the table the United States (US) index clearly dominates the other indexes during the period of the 1990s. The US market produced the highest geometric mean rate of return, and is also the least volatile (i.e., had the smallest standard deviation of returns) across this ten-year (121-month) period. The data show the Frankfurt DAX had the closest comparable pound-adjusted rate of return, but the DAX has a standard deviation of returns that is about twenty percent larger than that of the S&P 500. The standard deviation of returns for the Toronto 300 was the second smallest in this period, but the pound-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, indicating it produced the lowest amount of risk relative to return.

Adjusted to UK pounds, the implication of investing 1,000 [pounds sterling] 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 provides information on the correlation 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 Kingdom market is strongest with the US and Paris indexes and weakest with the Milan and Tokyo indexes. Given this information and all other factors being equal, one would expect the low correlation with the Tokyo and Milan markets to indicate great potential for diversification through these markets for the UK investor. However, results reported below show virtually nothing is gained for the UK investor by including the Italian market in his portfolio.

Given the data from these seven equity markets, efficient frontier portfolios were developed utilizing several different minimum weightings for the UK market component of the portfolio. Efficient frontier portfolios were determined by including all seven indexes in the hypothetical portfolio. Minimization of the standard deviation of the portfolio to ascertain the frontier was performed subject to the following constraints. The portfolio must earn a given rate of return (with several rates of return used to develop the frontier). Also the weighting of the indexes must sum to one and no index could be allowed to have negative weighting.

Table 3 presents the returns, standard deviations, and coefficients of variation for several possible portfolio combinations of the FTSE and other market indexes, where there is no minimum or maximum weighting preset for the FTSE. Figure 2 is a graphical representation of this table. The selected returns are six percent, eight percent, 10.07 percent, 11.26 percent, and 12 percent. The 10.07 percent return is chosen as one of the points to be determined on the frontier because that was the mean return for the UK market over the time period of this study (as reported in Table 1). The portfolio with the 11.26 percent return is the minimum volatility portfolio for the UK investor. These five portfolios are the minimum volatility portfolios for each rate of return listed in the table.

The UK market across this decade had a return of 10.07 percent and a standard deviation of returns of 21.75 percent (as reported in Table 1). The frontier portfolio with the 10.07 percent return reported in Table 3 has a standard deviation of 14.87 percent, indicating nearly a 1/3 reduction in volatility as the UK component is reduced from 100 percent down to only 16.7 percent of the respective portfolio. In fact the weight of the UK component varies in each frontier portfolio from a maximum of 16.70 percent to only 14.80 percent, with the weight of each of the other indexes also being varied as required to obtain the minimum volatility portfolio for that rate of return. That the UK component of the portfolio never exceeds 16.48 percent of any frontier portfolio is an important point clearly demonstrating the significant gains from international diversification for the UK investor.

Clark and Tullis (1999) have suggested that a 20 to 30 percent allocation to international equities would be appropriate for a previously domestic equity only portfolio. However, their point of view was from that of an American investor. The results reported here demonstrate that an UK investor needs to have a much larger portion of his equity portfolio allocated toward international investments.

Figure 2 is a graphic representation of the return and volatility data presented in Table 3. The further importance of international diversification becomes more evident when this figure is studied. It becomes obvious that portfolios with returns below 11.26 percent (i.e., that of the minimum volatility portfolio) are not on the efficient frontier, but rather are on the inefficient portion of the frontier. Of the portfolios reported in Table 3, only the two portfolios with returns of 11.26 and 12 percent are efficient. Both the 100 percent UK portfolio and the diversified portfolio producing 10.07 percent are actually inefficient portfolios (as are the portfolios with eight and six percent rates of return). To be invested in an efficient portfolio, Table 3 makes it clear that the UK investor could have no more than 16.67 percent of his portfolio assets invested in the UK market.

[FIGURE 2 OMITTED]

The frontier portfolio that returns 10.07 percent should be examined in contrast to the performance of the UK market. The UK investor could have earned that level of return by investing 100 percent of his assets in the UK market or by investing in the frontier portfolio that had only a 16.70 percent weighting for the UK component. The obvious difference between the two portfolios is the standard deviation of returns for each portfolio. The standard deviation for the UK-only portfolio is 21.75 percent, while the internationally diversified portfolio has a standard deviation of 14.87 percent. The internationally diversified portfolio that is located on the frontier offers the UK investor nearly a 1/3 reduction in volatility with no sacrifice in return.

