Contents:
• Introduction
• Comparison of Mean-Variance Efficiency
• Development of Trading Strategies
• Building the Country Forecasting Model
• Building the Industry Forecasting Model
• Comparison of Trading Strategies
• Conclusion
• Appendices

Introduction

In the past, both academics and practitioners have devoted much effort to developing asset allocation strategies using portfolios of countries’ equities.  Recently, some have shifted their focus to investigating whether forming portfolios of industries might be a more advantageous manner to engage in asset allocation.  Intuitively, this recent work seems to make sense given the more inclusive global economy.  As trade barriers fall, the same industries within different countries might respond similarly to the same fundamental and economical data, while reponses across countries tend to be similar.  Some people have attempted to develop forecasting models that take advantage of this more homogenous world economy.

Given this recent trend, we believed that it would be interesting to compare the traditional country asset allocation with the new industry asset allocation methodology.  In this analysis, we construct country portfolios, industry portfolios, and country-industry portfolios.  In the country portfolios, we include assets such as German equities, US equities, and Japanese equities.  In the industry portfolios, we include assets such as aggregate global Energy equities, aggregate global Finance equities, and aggregate global consumer goods equities.  In the country-industry portfolios we include assets such as German energy equities, US energy equities, Japanese financial equities.

Specifically, we conducted the following analysis:

1. A comparison of the Mean-Variance efficient frontiers for the country, industry, and country-industry portfolios.
2. Development of trading strategies to exploit the benefits of diversifying across countries and across industries.

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Comparison of Mean-Variance Efficiency

Data

To construct our analysis we used the following data from 04/90 through 12/99:

• For the country portfolios, we used G-7 Country returns from MSCI.
• For the industry portfolios, we used returns from MSCI.  We included aggregate global industries of energy, finance, materials, capital equipment, consumer goods, service, multi-industry, and gold mining.
• For the country-industry portfolios, we could not get comparable data that we used for the industry portfolios.  Consequently, we used a different set of data for this analysis.  We used MSCI data and for 5 countries (US, UK, Germany, Japan, France) chose a set of 6 industries that we believed were representative of the whole economy.  Those industries are Banking, Beverage & Tobacco, Construction, Electronics, Health, and Merchandising.  So, this gave us a set of 30 different asset classes for the country-industry portfolios.
• We take on the stand point of U.S. investor and convert all returns in USD.
• All data and analysis is stated in terms of monthly and not yearly basis.

Assuming a -30% short-selling constraint, no transaction costs and no taxes, we constructed mean-variance efficient frontiers for the country, industry, and country-industry portfolios.  The efficient frontiers appear below:

These results are more clearly seen in the above table.  In the table, we see that the country-industry portfolios outperform other two porfolio in term of mean, standard deviation, and monthly and yearly Sharpe ratios.
We believe these results make sense after an examination of the correlation matrices among the different asset classes in the different portfolios.  We also see that the industry portfolios look least attractive when looking at mean return, standard deviation and the Sharpe ratios.

To understand these results, we looked at the correlation matrices for the country and industry portfolios.  Before viewing the efficient frontiers, we expected to see high correlations among the G-7 countries in the country portfolios.  The reasoning for this is that the G-7 countries enjoy rather close trading relationships.  We also believed that increasing globalization would contribute to these high correlations.  With regard to the industries, we expected relatively lower correlations.  The reason for this is that despite increasing globalization, different industries might respond to similar economic events in a less similar way than the overall countries do.  Basically, we expected the industry portfolio efficient frontier to fall outside the country efficient frontier.

So, we were at first surprised by the efficient frontiers.  However, after viewing the correlation matrices, the results made more sense.  As can be seen in the following tables, the industries are generally more highly correlated than the countries.

Perhaps one reason for this result is that the US makes up more than half of each of the included industries.  The correlations among US industries are greater than correlations of US to non-US industries.  Consequently, it makes sense that giving the US a 50% weight in the aggregate world industries would increase the correlations among the global aggregate industries.

To see an example of this, view the table below.  In the yellow region are correlations among US industries.  In the grey region, are the correlations of US industries to German industries.  We can see that in general the correlations among the US industries are higher than the corresponding US-German correlations.  For example we see in the lone yellow cell that the correlation of the US beverage to US construction industry is .40, while the correlation of the US beverage to the German construction is only .25.

