Global Asset Allocation and Stock Selection

Assignment #1

Comparison of Investment Styles along Tactical Trading Strategies

Is it better to diversify across Countries or Sectors? This report attempts to answer this question by first analyzing 3 Investment Styles; Country-based, Sector-based and also a Mixed. For each investment style, a forecasting model was built and evaluated along 6 Trading Strategies such as Buy & Hold, 2-Longs, Long & Short etc. Click “ENTER” to find out the answer…

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Gold Asset Management

Artima Suraphongchai

Genzo Kimura

Jing Liu

Joseph Sun

Stefan Prawitz

February 2004

CONTENT

1. Executive Summary

2. Methodology

3. Correlation Analysis

4. Historical Efficient Frontier

5. Country Forecasting Models

6. Sector Forecasting Models

7. Tactical Trading Strategies

8. Evaluation

9. Appendix

1. EXECUTIVE SUMMARY

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Is it better to diversify across Countries or Sectors? With the proliferation of various equity indices, it has become easier to diversify across global sectors as well as across countries. The respective literature shows ambivalent answers in terms of long-term strategic asset allocation. In contrast to existing research, the focus of our research is on short-term tactical asset allocation.

In a first step, we select representative country and sector indices. As a representative sample of developed countries, we have picked MSCI indices for the United States, Germany, Japan and the United Kingdom, all denominated in US dollars. For sectors, we have chosen MSCI world indices for Financials, Health Care, Utilities and Materials, all denominated in US dollars. Selection criteria include the availability of historical return series, homogeneity among countries (members of G7), and heterogeneity among sectors (cyclicals and non-cyclicals). Secondly, we built one-month forecasting models for each asset class using no more than three variables. This is to ensure that we do not over-fit the models. Multiple regression results show solid adjusted R-squared statistics between 4% and 10% for country-based models and between 4% and 17% for sector-based models. Thirdly, both investment styles are evaluated along 6 tactical trading strategies, i.e. Buy-and-Hold (as a reference strategy), Long-or-Cash (no filter rule), Long-or-Cash (filter rule), 2-Long-Positions (equal weights), 2-Long-Positions (weights 2:1) and finally a combined Long-and-Short strategy.

The results show some evidence that country-based strategies are superior. In terms of cumulative return, the country-based investment style outperforms sector-based investing in 5 out of 6 trading strategies under review. Higher cumulative country-returns also lead to better Sharpe ratios for country-investing in 5 tactical trading strategies. In terms of risk measurement, we not only evaluated Sharpe ratios but also more intuitive criteria such as the percentage of months with non-negative returns and maximum single month losses. It turns out, that sector-based investing appears to be slightly less risky over time. However, as another important result drawn from historical efficient frontiers, diversification potential across time appears to be higher among countries than among sectors.

Apart from country-only and sector-only investing, we also tested a mixed style that is allowed to invest both in countries and sectors. We see evidence that mixed investment-styles perform substantially better in terms of risk and return than restricted investment-styles.

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2. METHODOLOGY

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2.1 Select Investment Styles

We have focused our analysis around three investment styles.

· Country-based Investing

For this investment style, four MSCI total return country indices are selected: United States, Japan, United Kingdom and Germany. All returns are converted to US dollars. The most important selection criterion was homogeneity. All countries under review belong to G7 in order to ensure that market capitalization is large enough and correlations to MSCI world are on a substantial level. This avoids a bias in our analysis.

· Sector-based Investing

The four MSCI world sector indices examined are Financials, Health, Utilities and Materials, all denominated in US dollars.[1] The main selection criterion was heterogeneity. That is, our selection includes both cyclical and non-cyclical sectors.

· Mixed Style

For this category, we examine a tactical portfolio that is allowed to invest in two countries and two sectors, i.e. United States, Germany, Financials and Health. Selection criteria include availability of long-term return series (resulting in comparable sample sizes) and quality of respective forecasting models. Analyzing all eight asset classes (i.e. four countries and four sectors) would have resulted in a severe bias since potential outperformance may result from higher degree of available investment options.

