Tijdschrift voor Economie en Management Vol. XXXV, nr. 1, 1990 Gold and Portfolio Diversification by S. VANDELOISE and M. VOS de WAEL * When investors choose their portfolio composition, they face a tradeoff between risk and return. A risk-averse investor will try to minimize risk for a given return. Modern portfolio theory has specified the conditions necessary for diversification leading to a risk reduction. The less correlated the assets, the more advantageous the diversification and the risk reduction. In search of risk reduction, negatively correlated assets are highly attractive. It was found by Levy and Sarnat (1984), Levy (1981)~ that such assets are quite unusual between highly developed countries even on the international level. In this paper we examine whether or not gold can be such an asset. Traditionally it is advised to invest five to ten percent of a given portfolio in gold. This is probably not due to its return, because over the long run it does not perform as well as bonds and stocks. Modern portfolio theory can now justify this old practice. The inclusion of gold would improve the risk-return characteristics of a stock portfolio because of the low correlation between this asset and stocks. Kolb (1985) studied the desirability of gold as a part of a portfolio. He mentioned a study by A. and E. Renshaw (1982) who found a slightly negative correlation between the percentage changes in the end of the quarter price for gold bullion and the percentage changes in the quarterly closing prices for &P 500 industrial stock price index. Their observations cover the 1972-1980 period. For monthly changes in those two variables, their result is slightly different : the correlation coefficient became positive but remained close to zero. Molb concluded * Dkpartement d'economie, Universitk de Liege.
that "gold would be particularly useful as an addition to a stock portfolio, assuming that this correlation continues to be so low" (1985, p. 99). The aim of this paper is to test the attractiveness of gold for a Belgian investor. The problem is slightly different since the price of gold on the Belgian Stock Exchange is influenced, on the one hand, by London gold fixings and, on the other hand, by the exchange rate between the dollar and the Belgian franc. This paper investigates Belgian and -4merican investors' viewpoints. In Section 1, we study the correlations between gold and other assets over the 1972-1988 period. We also calculate the risk reduction due to the inclusion of gold in a portfolio. Section 2 presents the results obtained over three sub-periods. Conclusions are given in Section 3. II. GOLD AND OTHER ASSETS - THE 1972-1988 PERIOD Our study extends from January 31st, 1972 to December 31st, 1988. We used monthly data to compute percentage changes in the price of gold and common stocks3. Two types of gold investments are considered to be relevant for Belgium : gold bullion (GOLD) and a gold coin, more specifically the "Ancien Souverain" (SOUV). The purchase of gold coins is more feasible for small investors and it allows them to achieve exactly the desired proportion of gold in the portfolio. For investment in common stocks, we chose the Belgian stock index return adjusted for dividends. Furthermore we also considered investment in Belgian government bonds. For the US case, only one type of gold investment is taken into account : London gold fixing (FIXING). Investment in common stocks is represented by the S&P 500 industrial stock price return, also adjusted for dividends. Returns are calculated relative to the Belgian franc for Belgium and relative to the dollar for the U.S. An annual investment horizon is assumed. We calculated the correlation coefficients between investment in gold, stocks and bonds and obtained a number of results summarized in Table 1 for Belgium and in Table 2 for the U.S.