The above table also explains why the country-industry portfolio outperforms other two portfolios. We can easily see that the dimensional diversification effects are melted into the correlation of US beverage with Germany construction. 40% of correlation of US beverage with US construction comes from the diversification benefit across industries within US. However, 25% of correlation of US beverage with German construction comes from the diversification across industry and country. This compounded effect gives us low correlation, which leads to better efficient frontier.

So, we conclude that it can indeed be advantageous to form portfolios of country-industries rather than simply countries only.  As can be seen from the table below, if we were to look only at countries the US would have a weight of about 120% whereas if we look at a country-industry portfolio the US drops to about 62%
Since the country-industry portfolio is optimal, we end up misplacing our assets across countries if we just look at country effect.
 
 

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Development of Trading Strategies

Before beginning our analysis we knew that developing portfolios that allocated among different countries could have benefits.  From the preceding mean-variance efficient frontier analysis, we learned that benefits could also be gained by developing portfolios that diversified among industry and country-industry asset classes.  Our intent was to develop trading strategies for both of these types of portfolios.  However, because of a lack of data and time and human resource constraints, we could not construct a trading strategy that would take advantage of the country-industry portfolios.  So, instead, we focused on developing a strategy for the industry portfolio.

We tested two different strategies from 01/1998 through 12/1999 for these industry portfolios and compared it to a trading strategy for country portfolios and a buy-and-hold MSCI index portfolio.

Fixed Weight Allocation Trading Strategy

To construct portfolios under this strategy, we used the unconditional expected return and standard deviation among industries based on the efficient frontier data that we previously discussed.  We formed a portfolio using the following weights.  To determine these weights we used the optimal weights for the 5% level of standard deviation.  We did not rebalance the weights during the entire holding period.  We simply formed a portfolio using the following weights in the first month and held the portfolio for 24 months.

Industry Fixed Weights:
 

	Energy	Materials	Capital Equipment	Consumer Goods	Services	Finance	Multi-Industry	Gold Mines
Weights	-0.30000	-0.30000	0.45700	0.61717	0.52470	-0.30000	0.37305	-0.07191

Country Fixed Weights:
 

	Canada	Japan	France	Italy	UK	Germany	USA
Weights	-0.3000	-0.3000	0.0465	-0.0283	0.1766	-0.1120	1.5171

Basically, this is a partial diversification strategy because we determined the weights using an optimization of historical data.  However, it has a limitation in that it is only based on historical data – it does not readjust the weights when new data is accumulated as the months go by.  So, this is not a forward-looking strategy.

Dynamic Weight Allocation Trading Strategy

In this strategy, we dynamically changed the portfolio weights each month.  To do this we used a forecasted return for each month. Yet, we used the unconditional, historical standard deviation and correlation matrix for each month’s optimization.  To get the forecasted monthly returns, we used a simple multi-variate regression model.

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Building the Country Forecasting Model

When we began to build the asset allocation model, our first step was to choose four predetermined variables that made economic sense to use in our final model for each country.  We included both global and local variables.

The variables we chose are:

GOIL_CHANGE - This variable is the month to month change in oil price.  The countries in our portfolio are all well-developed industrialized countries that rely heavily on oil both as a consumer product and an industrial output.  We believed that if the oil price moved unfavorably that consumers and companies within the countries might face increased costs, lowering corporate profits and consumer demand.  Our expectation on the net effect on the local stock market is certainly negative.

GTS - This is the spread between the US 10-year government bond and the 3 month T-bill and captures a global interest rate term structure.  This term structure could capture expected inflation and thus expected economic growth of the US economy.  For instance, if the term spread is positive, people expect some future inflation resulting from future economic expansion.  This would then affect the global stock markets as the US is the largest economic power and represents a large percentage of the world’s stock market capitalization.

LPBV - This is the Price/Book ratio.  Low P/B ratio suggests that there might be some distress in the companies within a country.  If there is distress and increased risk, investors would have to be compensated and future returns might be high.

LTS - This variable is the local term structure, which we defined as the spread between the local 10-year government bond and the 3-month short-term bond rate. We thought that term structure could capture the expected future inflation and the expected future state of the local economy.  For instance, if the term spread is positive, people expect some future inflation and future economic expansion.

