Commodity futures investing and commodity currency countries

Transcription

1 Commodity futures investing and commodity currency countries Abstract In this paper, we investigate whether investors in commodity currency countries (CCCs) benefit in terms of diversification by investing in commodity futures while they are already investing in their domestic equities. We find that commodities futures are risk diversifiers, irrespective of whether investors invest in them in their own market or through foreign markets. If they invest in commodities in their own market, they obtain diversification benefit even though their equity investment is already heavily exposed to commodities. However, if they invest through overseas markets, currency hedging is not necessarily beneficial for investors of all CCCs in terms of diversification. 1. Introduction As a result of global economic integration, diversification opportunities available to investors are declining, as financial market correlations are increasing (Errunza et al., 1999). Changes in diversification opportunities have caused investors to look into alternative asset classes such as commodities. However, commodities may not provide the same diversification opportunities for investors in different countries. Specifically, investors in commodity currency countries (CCCs) where commodities constitute a significant share of their exports may not obtain any diversification benefit from commodity investing if they already invest in their home equity market, which is substantially populated by commodity-producing firms. In this paper, we address whether these investors may obtain additional diversification opportunities by investing in commodity futures explicitly. We concentrate on Canada, Australia, and New Zealand as the CCCs for this study. While in prior studies individual commodities such as precious metals have been studied for investment purposes (consider Jaffe, 1989; Erb and Harvey, 2006; Hillier et al., 2006, and 1

2 references therein), commodity futures have been used more extensively in analyzing the role of commodities in mixed portfolios, which we consider in this paper. Two major factors that affect the preference for commodities are the diversification opportunities and the hedge against inflation they provide. Their low correlations with security returns have been documented by Bodie and Rosansky (1980), Elton et al. (1987), Edwards and Park (1996), and Erb and Harvey (2006), among others. Bessembinder and Chan (1992) and Bjornson and Carter (1997) find evidence that the returns on commodity futures are significantly related to business conditions, suggesting that commodities can counter the effects of business cycles. Moreover, Bjornson and Carter contend that having commodities in a portfolio may work as a hedge against inflation. Bodie (1983) finds that commodity futures tend to perform well when inflation is high. Jensen et al. (2002) and Gorton and Rouwenhorst (2004) also document the inflation hedging properties of commodities. The argument is that commodity futures prices represent the values of the raw commodities used to produce consumer goods. Taking a long position in these, therefore, allows one to profit from increases in their prices. As commodity prices increase during an inflationary period, long positions in commodity futures benefit, while security returns suffer. Using US equity and future index returns, however, Chance (1994) claims that the equity and commodity return correlations are considerably unstable. In fact, the correlations are quite large and positive for some extended periods and negative for other extended periods. Considering commodities as a stand-alone asset class, Jensen et al. (2000) conclude that they are a poor investment given their relatively low return and high volatility. In addition, Jensen et al. (2000) examine the performance of commodities in a mixed portfolio under alternative monetary regimes. They conclude that during restrictive monetary policy regimes, commodity futures have 2

3 substantial weight in the efficient portfolios. In contrast, under expansive monetary policy regimes, commodity futures have little or no weight in the efficient portfolios. More recent studies also document mixed results (Vrugt et al., 2004; Erb and Harvey, However, in general it can be concluded that some level of overall portfolio risk can be reduced with less than proportional return sacrificed by using commodities. Interest in commodities is expected to continue due to their scarcity and the demand from developing countries. Most of the existing studies mainly analyze commodity futures investments in the context of non-cccs such as the US, the UK, and Japan. In this paper, we fill a void by explicitly analyzing commodity futures investment from the perspective of commodity currency countries investors. Following Chen and Rogoff (2003) and Chaban (2009), we use Canada, Australia, and New Zealand. Interestingly, using these specific countries renders additional benefits in our analysis, since their commodity exports are not the same. This allows us to assess clearly the diversification opportunities for these countries given their commodity resources and asset markets. Using monthly data on commodity futures indices from 1992:06 to 2007:06, we test whether commodity futures provide diversification opportunities for the commodity currency countries investors. Through these tests, we assess whether investors in these countries can benefit by investing in commodities, even if they are already invested in the local stock and bond markets. We conduct the analysis in a mixed asset portfolio context. That is, we use stock, bond and commodities as distinct asset classes. Our conclusion is affirmative. However, the types of commodity futures used and the exchange rates can have significant bearing on the 3