TABLE l Correlation matrix of returns for investments in gold, stock and bonds. Belgian investor's viewpoint. GOLD 0,1640 0,3629 SOUV 0,87*** 0,1544 0,3664 B.STOCK -0,ll -0,12 1,o 0,1414 0,1912 B.BOND 0,035-0,05-0,006 0,0989 0,0209 Returns are calculated relative to BF ***: significant at the level a= l%, **or=5%, *:a= 10% TABLE 2 Correlation matrix of returns for investments in gold and stocks. US investor's viewpoint. FIXING U.STOCK Mean Stand.dev. FIXING l@ 0,1940 0,4070 U.STOCK -0,09 1,00 0,1187 0,1741 Returns calculated relative to the dollar ***: significant at the level a=l%, **:a=5%, *:a= 10% For Belgian investors, the variations of gold price are negatively correlated with the stock exchange index return. The results are, however, only significant at the 15% level. Notice also that from a Belgian viewpoint, the correlation between bonds and the other assets is not significantly different from zero,which is also interesting in a diversification perspective. Concerning the correlation between returns on investments in gold and stocks, the same conclusion is reached for the American investor as presented in Table 2. From the American viewpoint the evolution of the dollar does not have a direct influence on the price of gold. Notice that gold is not the only asset whose correlation with stocks is negative or very weak. Silver and oil also present similar characteristics (Solnik (1988)). If the correlation between gold and other investments continue to be negative or close to zero, the addition of gold to a portfolio is strongly advised to reduce portfolio risk. What was the proportion to be invested in gold? Using ex-post data4, the Assetall program5 was applied to derive various efficient portfolios. In Table 3 are listed several portfolio possibilities which seem feasible ; the proportion in-
vested in gold ranges from 3,6% to 19,24%. To be more realistic we have excluded short sales. Remember that this implies that proportions of any asset in the portfolio cannot exceed 100%. Moreover investment is restricted to three kinds of assets : stocks, gold and bonds. This table shows the sensitivity of the portfolio composition to the mean return. As mean returns increase the proportions invested in gold and stocks increase whereas the proportion invested in bonds decreases. Notice the resulting sharp rise in the portfolio risk. TABLE 3 Composition of efficient portfolios given a mean return. Belgian investor's viewpoint Portfolio return Proportions (in To) Mean (in %) Stand. Dev. Gold B.Bond B~tock (in %) 10,50 2,75 3,60 87,56 8,84 11,OO 4,04 6,73 77,45 15,82 11,50 5,53 9,85 67,36 22,79 12,OO 7,lO 12,98 57,26 29,76 12,50 8,70 16,ll 47,16 36,73 13,W 10,33 19,24 37,06 43,70 A more pertinent way to illustrate the advantage of gold is to compute the risk reduction implied by the inclusion of gold. We have chosen the mean return of the Belgian Stock Exchange index as the return aim of the Belgian investor. It is equal to 14,14%. The standard deviation of the portfolio decreases from 0,1912 to 0,1406 when the portfolio is diversified to include also bonds and gold (the corresponding optimal proportions are 26% for gold, 14% for bonds and 60% for stocks). Thus diversification between the three types of assets implies a risk reduction of 26,5070. This substantial cut is not surprising because of the slightly negative correlation between gold and stocks. In summary, over the 1972-1988 period, correlations between stocks and gold have been negative for both types of investors9 viewpoint. The fact that for Belgium, gold price depends not only on the London gold fixing but also on the exchange rate of the dollar did not lead us to a different conclusion between both viewpoints.