However, UK investors may feel the need to maintain some certain minimum amount of investing in the home market. What would be the implications of such a course of action? Table 4 reports the results of fixing the minimum weighting of the UK component of the investor's portfolio at 20 percent. In this table only the portfolios with expected returns of 11.3 and 12 percent are on the efficient frontier. The other three portfolios are on the inefficient portion of the frontier. Tables 5, 6, and 7 report the results of setting the minimum weight of the UK portion of the portfolio at 40, 60 and 80 percent, respectively. Results here are consistent with the results presented in Table 4. It should also be noted that when the UK weighting is set at a minimum of 60 percent, it is not even possible to reach the efficient portion of the frontier and the 12 percent return. With the UK weighting set at a minimum of 80 percent, it is not possible to generate portfolios producing either the six or 12 percent expected returns.

CONCLUSION

Modern portfolio theory suggests that an UK investor's domestic portfolio should benefit by investing in other markets that are not perfectly correlated with the UK market. In this study we see that diversification reduces risk significantly as the UK investor makes the necessary allocation to foreign markets. While during the decade of the 1990s, US investors were not significantly rewarded for international diversification it held great potential of UK investors. They would have experienced significant reductions in risk coupled with no reductions in return. Data across this time period using the market indexes for the United Kingdom and its G-7 partners clearly supports 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 have been a potent tool for UK investors as has been suggested in much of the academic research. The risk reduction benefits of diversification were evident. Given this recent historical experience, the UK investor must recognize that there is sufficient reason (in terms of risk reduction) to pursue international diversification.

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 Kingdom 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 information that allows investors to make a more informed investment decision.

REFERENCES

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

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

Beckers S. (1999). Investments Implications of a Single European Capital Market. The Journal of Portfolio Management, 25 (3), 9-17.

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

Clarke, R.G., and Tullis, R.M. (1999). How Much Investment Exposure is Advantageous on a Domestic Portfolio? The Journal of Portfolio Management, 25 (2), 33-44.

Eakes, M., Grant, D., and Woodard, N. (2000). Realized Rates of Return in Emerging Equity Markets. The Journal of Portfolio Management, 26 (3), 41-49.

Erb, C.B., Harvey, C.R., and 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., and 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., and 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., and Le Fur, Y. (1996). International Market Correlation and Volatility. Financial Analysts Journal, 52 (5), 17-34.

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

Wahab, M., and 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 Standard Coefficient
 Geometric Deviation of Variation
 Mean Return of Returns

London 10.55 21.75 2.062
Toronto 5.08 19.06 3.752
S&P 500 14.79 16.04 1.085
Paris 9.85 20.51 2.082
Frankfurt 12.36 19.20 1.553
Milan 5.72 30.46 5.325
Tokyo -3.63 28.92 -7.967

TABLE 2: Correlation coefficients for returns between indexes

 London Toronto S&P 500 Paris

London 1
Toronto 0.4541 1
S&P 500 0.4808 0.7832 1
Paris 0.4781 0.5528 0.6556 1
Frank. 0.3986 0.5559 0.6035 0.7550
Milan 0.3630 0.4260 0.3923 0.4193
Tokyo 0.2859 0.3278 0.3658 0.3735

 Frank. Milan Tokyo

London
Toronto
S&P 500
Paris
Frank. 1
Milan 0.4409 1
Tokyo 0.2593 0.2738 1

Table 3: Frontier Portfolios with no constraints on weightings
All values stated as percentages

 Weight of each index
 Portfolios in frontier portfolios

Annual Annual Coefficient S&P 500 Toronto London
Return Standard of
 Deviation Variation

6.00 15.79 2.632 7.23 34.13 14.8
8.00 15.21 1.901 24.84 21.67 15.58
10.07 14.87 1.477 41.96 9.04 16.7
11.26 * 14.82 1.316 52.15 1.28 16.67
12.00 14.85 1.238 57.57 0 16.48