4 diversification benefit. That is, the benefits obtained are dependent on how the investment is made. For the general analysis, we consider the investable commodity futures indices available in the US. We also use local commodity indices for comparison, and this does not change our conclusion qualitatively. The remainder of the paper is organized as follows. In the next section we describe the methodology, which is followed by the data section. Section 4 contains the results, and section 5 offers conclusions. 2. Methodology The research question we want to address is whether commodity futures provide diversification opportunities for commodity currency countries investors. To reach our conclusion, we employ several methodologies. However, before moving on to the specific methodologies, some detail on the return generation process from the futures is in order. We consider mixed portfolios, where investors invest in local equity and bond indices denominated in local currency, and in commodity futures denominated in foreign currency ($US). For the commodity futures, we consider investable commodity futures from the US market for investors in Canada, Australia, and New Zealand. The local currency return, R L, from the commodity investment is generated as a composite return: part of it comes from the futures investment (R $US ) denominated in US dollars and the remainder from the changes in the US dollar against the local currency, % $ US. In short, a non-us investor investing in US commodity futures invests not only in the commodity futures, but also, indirectly, in US dollars. The net local currency return is: 4

5 -1 (1) This requires us to distinguish the part of the return that is due to the performance of futures and that due to appreciation or depreciation of the US dollar. Following Eun and Resnick (1988), we estimate hedged return, R LH, as well as unhedged return, R LUH, using the following approximations. 1 R R$ US % US ; (2) LUH $ R LH R US f$ US $, (3) where f $ US is the forward premium for the US dollar. We use both types of returns for our analysis. In addition, to further assess the commodity diversification opportunities, we also report results based on local commodity price indices. However, these are not investable. We use mean-variance methodology (Markowitz (1952)) as well as spanning tests (Huberman and Kandel (1987). 2 We describe each methodology in brief below Mean-variance analysis The standard mean-variance optimization problem is formulated as follows min W ΣWsubject tow 1 1, (4) 1 Following Eun and Resnick (1988), we do not take into account the cost of hedging. Moreover, as shown later in the paper, hedging is not value enhancing for all investors. Hence, including the transaction cost will simply strengthen the argument against hedging. 2 De Roon and Nijman (2001) provide an excellent survey of spanning tests. However, Kan and Zhou (2008) provide a more recent overview on this topic. Also, for some recent applications, consider Eun et al. (2008) and Moerman (2008). 5

6 where W is a column vector of portfolio weights of different assets, is the variance-covariance matrix of the assets, and 1 is a column vector of ones of comparable dimension. The optimal portfolio is the solution to this problem. In order to avoid having to specify the target returns, which is more a task for the investors, we focus on constructing the global minimum-variance portfolio (GMVP). As our goal is to examine the gains from diversification obtained by taking into account the commodity futures, GMVP is sufficient to meet our need. The global minimum variance portfolio s asset allocation weights (W GMVP ) are given by the following 1 W GMVP 1 Σ 1. (5) 1 Σ Mean-variance spanning test The procedure proposed by Huberman and Kandel (1987) assesses whether an addition of new assets (test assets) can (statistically) significantly improve the efficient frontiers of the existing set of assets (benchmark assets). This test can be conducted under a regression framework. For our purpose the test asset is commodity futures and the benchmark assets include the local stocks and bonds. Then our regression equation is n R Lt R i 1 i it t, (6) where R Lt is the return from the test asset and Rit is the return from the benchmark asset i, for period t. We test the following hypothesis jointly: H n 0 0 and i 1. i 1 : (7) 6