FIGURE 1 Gold prices : London and Brussels 11. ANALYSIS OF SUB-PERIODS The full-sample period has been divided into different sub-periods to see whether the conclusions of the preceding section are invalidated or not. The 1972-1988 period could be meaningfully subdivided into periods with different characteristics. First, the London gold fixing was highly unstable. Secolid the dollar witnessed large fluctuations. Finally the internationalization of Stock Exchanges has increased dramatically. We will examine the influence of those characteristics on the correlation between gold and stocks. Figure 1 shows the evolution of the gold price on the Stock Exchanges of Brussels and London. The influence of the dollar is obvious especially from July 1980. The 1972-1988 period has been split into three parts6: - the January 1972 - July 1980 sub-period characterized by the dollar depreciation7. The London gold fixing was then in a rising phase. - the second sub-period begins in August 1980 and ends in March 1985, and corresponds to the recovery of the dollar. Meanwhile the gold price was in a bearish tendency. - the last sub-period extends from April 1985 to December 1988. It
FIGURE 2 BF/Dollar exchange rate 2 0 L " ' ~ 1 ~ ' " 1 " " ~ ' ~ 1972 ign 1982 1987 Years - BFMolhr FIGURE 3 Evolution of Belgian and US stock returns 1973 1978 1983 1988 U.Stock Years - B.Stock
includes the great depreciation of the dollar whereas the gold price was characterized by a rising trend. Table 4 presents, for each sub-period, the correlation coefficients between gold and stock from either the Belgian or the American viewpoints. It also shows correlation coefficients between American and Belgian Stock Exchange indexes and, finally,between gold prices as quoted on the Stock Exchanges of Brussels and London. TABLE 4 Correlation coefficients between returns on different investments and mean returns. Division into three sub-periods Correlation Jan. 72- Aug. 80- April 85- July 80 March 85 Dec. 88 ~old/~.~tock~ 0,218** 0,032-0,326** Fixing/U.Stock -0,241** 0,599*** 0,476*** B.Stock/U.Stock 0,533*** 0,135 0,766*** Gold/Fixing 0,905*** 0,853*** 0,472*** Mean returnsg Gold 0,3281 0,0779-0,0605 Fixing 0,3985-0,0453 0,0781 BStock 0,0588 0,2008 0,2347 UStock 0,0577 0,1589 0,1921 ***: significant at the level a= l%, **:a=5%, *:a= 10% For the 1972-1980 sub-period, the correlation coefficient between stocks and gold is positive for the Belgian investor whereas it is negative for his American counterpart. Thus investors from any country characterized by a stable exchange rate with the American currency would have been favoured when searching for an asset negatively correlated with stocks. As demonstrated by Figure 1 and Table 4, the gold prices on the two Stock Exchanges were strongly correlated : the impact of the BF/$ rate was weak. Thus the explanation of the opposite correlations (gold and stocks) between both viewpoints results essentially from a divergent stock indexes evolution as it appears on Figure 3. Notice that for Belgian non-risk averse investor, the gold return alone was highly attractive and gold could have been included in a portfolio despite its positive correlation.
During the second sub-period (1980-1985), the correlation coefficient is positive and different from zero at the 1 % level for the American investor and close to zero for the Belgian investor. The difference between the correlation coefficients is due to independent stock returns. Despite the appreciation of the dollar (which could counterbalance the bearish tendency of gold prices expressed in dollars), gold prices on the Brussels Stock Exchange (BF) still move closely with gold prices expressed in dollars. Therefore from the perspective of diversification, investors from the Brussels Stock Exchange were slightly favoured. Furthermore, from the viewpoint of the return, the Belgian investor had also an advantage when contrasted to his American counterpart since the mean return for gold was negative for the latter. During the 1985-1988 sub-period, the correlation coefficient between goid and stocks was negative from the Beigian viewpoint and positive from the American one. The advantage given by the negative coefficient to the Belgian investor is achieved at the expense of the negative mean return of gold on the Brussels Stock Exchange contrary to London. Gold prices as quoted in London and Brussels are much less correlated (0,472) during this last sub-period than during the previous ones. A rapid and severe depreciation of the dollar explains the divergent evolution of the correlations. The dollar depreciation offsets more than proportionally the increase of gold price in London and this results in a decreasing trend for gold in Brussels. Internationalization between stock exchanges results in a higher correlation between American and Belgian stock indexes. 111. CONCLUSIONS Over the 1972-1988 period the traditional strategy of including gold in the portfolio has been greatly justified by modern portfolio theory because the correlation between this asset and stocks was slightly negative or close to zero. Therefore the inclusion of gold in a portfolio leads to a risk reduction. This is true not only for the American investor but also for the Belgian investor although gold prices on the Brussels Stock Exchange depend not only on the London gold fixing but also on the dollar/bf exchange rate. Moreover, the division into sub-periods based on different criteria1' allows one to conclude that investors whose currency was highly correlated with the dollar did not have a systematic advantage