Our model for each country was:

Ri,t = ßi,0 + ßi,1(GOIL_CHANGEt-1) + ßi,2(GTSt-1) + ßi,3(LPBVt-1) + ßi,4(LTSt-1) + ßi

To conduct an in-sample analysis we ran a regression on this model from 03/86 through 12/96 and achieved the following results:
 

Portfolio	ß0	ß1	ß2	ß3	ß4	Adj. R^2
Canada	0.154  [3.2357]	0.000  [-1.33739]	-0.018 [-3.26775]	-0.070  [-2.76007]	0.009  [2.593713]	0.065
France	0.098623  [2.411944]	-0.000791  -[1.762586]	-0.011607  [-2.405433]	-0.034973  [-1.68526]	-0.006527  [-1.884557]	0.058
Germany	0.096122  [2.264839]	-0.001286 [-2.84851]	-0.01191  [-2.396189]	-0.027671  [-1.510483]	-0.001899  [-0.468597]	0.078
Italy	0.0364441  [1.2672888]	-0.001904 [-3.56841]	-0.009472  [-1.718906]	-0.004994  [-0.357266]	-0.008  [-1.674303]	0.106
Japan	0.038998  [1.098054]	0.000165  [0.280275]	-0.001128  [-0.178932]	-0.006963  [-0.895755]	-0.008119  [-1.142487]	0
UK	-0.10219  [-1.90172]	-0.0006  [-1.45506]	0.000528  [0.099424]	0.054743  [2.466964]	-0.00625  [-1.66049]	0.045

As you can see from the table the R^2 ranges from 0 for Japan to to .106 for Italy.  In general, GTS and LPBV seem significant across many of the countries.  The variable with the least predictive power appears to be LTS, although it is significant in Canada.  Also, our model seems to work least well in Japan where all of the variables appear insignificant.
We tested our model’s hit-rate both in and out of sample.  For the out-of-sample testing we used a period from 01/97 through 12/99.  For the most part, the hit rate of our country models was better than 50%, although we did have two asset classes (France and Germany) with hit rates out of sample less than 50%.

Correct Direction Analysis:
 

	Canada	France	Germany	Italy	UK	Japan
In-Sample Hits	88	75	73	78	80	75
%	68%	58%	56%	60%	62%	58%
Out-of-Sample Hits	20	14	17	21	25	19
%	56%	39%	47%	58%	69%	53%

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Building the Industry Forecasting Model

When we began to build the asset allocation model, our first step was to choose four predetermined variables that made economic sense, to use in our final model for each industry.  We should have had some industry-specific variables in the model as well.  However, we could not obtain global aggregate industry specific data.  So, we used global macroeconomic variables that we thought might make have predictive power across the different industries.

GOIL_CHANGE, GTS  – We included this variable based on the same reasoning that we used it in the country allocation model described previously.

USTBILL - This is the change in the US T-Bill rate.  We believe that local short-term rates often change in response to changes in the US short-term rate.  So an increase in the US short-term rate might trigger a change in the local rate, which would suggest lower future equity returns.

GPBV - This is the Price/Book ratio.  Low P/B ratio suggests that overall, in companies across different industries, there might be some distress.  If there is distress and increased risk, investors would have to be compensated and future returns might be high.

Our model for most industries was:

Ri,t = ßi,0 + ßi,1(GOIL_CHANGEt-1) + ßi,2(GPBV t-1) + ßi,3(GTS t-1) + ßi,4(USTBILL t-1) + ßi

As you can see from the following table, we chose not to include certain variables in certain countries.  The omitted variables are represented by N/A in the table.  We excluded these variables if we ran a preliminary regression and observed a 0 coefficient.  To conduct an in-sample analysis we ran a regression on this model from 03/86 through 12/96 and achieved the following results:
 
 

Portfolio	ß0	ß1	ß2	ß3	ß4	Adj. R^2
Capital Equipment	0.0805442  [1.5506339]	-0.000536  [-1.530337]	-0.027422  [-1.308713]	-0.005082  [-1.269042]	-0.000643  [-0.590765]	0.016
Consumer Goods	0.1132005  [2.5961709]	-0.000631  [-2.145834]	-0.03708 [-2.108149]	-0.008564  [-2.547762]	-0.000775  [-0.847678]	0.081
Energy	0.122138  [2.9883113]	-5.53E-05  [-0.20069]	-0.043893  [-2.662255]	-0.007414  [-2.35294]	0.0004628  [0.5403011]	0.035
Finance	0.187  [3.187]	N/A	-0.072  [-3.019]	-0.008  [-1.753]	N/A	0.053
Gold	-0.052  [-0.471]	N/A	0.028  [0.631]	-0.0018  [-0.207]	-0.002  [-1.067]	0.000
Materials	0.090  [1.609]	-0.001  [-1.336379]	-0.033  [-1.469699]	-0.004  [-0.825565]	0.000  [0.0326066]	0.003
Multi-Industry	0.093  [1.801]	-0.001  [-1.535]	-0.032  [-1.545]	-0.006  [-1.409]	-0.001  [-0.676]	0.025
Services	0.114  [2.509]	N/A	-0.042  [-2.283]	-0.005  [-1.569]	-0.001  [-0.544]	0.035