7 The rejection of this null hypothesis indicates the existence of diversification benefits of the test asset, which in our case is the commodity futures. 3. Data We use MSCI benchmark country equity indices for Australia, Canada, and New Zealand as well as for the US. We include the US for comparability, since it is a non-commodity currency country. The bond indices are total return indices for all maturity bonds from the Citigroup database. All of these indices are denominated in local currencies. We consider several futures indices. For our main analysis, we use the S&P-GSCI (formerly the Goldman Sachs Commodity Index) total return index. Given that in the literature, GSCI is used extensively (see Chance, 1994; Jensen et al., 2000, 2002; Vrugt et al., 2004, and references therein), we use GSCI for our general analysis. In addition, because of the variations in the compositions of different commodity indices and their investment potential, we also consider the Dow Jones-UBS Commodities Index (formerly the DJAIG Commodities Index) and the Commodity Research Bureau Index (CRBI). Due to data limitations, for the latter indices, we use the spot indices as opposed to total return indices. However, our results should not suffer from this limitation. 3 Moreover, to provide support, we also consider the spot index for S&P-GSCI. From here on S&P-GSCI is denoted as GSCI. All the commodity indices are denominated in US dollars. Returns are estimated using log differences of corresponding indices. Changes in the US dollar against respective local currencies and forward premiums are calculated from exchangerate and forward-rate data series for the given countries. All data series along with the spot- and forward-rate data are from DataStream. We use monthly data from 1992:06 to 2007:06. 3 We elaborate on it later on in section

8 To test the robustness of our conclusions, we also conduct a spanning test using local commodity indices, and report it at the end of the results section. Following Chaban (2008), we obtain the total commodities price indices for Canada and Australia from their central banks. The index data for New Zealand are from Australia and New Zealand Banking Group Limited. Except for Canada, these indices are denominated in local currencies. For Canada, US dollars are used. To address this difference, for this part of our analysis, we convert the Canadian bond and equity indices to the US dollar equivalent and estimate the returns. 4. Results For the general analysis, we use the GSCI total index returns (GSCItot), and respective equity and bond indices for individual countries. We first present the general analysis. Then we present an analysis using other investable commodities indices. All results are from the perspective of investors of each individual country, and return estimations are in local currencies. Finally, we report results pertaining to the local commodity indices for the individual countries General analysis using GSCI total return index Table 1 reports the summary statistics. In general, bond investments are the least risky and commodity futures investments are the most risky, even after hedging (on the GSCI futures) is taken into account. The best performance of bond and equities is from Canada (0.84% and 0.60%, per month respectively). However, whereas the US and Australian equity performances (0.71% and 0.75%, per month) are comparable, equity performance for New Zealand is poor (0.38%, per month). For the Kiwi state, the bond market performed better (0.57%, per month). 8

9 In addition, hedging for the commodity returns does not have the same impact for all the countries. [Insert Table 1 here] To get some insight into these findings, we consider the correlation values in Table 2. One interesting observation emerges for all the commodity currency countries, as well as for the US: the correlation between the stock returns and the bond returns is negative. For the time period we are covering, we find the correlations to be substantially negative ( , , , and , for the US, Canada, Australia, and New Zealand, respectively). This decoupling of stocks and bonds is significant and unusual. According to Dopfel (2003), even with variability, the correlation has historically been moderately positive (around +.19 for the US market). More recently, Campbell et al. (2009) report that the covariance between US Treasury bond returns and stock returns has moved considerably over time. It was slightly positive on average in the period and was particularly high in the early 1980s and negative in the early 2000s. The presence of the negative correlation in our data creates a strong preference for bonds. Consequently, this may lead to the rejection of the hypothesis that commodity futures investing provides diversification opportunity. However, if within this context commodity futures are found to provide diversification benefits that would bring robustness to our results. 4 [Insert Table 2 here] 4 For detail on the potential explanations for the negative correlation, also consider Li (2002) and Krishnan et al. (2007). 9