The diagram below summarizes the three different perspectives on the asset universe.

2.2 Build Forecasting Models

We created one-month return forecasts for all asset classes under review. Each model is limited to three variables in order to avoid over-fitted models that are more likely to fail out-of-sample.

2.3 Analyze along Tactical Trading Strategies

All investment styles are evaluated along a set of tactical trading strategies. These include simple and modified long-or-cash, multiple long-positions as well as combined long-and-short strategies.

2.4 Evaluate along Set of Performance Criteria

We evaluate investment styles using a set of criteria, ranging from average returns over Sharpe ratios to more intuitive indicators such as percentage of months with non-negative return or maximum single-month loss.

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[1] These classifications are according to Global Industry Classifications Standards (GICS). See appendix for detailed descriptions of each sector.

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3. CORRELATION ANALYSIS

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3.1 International Equity Correlations

We examined the correlation structure for all four country indices and MSCI world. The dataset starts in January 1988 and ends in December 2003. The correlation matrix below displays summary results.

Correlations	World	US	Germany	Japan	UK
World	1
US	0.8335	1
Germany	0.6668	0.5319	1
Japan	0.7169	0.3213	0.3097	1
UK	0.7792	0.6440	0.5686	0.4377	1

As expected, US equities show highest correlation to the world index. UK and Germany display highest correlations with the US market. In general, Japan seems to be least correlated to other markets.

However, correlation is not static over time. The 3-year and 5-year rolling correlations versus MSCI world are shown on the chart below.

From the trendlines, we see that correlations of all the assets have been on an increasing trend over the past 16 years, with the exception of Japan. In the last 5-year period, the correlation of US, Germany and UK vs. the MSCI world reached historically high levels with 97%, 85% and 88% respectively. Although literature suggests ambivalent points of view, we support the hypothesis of generally increasing international equity correlations.

3.2 Sector Correlations

The dataset for the correlation analysis starts in January 1988 and ends in December 2003. The correlation matrix below displays summary results.

Correlations	World	Financials	Health	Utilities	Materials[2]
World	1
Financials	0.9779	1
Health	0.9413	0.9234	1
Utilities	0.9926	0.9534	0.9371	1
Materials	0.7428	0.7304	0.7363	0.7213	1

We see that all sectors have high correlations with the MSCI World returns, with Financials, Health and Utilities well above 90%.

The following graph shows how 3-year and 5-year rolling correlations have evolved over time. Again, we see some evidence that correlations are generally on an increasing trend across all sectors.

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2 Return data for Materials only available from January 1995.

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4. HISTORICAL EFFICIENT FRONTIER

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Based on the correlation analysis in the previous section and on historical returns, we are able to draw efficient frontiers for each of the investment styles under review.

For our selection of asset classes, it turns out that the efficient frontier for country-investments is well above the one for sector-investments. There are two main reasons for the worse performance of sector-portfolios. First of all, average returns on the examined sector indices have been significantly lower. Country average returns (except for Japan, of course) were significantly higher during the sample period.

Secondly, diversification potential among selected countries was much higher than among selected sectors that are all highly correlated to each other. However, as correlations appear to increase for both countries and sectors, the difference of diversification potential between both investment styles might fade.

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5. COUNTRY FORECASTING MODEL

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5.1 Variables

The list below displays all variables that contribute to a one-month country return forecasting model for at least one of the asset classes examined.[3]

· Change in crude oil price

· Price-earnings ratio

· Change in yield spread over 10-year US Treasuries

· Dividend yield

· Price-book ratio

· Change of term structure

All variables are lagged one month. Furthermore, each model is limited to a maximum of three variables in order to avoid over-fitted models that are more likely to fail out-of-sample. Each country appears to be sensitive to an individual combination of variables. There is no single variable that seems to have predictive power for all countries. However, change in crude oil price and price-earnings ratio contributes to all forecasting models except for Japan.

