Combining Sector and Country Tilts

The next table shows a range of non-U.S. indexes, along with the correlation of returns with the U.S. market as a whole. Moreover, we have also calculated the average correlation of the U.S. industry sector indexes with each of the international indexes.

Just by looking at the two tables, you can see that the sector and country correlations with the U.S. market are about equal, with some significant exceptions (e.g., Japan). Equally as interesting, the average correlation between the country indexes and U.S. sectors appears to be quite low, suggesting the existence of potential gains from diversifying across both countries and sectors.

Okay, now that we've set the seen, let's move on to our optimization experiments.

Our first task was to establish a benchmark against which to compare the results of our experiments. We chose the Dow Jones U.S. Total Market Index over the same January, 1994 to December, 2000 period covered by our data. Now, some people could reasonably argue that , given that the universe of our potential investments covers both domestic sectors and foreign countries and regions, the appropriate benchmark would be a global equity index like the Morgan Stanley All Country World Index. We have a lot of empathy with that view; however, when you get right down to it, we think that most investors have a home country bias, and therefore use the domestic equity market as their primary benchmark. For this reason, we will do the same in this analysis.

Our challenge, then, is to improve on the results obtained by the DJUSTMI, which delivered average annual returns of 18.60% over the 1/94 through 12/00 period, with a standard deviation of 17.29%, or a very impressive 1.08% of return per unit of risk.

For our first optimization run, the only constraint we set was that a maximum of 15% of the portfolio could be invested in any single index. When we ran our optimization to match the 17.29% standard deviation of the benchmark portfolio, we ended up with a portfolio that delivered expected average annual returns of 28.54%, or a whopping 1.65% of return per unit of risk. The underlying asset allocation for this portfolio was as follows: 15% each to U.S. Energy, U.S. Healthcare, U.S. Technology, U.S. Utilities, and Sweden; 11% to Switzerland, 8% to Brazil, and 6% to U.S. REITs. By now the careful reader is saying, "wait a minute. The country indexes differ in terms of their underlying industry weightings. What is the overall industry mix in the optimized portfolio?"

Based on country index industry weightings at the end of 2000, here is the answer to this question:

After considering this result for a bit, we came back to a point we raised last month when we discussed country tilts. To wit, optimization is essentially a mechanical process, based on historical data, that is best used in combination with, rather than as a substitute for human judgement. One example of this was our decision to limit the investment in any single sector or country index to no more than 15% of the total portfolio, as a way of ensuring some minimal degree of diversification and thereby guarding against two risks: (1) that our data don't accurately represent what was really going on in the past and (b) that even if they are accurate, the future won't be exactly like the past.

With this in mind, we changed two rules for our next optimization. First, we substituted the Emerging Markets Index for Brazil, Mexico, Taiwan, Korea, and Malaysia Indexes. Second, we required that at least five percent of the portfolio be invested in both the Japan Index and the Emerging Markets Index. In the case of the former, our logic was that recent results unfairly penalize the country in an optimization, and don't accurately capture what we see as the future opportunity available there. In the case of the latter, we said that given the high individual country risks, we'd rather be in emerging markets generally rather than specific countries.

The result was broadly similar to our previous optimization run. This time we ended up with expected average annual returns of 24.79%, with a standard deviation of 17.29%,or a still very impressive 1.43% of return per unit of risk taken on. Again, we allocated 15% each to U.S. Energy, Healthcare, and Technology. In addition, we allocated 15% each to U.S. Financial Services, Sweden and Switzerland, as well as our minimum mandated 5% each to Japan and Emerging Markets. In terms of overall industry weightings, the results were as follows:

To further understand the forces driving the improvements in these expected risk adjusted returns, we conducted two further analyses. First, we looked at the correlations between the eight subasset classes used in the second portfolio, using data from the 1/94 to 12/00 period. Unsurprisingly, most of the correlations were quite low; in fact, the average correlation across the 28 separate pairs was only .375.

The second analysis took a closer look at the respective impacts of diversifying across industry sectors and across countries. We began by calculating the expected return and risk for a portfolio using just our industry weightings, based on historical data for the respective Dow Jones World Sector Indexes. This resulted in an expected average annual portfolio return of 18.75% with a standard deviation of 16.38%, or 1.145% of return per unit of risk. We then looked at the expected returns and risk for a portfolio that matched our country weightings of 60% U.S., 15% each to Sweden and Switzerland, and 5% each to Japan and emerging markets. This yielded an expected average annual portfolio return of 18.11% with a standard deviation of 16.59%, or 1.09% of return per unit of risk. Averaging the two results together yields a crude measure of 18.43% average return, with an expected standard deviation of 16.49%. It would thus appear that the interaction of country and sector diversification added a further 6.36% to expected returns, while adding only .80% to expected standard deviation.

Finally, we performed "the acid test": we checked to see how our second model portfolio would have performed this year through the end of August. Unfortunately, its returns of (19.4%) have substantially lagged behind those for the Dow Jones U.S. Total Market Index, which was off only (14.2%) year-to-date. What's going on? In a nutshell, as the table below shows, the historical correlations haven't held up very well this year, with more sub-asset classes moving down together than one would have expected based on historical data from January, 1994 to December, 2000 (a period that did not see a worldwide economic slowdown like we have been experiencing this year).

To put this in perspective, if you had put 50% of the equity portion of your portfolio in the Dow Jones U.S. Total Market Index iShare (IYY), and the other 50% in the Vanguard Total International Stock Market Index Fund (VGTSX), your year-to-date return would have been (15.8%).

This brings us full circle to where we started out last year, when we announced that we would be using much broader asset class definitions than we had in the past, and then looking at different tilts within those broad classes. The logic behind our move to broad asset class definitions was that in an era of rapid economic change, a lot of the historical assumptions about the way the economy works and the way different parts of it related to each other may not hold in the future. If this was the case, some of the historically valid approaches to enhancing risk-adjusted returns might also be undermined. We thought then, as we still do, that the last relationships to be undermined would be those between broadly defined sets of asset classes. The analysis we have done and reported in this month's issue of The Index Investor would seem to further support this judgement. Clearly, based on historical data, we have shown that it is theoretically possible to substantially improve risk adjusted returns by making a combination of sector and country tilts within the broad equity asset class. However, as noted above, this year our theory doesn't seem to be holding up in practice, most likely because it is encountering economic conditions not covered by the historical data. As a result, an active management approach (sector and country tilts) has once again failed to deliver returns that are superior to those from straightforward broad indexing of broadly defined asset classes. And that may be the most important insight of all.

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