10 Next, we consider the correlations between equity returns and commodity returns. Theoretically, superior stock market performance is indicative of a higher level of economic activity, and consequently higher demand for commodities. Commodity currency countries equity market performance should reflect the performance of their commodity-producing firms, leading to a positive correlation between equity and commodity return performance. We find that for the US (which is not a commodity currency country), equity returns are positively correlated with the commodity (i.e., GSCI) returns (correlation of ). However, the correlation is relatively weak. On the contrary, for Canada and Australia, equity markets are more strongly correlated with the GSCI return (correlations of and , respectively). For New Zealand, the correlation is close to zero ( ). The strong correlation between the Canadian market and the GSCI return is due to the fact that the GSCI index is heavily weighted in energy (Table 3 contains the weightings of different commodities subgroups). In addition, Canada and Australia are exporters of industrial metals and precious metals, which have substantial weights in the index as well. However, New Zealand does not have any of these commodities as their exports, and this is reflected in the low correlation. Clearly, commodity index composition has significant bearing on diversification opportunities, which we explore in more detail in the next section using other commodity indices. [Insert Table 3 here] When demand for commodities increases, currencies of CCCs are expected to be in demand as well, causing the US dollar to depreciate against these currencies. Therefore, we should 10

11 expect to observe negative correlations between commodity returns (as measured in US dollars) and changes in the value of the US dollar against local currencies, that the correlation between the commodity returns (GSCItot) and % $ US. Our results show % $ US is negative for all the countries ( for Canada, for Australia and for New Zealand). As a result of these negative correlations, investors who choose not to hedge exchange-rate risk will receive local-currency returns (GSCIUH) that are lower than they would get if they hedge the exchangerate risk using forward contracts (GSCIH), as shown in Table 1. However, hedging increases the correlation between local equity market and commodity returns, thus reducing the diversification benefits the investor would receive if the investment is not hedged. For Canada the correlation increases from to , for Australia to , and for New Zealand to All of these observations have significant bearing on the asset allocation, which we consider next. Table 4 presents the allocation for the global minimum variance portfolio (GMVP). For all countries, two-asset portfolios consisting of stocks and bonds are compared with three-asset portfolios, which include commodity futures along with stocks and bonds. By looking at the Coefficient of Variations (CVs) of these portfolios, it is evident that commodity futures have diversification benefit. However, the allocations to the commodity futures are the lowest, ranging from 2.3% to 5% depending on the country. The highest allocations are for bonds. Given the low risk level of bonds and the unusual negative correlation between stocks and bonds, as discussed earlier, allocation to bonds is in the 80% range for all countries. For commodity currency countries, hedged and unhedged GMVPs do not differ substantially. Still, the CVs appear to suggest that Canadian investors are better off without hedging, while investors in 11

12 Australia and New Zealand are better off with hedging. It should be recognized that the low allocation to commodities is due to the construction of the portfolio. If the portfolio is set up for large target return, the allocation to commodities will be larger. In addition, the allocation is substantially affected by the period being considered, when the risk and return profile of bonds were substantially favorable. [Insert Table 4 here] Panel A of Table 5 reports the results of the spanning tests. For the US and Canada, both F and Wald tests reject the null hypothesis, leading to the conclusion that commodity futures have diversification value for US and Canadian investors. However, it is not rejected for Australia even at the 10% level. Mixed results are obtained for New Zealand. For the unhedged portfolio the null is rejected at the 5% level; however, it is not rejected even at the 10% level for the hedged portfolio. We explore this mixed result further in the next section. For brevity, we only discuss the spanning tests in the remaining sections. [Insert Table 5 here] 4.2. Spanning test with different spot futures index returns Here we consider other commodity futures indices, the Dow Jones-UBS Commodities Index (DJI), and the Commodity Research Bureau Index (CRBI), along with the GSCI. Due to data limitations, we use the spot index returns. However, conclusions made using these indices should not differ qualitatively relative to the conclusions that might be made using total return indices, as the correlations between these two types of indices are usually strong. For example, 12