The table below shows which variables contribute to the individual models.

	US	Germany	Japan	UK
Oil Price Change
Price-Earnings Ratio	[4]	^4		[5]
Change in Yield Spread		[6]
Dividend Yield			[7]
Price-Book Ratio			[8]
Change of Term Structure				[9]

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3 The exact specification and economic intuition of each variable is discussed in the appendix.

4 refers to P/E ratio of US equities

5 refers to P/E ratio of UK equities

6 change in spread of 10-year German Bunds over 10-year US Treasuries

7 refers to Dividend Yield of Japanese equities

8 refers to Price-Book Ratio of Japanese equities

9 refers to UK term structure

5.2 Summary of Predictive Regressions

The tables below summarize multiple OLS-regression results. Adjusted R-squared statistics vary from 4% to 10%, which is solid given the sample size of 192 (180) observations. Furthermore, t-statistics show that most coefficients are highly significant. The sign of coefficients also matches our economic intuition, e.g. negative impact of increasing oil prices or positive impact of increasing dividend yields.

Dependent Variable	MSCI US (total return, monthly)
Observations	192 (1/1988 – 12/2003)
R Square	11.22%
Adjusted R Square	10.28%
Standard Error	0.0403
	Coefficients	t Stat	P-value
Intercept	0.0472	4.2170	0.0000
Oil Price Change	-0.0948	-3.4674	0.0007
US Price-Earnings Ratio	-0.0017	-3.3421	0.0010

Dependent Variable	MSCI Germany (total return, in USD, monthly)
Observations	192 (1/1988 – 12/2003)
R Square	7.26%
Adjusted R Square	5.78%
Standard Error	0.0643
	Coefficients	t Stat	P-value
Intercept	0.0422	2.3517	0.0197
Oil Price Change	-0.1073	-2.4562	0.0150
US Price-Earnings Ratio	-0.0015	-1.8822	0.0614
Change in 10y Spread over UST	0.0412	1.9434	0.0535

Dependent Variable	MSCI Japan (total return, in USD, monthly)
Observations	180 (1/1989 – 12/2003)
R Square	5.39%
Adjusted R Square	4.32%
Standard Error	0.0679
	Coefficients	t Stat	P-value
Intercept	-0.1398	-2.1721	0.0312
Japan Dividend Yield	0.1400	2.6017	0.0101
Japan Price-to-Book	0.0117	1.1286	0.2606

Dependent Variable	MSCI UK (total return, in USD, monthly)
Observations	192 (1/1988 – 12/2003)
R Square	6.62%
Adjusted R Square	5.13%
Standard Error	0.0461
	Coefficients	t Stat	P-value
Intercept	0.0402	2.8189	0.0053
Oil Price Change	-0.0639	-2.0399	0.0428
UK Price-Earnings Ratio	-0.0019	-2.2648	0.0247
Change of Term Structure	-0.1374	-1.8629	0.0640

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6. SECTOR FORECASTING MODEL

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6.1 Variables

The list below displays all variables that contribute to a one-month sector return forecasting model for at least one of the asset classes examined.[10]

· Change in crude oil price

· Yield Change of 10-year US treasuries

· US Price-earnings ratio

· Change of term structure

All variables are lagged one month. Furthermore, each model is limited to a maximum of three variables in order to avoid over-fitted models that are more likely to fail out-of-sample. Based on the high correlation shown in the previous section, it is not surprising that certain variables exhibit high predicting power across all sectors. For example, change in crude oil price and US price-earnings ratio contributes to all forecasting models. Similar model specifications lead to the fact that highly correlated sectors have comparable expected returns.

The table below shows which variables contribute to the individual models.