As you can see, our R^2 range from 0 in Gold to .081 in Consumer Goods.  Overall the R^2s are much worse in the industry model than in the country model.  Certainly, we believe the reason for this is that we could not include any industry-specific variables in our industry model.  Had we been able to do this, we feel that the models would have had more significant forecasting power.

In general, the GPBV appears to be the variable with the most significance, while the USTBILL appears to be the least significant.  One point to note is that the signs are on the coefficients are negative.  We believe the signs are correct.  However, we recognize that we include no variable that could capture the upside potential of the market.  This is especially problematic because the most significant variable is GPBV.  The value for this variable can never be negative.  So, had we been able to incorporate variables that capture upside potential, perhaps the model would have had more predictive power.  Perhaps, one way to make use of this model is to develop a trading strategy in which if the model predicts a negative return, optimize and invest in the industries.  If the model predicts a positive return, do not trust the model, and invest in a Eurobond.

Hit Rate Analysis:
 

	Capital Equip	Consum Goods	Energy	Finance	Gold	Materials	Multi- Industry	Services
In-Sample	51%	63%	60%	63%	55%	59%	56%	63%
Out-of- Sample	42%	47%	39%	50%	39%	50%	33%	31%

We see that the in-sample seems quite good.  However, the out-of-sample hit ratio is not impressive.  This is especially true when compared to the out-of-sample hit ratio for the country model.  In the country models, the out-of-sample hit ratios range from 39% to 69%, and most countries are above 50%.  With the industries, the out-of-sample hit rates range from 31% to 50%.  Only two industries have hit ratios at 50%.  This is to be expected given the fact that our industry model has less predictive power than the country model and almost always predicts a negative return for the month.

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Comparison of Trading Strategies

We compared performance of above two strategies for each country and industry portfolio with MSCI world index portfolio.  Following are the result table and graph of the different trading strategies:

As evident from the graph and table, the dynamic allocation strategy for industry did the worst, slightly lower than MSCI buy-and-hold strategy.  But this result is kind of expected in the sense that our forecasting model for industry has some drawback.  With a better model, however, the dynamic strategy for country was better than MSCI benchmark.  So, we can see that if we have better information and a better model, the active strategy can enhance our wealth.  The relatively poor job of the fixed allocation strategy for country demonstrates the drawback that we already mentioned.  Since the fixed allocation does not count the changes of expected return, volatility, and correlation, it may lead us to misplace the weight across different asset classes.  On the other hand, the outstanding job of the fixed allocation strategy for industry can tell us another advantage of the industry mixture we can take advantage of.  This outstanding job might indicate that the industry’s key factors affecting optimization of portfolio, like correlation, have not changed much compared to that of the country portfolio.

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Conclusion

The most popular way of constructing international portfolios is to choose the right countries and to invest in an index of those countries.  Yet, as we demonstrated in our research, it is clear that the industry effects play as important a role as the country effects.  Consequently, it is advisable to form portfolios that have both country and industry effects.  In our analysis, by simply adding six industries, we can improve portfolio performance significantly.  To benefit fully from adding industries to an asset allocation mix, it appears that one would want to use country-industries and not simply aggregate global industries or a country-only portfolio.  It seems that the best way to take advantage of this is to build a forecasting model with both global and industry-specific variables and then dynamically re-weight the portfolio each month.  This would allow the investor to take full advantage of the benefits of diversification.  In future research projects, we would hope to conduct this type of research.

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Appendices

Exhibit 1: Mean returns, Standard deviation for each asset in country, industry, country-industry portfolio
Exhibit 2: Correlation matrix of countries within industry
Exhibit 3: Correlation matrix of country-industry portfolio