13 the total return GSCI that we used in our general analysis earlier has a correlation of with its spot version (see Table 6). [Insert Table 6 here] Performances of commodity indices are substantially affected by their constituents and their weights (see the weights in Table 3). The GSCI is most heavily weighted in energy, which is an important export item of Canada. The DJI, with higher weights on energy, grains and seeds, and industrial metals, is much more representative of the exports of Canada and Australia. The index also puts a reasonable amount of weight on livestock and meat, which is a major category of exports of New Zealand. In contrast, the weighting for the CRBI is much more even for most of the commodities. However, it also places a substantial weight on soft commodities (e.g., coffee, sugar, and cotton). In general, the GSCI is the most concentrated and the CRBI the most uniform in terms of weighting. The correlations among the returns from these indices, local bonds and stock indices, and changes in the US dollar against the respective currencies are presented in Table 6. For all local equity markets, the correlations with DJI are higher than with the other two indices. This indicates that DJI is more representative of the exports of all commodity currency countries. This is especially true for Canada (correlation of ) and Australia (0.1386). In contrast, this is not the case with the CRBI. The correlations are much lower for Canada (0.0773) and even negative for Australia ( ). As noted earlier, this index does not represent the exports of these two countries as heavily as the other two indices do. It is a different case for New Zealand. Live stocks and meat and soft commodities such as wool are its main exports. Since the CRBI 13

14 has higher weights on these commodities, it is no surprise that New Zealand s equity market is most positively correlated with it. Panel B and Panel C of Table 5 present the results of the spanning tests. For the DJI, for all countries except for Australia, the null hypothesis is rejected at the 1% level ( for both hedged and unhedged cases). For Australia, the hypothesis is rejected at the 1% level for the hedged case and at the 5% level for the unhedged case. Panel C presents results for the CRBI. The null hypothesis is rejected for all the countries at the 1% level. The results from both indices indicate that commodity index futures have diversification value for all local investors. A couple of observations are in order for the relative improvements observed when DJI and CRBI are used. First, from Table 6, the correlation of bond returns with either DJI or CRBI returns is lower than with GSCI returns. Second, due to its more even weighting, the CRBI is less correlated with Canadian and Australian equities markets than are the other two indices. Both observations have significant bearing on the observed increases in the diversification contribution of both the DJI and CRBI, as can be noted by the improvement in test statistics. Also, when commodities do better, CCCs should see appreciation of their currencies against the US dollar. We find this to be the case in our analysis, with the DJI having the highest (among the three indices) negative correlation with the changes in the value of the US dollar. In summary, using the information in the previous section and this section, we can conclude that the diversification benefits that investors in CCCs can obtain from investable commodity futures available in the US market depend on a few factors: 1) the kind of commodity futures being used; 2) the exchange-rate movements against the US dollar; and 3) other assets in the investors portfolios. In some cases, investors may obtain benefits by investing in commodity 14

15 futures that are closely related to their commodity exports. The value generator in this case is the interaction of exchange rates with the futures returns, which is the case with Canadian and Australian investors investing in DJI. In other cases, investors may benefit by investing in commodity futures that are more heavily weighted in commodities that they do not export, such as the case of investors in New Zealand investing in the GSCI. Even though our analysis ignored hedging cost, our results indicate that the value of currency hedging is at best mixed. This conclusion is comparable to the existing findings. For example, in assessing US investors' performance from international diversification, Levy and Lim (1994) find that almost all the unhedged strategies outperformed the hedged strategies for , while the opposite held for They explain these by the biasedness of forward rates in predicting future spot rates. Using data for Canada, Germany, Japan, Switzerland, and the United Kingdom, Morey and Simpson (2001) find that an unhedged strategy performs better than a hedged strategy in general Spanning test using local commodity index returns Gorton and Rouwenhorst (2006) find that commodity futures and the stocks of commodityproducing companies are not perfectly correlated. This potentially implies that equity markets of the CCCs need not be strongly correlated with the commodity markets. If that is the case, it would be indicative of the availability of diversification opportunity. Here we explore this potential in a slightly different manner than the tradition. We generate return data for commodity futures by using local commodity price indices of Canada, Australia, and New Zealand. The advantage of this approach is that these indices are reflective of the major commodities that these individual countries export. In addition, there is no issue of exchange 15