 Weight of each index in frontier portfolios

Annual Paris Frankfurt Milan Tokyo
Return

6.00 8.31 14.48 1.17 19.89
8.00 3.56 17.85 0.99 15.52
10.07 0 21.24 0.44 10.62
11.26 * 0 21.95 0 7.74
12.00 0 21.49 0 4.46

* Minimum standard deviation portfolio

Table 4

Frontier Portfolios with UK weighting set at a minimum of 20 percent
All values stated as percentages

 Weight of each index
 Portfolios in frontier portfolios

 Annual Coefficient S&P 500 Toronto London
Annual Standard of
Return Deviation Variation

 6.00 15.82 2.637 4.42 33.60 20
 8.00 15.23 1.904 22.16 21.52 20
10.07 14.89 1.479 40.45 8.43 20
11.30 * 14.83 1.312 50.91 0 20
12.00 14.87 1.239 55.71 0 20

 Weight of each index in frontier portfolios

Annual Paris Frankfurt Milan Tokyo
Return

 6.00 7.39 14.38 0.72 19.49
 8.00 2.44 18.26 0.53 15.09
10.07 0 20.62 0 10.50
11.30 * 0 21.40 0 7.69
12.00 0 20.47 0 3.82

* Minimum standard deviation portfolio

Table 5

Frontier Portfolios with UK weighting set at a minimum
of 40 percent All values stated as percentages

 Weight of each index
 Portfolios in frontier portfolios

Annual Annual Coefficient S&P 500 Toronto London
Return Standard of
 Deviation Variation

 6.00 16.48 2.747 0 30.65 40.00
 8.00 15.86 1.983 12.61 18.78 40.00
 10.07 15.52 1.541 30.57 5.02 40.00
11.06 * 15.47 1.399 38.54 0 40.00
 12.00 15.54 1.295 44.73 0 40.00

 Weight of each index in frontier portfolios

Annual Paris Frankfurt Milan Tokyo
Return

 6.00 0 9.94 0 19.41
 8.00 0 15.22 0 13.39
 10.07 0 15.94 0 8.47
11.06 * 0 16.08 0 5.38
 12.00 0 15.11 0 0.15

* Minimum standard deviation portfolio

Table 6
Frontier Portfolios with UK weighting set at a minimum of 60 percent
All values stated as percentages

 Weight of each index in
 Portfolios frontier portfolios

 Annual Annual Coefficient S&P 500 Toronto
 Return Standard of
 Deviation Variation

 6.00 18.12 3.02 0 16.54
 8.00 17.33 2.166 3.01 15.4
 10.07 17.01 1.689 20.52 1.73
 10.82 * 16.97 1.568 25.79 0
 12.00
([dagger])

 Weight of each index in frontier portfolios

 London Paris Frankfurt Milan Tokyo

 60.00 0 0 0 23.46
 60.00 0 10.20 0 11.40
 60.00 0 11.38 0 6.37
 60.00 0 11.00 0 3.03

* Minimum standard deviation portfolio

([dagger]) With the UK weighting set at a minimum of 60 percent, it is
impossible to generate a portfolio with a 12 percent
rate of return

Table 7
Frontier Portfolios with UK weighting set at a minimum of 80 percent
All values stated as percentages

 Weight of each index in
 Portfolios frontier portfolios

 Annual Annual Coefficient S&P 500 Toronto
 Return Standard of
 Deviation Variation

 6.00
([dagger])

 8.00 19.48 2.435 0 7.85

 10.07 19.14 1.901 10.03 0

 10.58 * 19.12 1.807 13.22 0

 12.00
([dagger])

 Weight of each index in frontier portfolios

 London Paris Frankfurt Milan Tokyo

 80 0 0 0 12.15

 80 0 6.44 0 3.53

 80 0 6.07 0 0.71

* Minimum standard deviation portfolio

([dagger]) With the UK weighting set at a minimum of 80 percent, it
is impossible to generate a portfolio with a 12 percent
rate of return

Figure 1

Value of 1,000 [pounds sterling] invested for ten years

London 2727
S&P 500 3974
Toronto 1642
Paris 2559
Frankfurt 3207
Milan 1745
Nikkei 691

Note: Table made from bar graph.