	Financials	Health	Utilities	Materials
Oil Price Change
Yield Change of 10-year UST
US Price-Earnings Ratio
Change of US Term Structure

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[1]⁰ The exact specification and economic intuition of each variable is discussed in the appendix.

6.2 Summary of Predictive Regressions

The tables below summarize multiple OLS-regression results. Adjusted R-squared statistics vary from 5% to 17%, which is solid given the sample size of up to 262 observations. Furthermore, t-statistics show that all coefficients are highly significant. The sign of coefficients also matches our economic intuition, e.g. negative impact of increasing oil prices or positive impact of decreasing long-term interest rates.

Dependent Variable	MSCI World Financials (total return, in USD, monthly)
Observations	262 (1/1982 – 12/2003)
R Square	10.22%
Adjusted R Square	9.18%
Standard Error	0.0402
	Coefficients	T Stat	P-value
Intercept	0.0295	3.7659	0.0002
Oil Price Change	-0.0776	-3.3385	0.0010
Yield Change of 10-year UST	-0.0209	-2.4714	0.0141
US Price-Earnings Ratio	-0.0010	-2.5893	0.0102

Dependent Variable	MSCI World Health (total return, in USD, monthly)
Observations	262 (1/1982 – 12/2003)
R Square	8.69%
Adjusted R Square	7.63%
Standard Error	0.0399
	Coefficients	T Stat	P-value
Intercept	0.0295	3.7956	0.0002
Oil Price Change	-0.0636	-2.7622	0.0062
Yield Change of 10-year UST	-0.0182	-2.1699	0.0309
US Price-Earnings Ratio	-0.0011	-2.7867	0.0057

Dependent Variable	MSCI World Utilities (total return, in USD, monthly)
Observations	192 (1/1988 – 12/2003)
R Square	5.71%
Adjusted R Square	4.72%
Standard Error	0.0417
	Coefficients	t Stat	P-value
Intercept	0.0331	2.8510	0.0048
Oil Price Change	-0.0686	-2.4233	0.0163
US Price-Earnings Ratio	-0.0012	-2.2920	0.0230

Dependent Variable	MSCI World Materials (total return, in USD, monthly)
Observations	108 (1/1995 – 12/2003)
R Square	18.91%
Adjusted R Square	16.57%
Standard Error	0.0580
	Coefficients	t Stat	P-value
Intercept	0.0729	2.7435	0.0072
Oil Price Change	-0.1517	-2.9543	0.0039
US Price-Earnings Ratio	-0.0026	-2.4046	0.0180
Change of Term Structure	-0.1894	-2.8558	0.0052

6.3 Direction Count

The table below compares the number of months in which the forecasting model delivers the correct direction of next month’ return using the Country- and Sector-based trading strategies. It is important to compare these numbers to the percentage of correct directions resulting from a simple buy-and-hold strategy. For example, if we are investing during a bull market, and the percentage of positive return months over the full sample is around 65%, this will be the number that the forecasting model has to beat, and not 50%.

Country-based Investing

	Adjusted R square	Correct Direction Count	Total Observations	Percentage	Buy-and-Hold
US	10.28 %	134	192	70%	63%
Germany	5.78 %	126	192	66%	58%
Japan	4.32 %	104	180	58%	46%
UK	5.13 %	118	192	61%	57%

Sector-based Investing

	Adjusted R square	Correct Direction Count	Total Observations	Percentage	Buy-and-Hold
Financials	9.18 %	168	262	64%	66%
Health	7.63 %	175	262	67%	65%
Utilities	4.72 %	127	192	66%	60%
Materials	16.57 %	76	108	70%	59%

As expected, the percentage of correct direction predictions is higher for models that have higher R square statistics. The better the fit of the model, the better is its performance in predicting the correct direction

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7. TACTICAL TRADING STRATEGIES

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As mentioned above, we tested different investment styles’ performance when simple tactical trading strategies are applied.[11]

· Strategy 0: Buy-and-Hold

This is a simple Buy-and-Hold strategy with equal weights for all assets. This is our reference strategy to which results can be compared.