16 rate involved, which sometimes makes it difficult to ascertain the pure diversification benefit that may be obtained by investing in commodities. Even though these are not investable indices, we get a qualitative sense of diversification opportunity. [Insert Table 7 here] The results of the spanning tests are presented in Table 7. 5 For all of the countries, both the F and Wald tests reject the null hypothesis at the 1% level. This indicates that even if the equity market is heavily populated by the commodity-producing companies, investing in commodities and the equity market simultaneously creates value in terms of diversification for local investors in the commodity-producing countries. 5. Conclusions In this paper, we explore whether investors from commodity currency countries (CCCs) who are already invested in their domestic equity markets, which are heavily weighted in commodityproducing companies, obtain additional diversification from investing in commodity futures indices. For this purpose, we analyze mixed asset portfolios involving local equities, bonds and investable US commodity futures, from the perspective of investors in Canada, Australia, and New Zealand. We find that these investors may find some diversification benefits by investing in US commodity futures based on S&P-Goldman Sachs Commodity Index, Dow Jones-UBS Commodities Index, and Commodity Research Bureau Index. Different contracts are preferable for investors from different countries due to their constituents and constituents weights. However, as is the case with any international investment, the fluctuations in the exchange rate of each country against the US dollar play a key role. Considering unhedged as well as hedged 5 For Canada the local commodity price index is available in US dollars. We made the necessary currency adjustment for stock and bond indices to make the results consistent. 16

17 investment in commodity futures, we do not find any clear advantage in favor of hedging for investors of all countries in terms of diversification. Hedging exchange rate exposure makes the foreign returns from the commodity investment much more correlated to the CCCs equity markets, reducing the diversification benefit that it may produce. Acknowledgement We would like the thank Sobey School of Business and Saint Mary s University for valuable support and resources. References Bessembinder, K., Chan, K., Time-varying risk premia and forecastable returns in futures markets. Journal of Financial Economics 32, Bjornson, B., Carter, C. A., New Evidence on Agricultural Commodity Return Performance under Time Varying Risk. Journal of Agricultural Economics 79 (3), Bodie, Z., Commodity Futures as a Hedge against Inflation. Journal of Portfolio Management Spring, Bodie, Z., Rosansky, V. I., Risk and Return in Commodity Futures. Financial Analysts Journal 36 (3), Campbell, J.Y., Sunderam, A., Viceira, L.M., Inflation Bets or Deflation Hedges? The Changing Risks of Nominal Bonds. Harvard Business School Working Paper no. 09/088. Boston, MA. Chaban, M., Commodity Currencies and Equity Flows. Journal of International Money and Finance 28, Chance, D., 1994, Managed Futures and Their Role in Investment Portfolios. The Research Foundation of the Institute of Chartered Financial Analysts, Charlottesville, VA. Chen, Y., Rogoff, K., Commodity Currencies. Journal of International Economics 60 (1), De Roon, F.A., Nijman, T.E., Testing for Mean Variance Spanning: A Survey. Journal of Empirical Finance 8,