or disadvantage for a gold investment. Both the first and the last corresponding sub-periods are characterized by a depreciating dollar and by increasing prices at the London gold fixing. However the sign of the correlation coefficient between gold and stocks changed from one period to the other. Since August 1980, the large fluctuations of the dollar have led to a divergent evolution of the gold price on the London and Brussels Stock Exchanges : in contrast with the London Stock Exchange, the Brussels Stock Exchange offered a nil lor even a negative correlation coefficient over the last two sub-periods but, when negative, it was at the expense of a negative return which is not interesting for investors. In the future, the financial internationalization of the Stock Exchanges will result in stocks tending to move more and more together. TL ---c--- &L -&: -- ---cc: :--Am -----A:- I IICI CIVI C LII~ LUI I C~QLIUII LUCIIICICIILS QLLUI UIII~ io American and Be:- gian viewpoints could have opposite signs if both following conditions are fulfilled : first, a divergent movement between the London gold fixing and the dollar exchange rate and second, a more than proportional balancing of the fluctuations in the price of the dollar relative to changes in the gold price at the London fixing. APPENDIX Variables Percentage changes in gold price on the Belgian Stock Exchange Percentage changes in the price of the "Souverain ancien" Belgian Stock Index return (Adjusted for dividends) Return of Belgian Government bonds Percentage changes in London gold fixings S&P 500 Industrial stock price index return (Adjusted for dividends) Name GOLD SOUV B.STOCK B.BOND FIXING U.STOCK Source DRI Newspaper (Echo de la Bourse) OECD Financial Statistics DRI IMF International Statistics OECD Financial Statistics NOTES 1. The authors would like to thank Professor A. Minguet and an anonymous referee for helpful comments and suggestions. 2. Since 1970 correlation coefficients between indexes of highly developed countries have been mainly positive. Negative correlation coefficients can be reached between e.g. Brazil and most developed countries. However less developed countries are usually characterized by political risk.
3. All the variables and sources are presented in appendix. 4. Our results are of course sample dependent. However the use of ex-post data should not be a problem in this case since our conclusion relies principally on the correlation coefficients and, correlations and efficient sets have been shown to be more stable over time (Levy & Lerman 1988, Jorion 1985). Therefore we think that our conclusion could be applied to the future. 5. The Assetall program is a quadratic program by R. Radcliffe and allows to derive efficient portfolios with and without short sales. 6. We divided the total period into sub-periods according to other criteria as the evolution of the gold price and of the Stock Exchange. The resu!ts do not alter our conclusions obtained with the analysis based on the dollar evolution. 7. See Figure 2 for the BF/dollar exchange rate evolution and Figure 3 for the evolution of Belgian and US stock returns. 8. Gold : gold bullion quoted on the Brussels Stock Exchange, whose price depends on the London gold fixing (Fixing) and on the BF/$ exchange rate. 9. Returns are calculated relative to the BF for Gold andb.stock, and relative to the dollar for Fixing and U.Stock. 10. See Note 6. REFERENCES Jorion P., 1985, International Portfolio Diversification with Estimation Risk, Journal of Business. Kolb R., 1985, Understanding Futures Markets, (Scott, Foresman & Company). Levy H., 1981, Optimal Portfolio of Foreign Currencies with Borrowing and Lending, Journal of Money, Credit and Banking, 325-342. Levy H. & Lerman Z., 1988, The Benefits of International Diversification in Bonds, Financial Analyst Journal, 56-64. Levy H. & Sarnat M., 1984, International diversification in Portfolio and Investment Selection : Theory and Practice,629-664. Markowitz H., 1952, Portfolio Selection, Journal of Finance 7, 77-91. -, 1987, Mean-Variance Analysis in Portfolio Choice and Capital Markets, (Blackwell, New-York.) Renshaw A. and E., 1982, Does Gold Have a Role in Investment Portfolios?, The Journal of Portfolio Management, 28-31. Sherman E., 1982, Gold : a Conservative Prudent Diversifier, The Journal of Portfolio Management, 21-27. Solnik B., 1988, Gold and Gold-Linked Investments, in International Investments, (Addison Wesley).