· Strategy 1A: Long-or-Cash (No Filter Rule)

This simple Long-or-Cash strategy compares highest forecasted return to current one-month Eurodollar deposit return. If highest forecasted return exceeds deposit return, a full long position is taken in the respective asset.

· Strategy 1B: Long-or-Cash (Filter Rule)

This strategy is similar to strategy 1A. However, the highest forecasted return must exceed one-month Eurodollar deposit return by at least 0.01% on a monthly basis. Actually, this can be called a filter rule. Only if the projected return passes this filter rule, a full long position will be taken in the respective asset.

· Strategy 2A: 2-Long-Positions (Equal Weights)

This strategy modifies 1A. It compares the two highest return forecasts to the current return on a one-month Eurodollar deposit. If both forecasts exceed deposit return, we will be long in these two assets. If only one asset exceeds deposit return, we will only invest in one asset class and deposit the rest. Both positions are equally weighted.

· Strategy 2B: 2-Long-Positions (Weights 2:1)

This strategy modifies 2A. The difference is the overweight of the asset with highest forecast. In other words, highest returns and second highest have weights of two thirds and one third respectively.

· Strategy 3: Long-and-Short

This strategy will go long in asset with highest positive forecast and short the lowest negative return forecast. Again, a positive forecast must exceed the current deposit return. If there are no positive forecasts, this will result in a full deposit position. If there are no negative forecasts, no short position is taken. Therefore, this strategy can result in the following position combinations: a) 1 Long and 1 Short, b) Deposit and 1 Short, c) 1 Long, d) Deposit.

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[1]¹ In the section dealing with efficient frontiers, we stated that diversification potential among countries seems to be higher than among sectors. However, this applies only for portfolios that achieve diversification by taking simultaneous (optimized) positions in many assets. However, in our research, we examine tactical portfolios that achieve diversification only across time. Our tactical trading strategies rebalance positions frequently, but do not take many simultaneous positions.

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8. EVALUATION

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Now, we are ready to evaluate investment styles based on the returns created from tactical trading strategies. We use a set of criteria, ranging from average returns over Sharpe ratios to more intuitive indicators such as percentage of months with non-negative return or maximum single-month loss. For each category, we calculate the average rank of the respective investment style.

8.1 Average Return[12]

	Country-only	Rank	Sector-only	Rank	Mixed Style	Rank
0	0.0072	3	0.0074	2	0.0091	1
1A	0.0177	2	0.0136	3	0.0179	1
1B	0.0162	2	0.0138	3	0.0172	1
2A	0.0159	1	0.0122	3	0.0155	2
2B	0.0165	1	0.0126	3	0.0163	2
3	0.0170	2	0.0155	3	0.0184	1
Avg		1.83		2.83		1.33

In terms of average return, country-based investing style is clearly superior to sector-based investing. However, both styles are dominated by the mixed approach.

For country-only investing, strategy 1A (long-or-cash, no filter) yields best average returns. For the mixed style investor, strategy 3 (combined long-short positions) results in highest overall return.

8.2 Standard Deviation

	Country-only	Rank	Sector-only	Rank	Mixed Style	Rank
0	0.0435	3	0.0420	1	0.0431	2
1a	0.0506	3	0.0419	1	0.0434	2
1b	0.0423	3	0.0359	1	0.0385	2
2a	0.0380	3	0.0340	1	0.0343	2
2b	0.0401	3	0.0362	1	0.0363	2
3	0.0375	1	0.0411	2	0.0448	3
Avg		2.67		1.17		2.17

In terms of standard deviation of monthly returns, the sector-only approach dominates. On the other hand, standard deviation is higher for most country-style strategies. The lowest overall standard deviation could be achieved by combining a sector-based style and strategy 2A (2-long-positions with equal weights).