18 Dopfel, F.E, Asset Allocation in a Lower Stock-Bond Correlation Environment. Journal of Portfolio Management Fall, Edward, F. R., Park, J. M., Do Managed Futures Make Good Investments? Journal of Futures Markets 16 (5), Elton, E. J., Gruber, M. J., Rentzler, J.C., Professionally Managed, Publicly Traded Commodity Funds. Journal of Business 60 (2), Erb, C.B., Harvey, C. R., The Strategic and Tactical Value of Commodity Futures. Financial Analysts Journal 62, Errunza, V., Hogan, K., Hung, M., Can the Gains from International Diversification Be Achieved without Trading Abroad? Journal of Finance 54 (6), Eun, C.S., Resnick, B.G., Exchange Rate Uncertainty, Forward Contracts, and International Portfolio Selection. The Journal of Finance 43 (1), Eun, C.S., Lai, S., Huang, W., 2008, International Diversification with Large- and Small-cap Stocks. Journal of Financial and Quantitative Analysis 43 (2), Gorton, G., Rouwenhorst, K. G., Facts and Fantasies about Commodity Futures. Financial Analysts Journal 62, Hillier, D., Draper, P., Faff, R., Do Precious Metals Shine? An Investment Perspective. Financial Analysts Journal 62, Huberman, S.L., Kandel, S., Mean variance spanning. Journal of Finance 42, Jaffe, J. F., Gold and Gold Stocks as Investments for Institutional Portfolios. Financial Analysts Journal 49, Jensen, G. R., Johnson, R. R., Mercer, J.M., Efficient Use of Commodity Futures in Diversified Portfolios. Journal of Futures Markets 20 (5), Jensen, G. R., Johnson, R. R., Mercer, J.M., Tactical Asset Allocation and Commodity Futures, Journal of Portfolio Management Summer, Kan, R., G. Zhou Tests of Mean-Variance Spanning. Unpublished Working Paper. Rotman School of Management. Toronto, ON, Canada. Krishnan, C. N. V., Petcova, R., Ritchken, P., Correlation Risk. Unpublished Working Paper. Weatherhead School of Management, Case Western Reserve University. Cleveland, OH. 18

19 Levy, H., Lim, K.C., Forward Exchange Bias, Hedging and the Gains from International Diversification of Investment Portfolios. Journal of International Money and Finance 13 (2), Li, L., Macroeconomic Factors and the Correlation of Stock and Bond Returns. Unpublished Working Paper. Yale University, New Haven, CT. Markowitz, H.M., Portfolio selection. Journal of Finance 7, Moerman, G.A.,2008. Diversification in Euro Area Stock Markets: Country versus Industry. Journal of International Money and Finance, 27, Morey, M.R., Simpson, M.W., 2001.To Hedge or Not to Hedge: The Performance of Simple Strategies for Hedging Foreign Exchange Risk. Journal of Multinational Financial Management 11, Vrugt, E., Bauer, R., Molenaar, R., Steenkamp, T., Dynamic Commodity Timing Strategies. Limburg Institute of Financial Economics Working Paper no. 04/012. Maastricht, The Netherlands. 19

20 Table 1 Summary statistics Panel A: Summary statistics for the US Stocks Bonds GSCItot Mean Std. dev Min Max Skewness Kurtosis Panel B: Summary statistics for Canada Stocks Bonds GSCItot GSCIUH GSCIH % $ ƒ $US Mean Std. dev Min Max Skewness Kurtosis Panel C: Summary statistics for Australia Stocks Bonds GSCItot GSCIUH GSCIH % $ ƒ $US Mean Std. dev Min Max Skewness Kurtosis Panel D: Summary statistics for New Zealand Stocks Bonds GSCItot GSCIUH GSCIH % $ ƒ $US Mean Std. dev Min Max Skewness Kurtosis In all panels, Stocks and Bonds represent stock and bond returns in respective markets, denominated in local currencies. GSCItot represents the return of the GSCI total return index, denominated in US dollars. Unhedged futures return in local currency is denoted by GSCIUH and hedged return by GSCIH. % $ and ƒ $US denote change in the US dollar against the local currency and forward premium, respectively. 20

21 Table 2 Correlations Panel A: Correlations for the US Stocks Bonds GSCItot Stocks 1 Bonds GSCItot Panel B: Correlations for Canada Stocks Bonds GSCItot GSCIUH GSCIH % $ ƒ $US Stocks 1 Bonds GSCItot GSCIUH GSCIH % $ ƒ $US Panel C: Correlations for Australia Stocks Bonds GSCItot GSCIUH GSCIH % $ ƒ $US Stocks 1 Bonds GSCItot GSCIUH GSCIH % $ ƒ $US Panel D: Correlations for New Zealand Stocks Bonds GSCItot GSCIUH GSCIH % $ ƒ $US Stocks 1 Bonds GSCItot GSCIUH GSCIH % $ ƒ $US In all panels, Stocks and Bonds represent stock and bond returns in respective markets, denominated in local currencies. GSCItot represents the return of the GSCI total return index, denominated in US dollars. Unhedged futures return in local currency is denoted by GSCIUH and hedged return by GSCIH. % $ and ƒ $US denote change in the US dollar against the local currency and forward premium, respectively. 21

22 Table 3 Commodity sector weights as of mid-2009 GSCI DJI CRBI Energy 69.61% 33.00% 18.00% Grains and Oilseeds 9.63% 21.00% 18.00% Industrials 8.26% 20.30% 12.00% Livestock 4.38% 6.70% 12.00% Precious Metals 3.13% 10.70% 17.00% Softs 4.99% 8.30% 23.00% Total % % % Source: The entries are estimated by the authors on the basis of the information provided by Goldman Sachs, Dow Jones, and Commodity Research Bureau. Some of the values are rounded. 22

23 Table 4 Global minimum variance portfolio (GMVP) allocations Panel A: US Portfolio Two-asset Three-asset Stocks Bonds GSCItot CV Panel A:Canada Portfolio Two-asset Three-asset (unhedged) Three asset (hedged) Stocks Bonds GSCItot CV Panel A: Australia Portfolio Two-asset Three-asset (unhedged) Three-asset (hedged) Stocks Bonds GSCItot CV Panel A: New Zealand Portfolio Two-asset Three-asset (unhedged) Three-asset (hedged) Stocks Bonds GSCItot CV In all panels, two-asset portfolios represent portfolios consisting of only Stocks and Bonds. Three-asset portfolios represent portfolios with Stocks, Bonds, and commodity (GSCItot) investments. Allocations are for investors of respective countries. Returns used to calculate the allocations are in local currency. CV stands for coefficient of variation. 23

24 Table 5 Results of the spanning tests Panel A. Spanning tests using GSCI US Canada Australia New Zealand Unhedged Hedged Unhedged Hedged Unhedged Hedged F stat p-value ** *** ** ** Wald stat p-value *** *** ** ** Panel B. Spanning test using Dow Jones index US Canada Australia New Zealand Unhedged Hedged Unhedged Hedged Unhedged Hedged F stat p-value *** *** *** ** *** *** *** Wald stat p-value *** *** *** ** *** *** *** Panel C. Spanning test using CRB index US Canada Australia New Zealand Unhedged Hedged Unhedged Hedged Unhedged Hedged F stat p-value *** *** *** *** *** *** *** Wald stat p-value *** *** *** *** *** *** *** This table presents F and Wald statistics along with the p-values of the mean variance spanning tests. The null hypothesis of the spanning test is that commodity futures do not improve portfolio diversification. *** and ** represent significance at the 1% and the 5% level. 24

25 Table 6 Asset and commodity index correlations Panel A. US Stock Bond GSCItot GSCI DJI CRBI Stock 1 Bond GSCItot GSCI DJI CRBI Panel B. Canada Stock Bond GSCItot GSCI DJI CRBI % $US Stock 1 Bond GSCItot GSCI DJI CRBI % $US Panel C. Australia Stock Bond GSCItot GSCI DJI CRBI % $US Stock 1 Bond GSCItot GSCI DJI CRBI % $US Panel D. New Zealand Stock Bond GSCItot GSCI DJI CRBI % $US Stock 1 Bond GSCItot GSCI DJI CRBI % $US In all panels, Stocks and Bonds represent stock and bond returns in respective markets, denominated in local currencies. GSCItot represents the return of the GSCI total return index, DJI the Dow Jones-UBS Commodities Index and CRBI the Commodity Research Bureau Index, all denominated in US dollars. % $ denotes change in the US dollar against the local currency. 25

26 Table 7 Spanning test with local commodity index Canada Australia New Zealand F-test p-value *** *** *** Wald test p-value *** *** *** This table presents F and Wald statistics along with the p-values of the mean variance spanning tests. The null hypothesis of the spanning test is that commodity futures do not improve portfolio diversification. *** represents significance at the 1% level. 26