8.3 Sharpe Ratio

	Country-only	Rank	Sector-only	Rank	Mixed Style	Rank
0	0.17	3	0.18	2	0.21	1
1a	0.35	2	0.32	3	0.41	1
1b	0.38	2	0.38	3	0.45	1
2a	0.42	2	0.36	3	0.45	1
2b	0.41	2	0.35	3	0.45	1
3	0.45	1	0.38	3	0.41	2
Avg		2.00		2.83		1.17

In order to consolidate information from the previous categories, we calculated Sharpe ratios for all combinations of investment styles and trading strategies. It turned out that the mixed style delivers the best return per unit of standard deviation. Country-only investing dominates sector-only investing due to better returns while standard deviations are only slightly higher.

8.4 Percentage of Months with Non-negative Returns

	Country-only	Rank	Sector-only	Rank	Mixed Style	Rank
0	63.0%	2	60.9%	3	65.1%	1
1a	69.3%	3	76.6%	1	76.0%	2
1b	77.6%	3	88.0%	1	85.9%	2
2a	71.9%	3	76.6%	2	78.6%	1
2b	68.8%	3	77.1%	1	77.1%	1
3	66.7%	2	68.2%	1	66.7%	2
Avg		2.67		1.50		1.50

In addition to the Sharpe ratio, it might be useful for the very risk-averse investor to know the probability of a profit/loss in a single month. The table above shows that he should not be too scared when investing in sectors only. The highest probability of positive single-month returns could be achieved by combining a sector-based style with filtered long-or-cash strategy. In this case, only in 12% of months a negative return will occur.

8.5 Maximum Single Month Profit

	Country-only	Rank	Sector-only	Rank	Mixed Style	Rank
0	0.1194	2	0.1123	3	0.1236	1
1a	0.2426	2	0.2468	1	0.2369	3
1b	0.2023	3	0.2468	1	0.2369	2
2a	0.1245	3	0.1544	2	0.1602	1
2b	0.1638	3	0.1852	2	0.1858	1
3	0.1774	3	0.2468	1	0.2369	2
Avg		2.67		1.67		1.67

In terms of maximum single month profits, sector-based investing is superior to country-based investing. Our sector forecasting models are doing well in capturing high single-month profits with high precision.

2.1. Maximum Single Month Loss

	Country-only	Rank	Sector-only	Rank	Mixed Style	Rank
0	-0.1260	2	-0.1236	1	-0.1450	3
1a	-0.0927	1	-0.1145	3	-0.1133	2
1b	-0.0913	2	-0.1145	3	-0.0590	1
2a	-0.0842	1	-0.1117	2	-0.1117	2
2b	-0.0774	1	-0.1123	2	-0.1123	2
3	-0.0696	2	-0.1145	3	-0.0667	1
Avg		1.50		2.33		1.83

For investors considering leverage on their tactical trading strategies, it is crucial to know the size of a loss that might occur during a single month. In this category, we examine maximum single month losses that have occurred when applying the respective style and strategy. It turns out that country-style investing is superior in minimizing extreme losses.

2.1. Summary of Results

As expected, the overall picture is ambivalent. While country-based investment styles outperform sector-investments significantly, it appears that this can only be achieved with taking higher risks. However, in terms of the Sharpe ratio, countries still do better than sectors. The ability to minimize single month losses is superb when a sector-based investment style is combined with a cautious trading strategy. Recall that the combination of filtered long-or-cash strategy with sector-investments yielded positive returns in 88% of the months. However, when it is important to avoid large single month losses, country-investments appear to be more appropriate than sector-investments. As far as mixed style investing is concerned, we see some evidence that it is superior to both restricted styles in most categories.

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APPENDIX

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Appendix 1: Sector Description

Appendix 2: Economic Intuition of Variables

Appendix 3: Performance of Investment Styles

Appendix 4: GARCH Likelihood Function

Appendix 1: Sector Descriptions