An issue of considerable concern to many investors is how to protect their portfolios from a broad decline in the U.S. equity market, particularly in light of weakness in the U.S. dollar and the economic fundamentals that are driving this. It may seem obvious, then, for investors to look to invest more heavily in foreign assets. Roger Nussbaum provided some thoughts on which countries might provide the best protection from “U.S. market deterioration” in this article.

Among developed economies, he suggested looking at Australia (NYSEARCA:EWA), Sweden (NYSEARCA:EWD), Norway, and Ireland (NYSE:IRL). Let’s also look at the Netherlands (NYSEARCA:EWN), which Roger referred to in his original article. Roger analyzes the fundamentals of economies and makes his suggestions on this basis. I am in no way an expert at analyzing foreign economies and their prospects, but I believe that it is instructive to examine how allocations to various foreign economies looks from the perspective of quantitative asset allocation. The main question that I wanted to examine from a quantitative perspective was whether investment in these ETFs (EWA, IRL, EWD, and EWN) would provide cover from a broad decline in U.S. equities.

To analyze whether an asset can protect you from a decline in the U.S. market, there are a number of statistical measures that can be applied. The first and simplest measure of whether funds track the S&P500 is to look at the correlation matrix between total returns—and we use monthly data:

The correlation matrix above shows the correlation between each of the country-specific ETFs with the S&P500 (NYSEARCA:SPY), the Russell 3000 (NYSEARCA:IWV), and the NASDAQ (QQQQ). The good news is that each of the country-specific ETFs exhibits correlations to the U.S. markets that are well below 100%, which means that these do not move in lockstep with U.S. markets. Having looked at the correlations, it is then of interest to look at the Beta and R-squared values for these ETFs relative to the S&P500:

Now the picture is a somewhat more subtle. Beta for each of these ETFs is greater than 100%. This means that moves in the S&P500 tend to be amplified in these funds. If the S&P500 drops by 1%, EWA tends to drop by 1.2% (120% x 1%). EWD tends to drop 1.69% for a drop in the S&P500 of 1%. This is not a tendency that you want if you are trying to insulate your portfolio from the S&P500. On the other hand, R-squared is quite low for these ETFs. R-squared (also notated as R^2) tells us the fraction of the variance in the fund that can be explained by the S&P500. Only 32% of the variance in EWA can be explained by moves in the S&P500—so the vast majority of the variability in EWA is caused by other factors. Before moving further, I will note that many international indices exhibit high Beta and low R-squared—this is a common trait. But what does it mean for the investor? **High Beta and low R-squared means that these funds have high volatility compared to the S&P500**. This is something that the correlation coefficient tells us nothing about. High volatility means high risk. How high? Over the last three years, the standard deviation in return (the standard measure of volatility) is far higher for each of these ETFs than for the S&P500 (SPY):

The S&P500 has exhibited a standard deviation in annual return of about 7% for the last three years. EWA and EWD have been more than twice as volatile as the S&P500. IRL has been almost three times as volatile as the S&P500.

This case reveals a problem with seeking shelter from the U.S. economy in these broad foreign index funds. Correlation, related to R-squared, measures the degree to which two assets move together. A high-Beta, low R-squared asset can amplify swings in the U.S. market but have so much **additional volatility** that the correlation is fairly low. What this means is that a market decline in the U.S. also has a good probability of causing a decline in these ETFs---but there will also be a lot of other volatility that may go work with or against such moves. Consider, for example, a portfolio made up of 25% each of EWA, EWD, EWN, and IRL. Would this portfolio provide protection against a market downturn in the U.S.? If you just look at the low correlations, you might think so but the other statistical measures would suggest that the protection is not so great. In the three year period from 1/1/2000 to 12/31/2002, SPY generated an average return of -12.7% per year, with a standard deviation in annual return of 18.9%. This was the heart of the most recent U.S. bear market. How would our equally-allocated international portfolio have fared?

Over this three-year period, our international portfolio averaged -10.48% per year with a standard deviation of 23.5%. This is not a lot of protection from the S&P500, even though the average returns were not, on average, quite as bad. Now, I will certainly grant that this is only a single anecdotal case, but this is exactly the type of behavior that the statistics suggest (i.e. the low Beta/high-R-squared from the most recent three years). Maybe the next market downturn will be driven by weakness in the U.S. economy relative to other countries in such a way that these statistics will not hold.

There is, unfortunately, another issue in the statistics that gives me concern with investing in these economies as a protection against a U.S. market decline: these country indices have generated unsustainably high annual returns over recent years, even compared to their risk levels. This means that there is a higher probability of under-performance in the foreseeable future---assets cannot out-perform their associated risk levels forever. Let me begin this part of the discussion by comparing the trailing three-year performance of the portfolio equally allocated to the four foreign ETFs with Quantext Portfolio Planner’s Monte Carlo projections:

There is no arguing that this portfolio has out-performed dramatically over the past several years. Who would be unhappy with an average annual return of 25% per year for bearing a very reasonable standard deviation of 12.8% (the long-term standard deviation of the S&P500 is about 15%)? The problem, however, is that this level of return is not sustainable—**especially at this kind of risk level**. This is where the Monte Carlo simulation comes in. Quantext Portfolio Planner [QPP] projects that this portfolio will generate 13.8% per year, on average, with a standard deviation of 25% in the medium- to long-term. On a forward looking basis, QPP projects that this portfolio will dramatically outperform the 8-9% that is projected for the U.S. equities markets, but at the cost of bearing a much higher level of risk. Further, a period of outsized gains must ultimately be followed by a period of declines to get the risk and return back in balance.

[Note: In a recent article, we looked at QPP’s projections for long-term expected returns and risks from a range of asset classes, and compared to projections from a well known institutional advisor.]

While all estimates about future risk and return are uncertain, the values generated by QPP are reasonable.

At this point, it makes sense to sanity-check the Quantext Portfolio Planner projections. Are the QPP numbers realistic? How can they be motivated? To begin this discussion, note that the QPP projections above used only the most recent three years of data for these ETFs---the model has no information about earlier performance of these funds or their asset classes and the Monte Carlo simulation was run with default settings. The QPP projection for the equally-allocated portfolio is for a return of 13.8% with a standard deviation of 25%. When we look at the performance of the equally-allocated portfolio over the trailing ten year period (seven years more data), we obtain the following results:

Over the most recent ten year period, the equal-weight portfolio generated 14% in average return with 19.73% in standard deviation, reasonably close to our projections from QPP. These longer-term historical statistics show far lower returns than we have seen from this portfolio over the most recent three years. The real question for investors looking to these markets is whether they are willing to bet that these international markets will perform in the future more like the longer-term history or more like the most recent three years. Historically, asset classes that have generated annual returns that out-strip their risk levels (the way that these international funds have in recent years) have corrected back over time—mean reversion in action.

Let’s try to re-cap these issues and then look at them in broader context. Many international markets have out-stripped domestic stock market performance over the past several years. Investors’ appetites for taking on these assets have been helped along by the very low volatility environment that we have seen in global markets over this period. The fact remains, however, that high Beta / low R-squared asset classes are not necessarily a great source of protection from a domestic downturn. **An asset with Beta greater than 100% but high volatility can have a fairly low correlation to the S&P500 but still amplify your portfolio exposure to U.S. market moves**. The correlations can be fairly low simply because there is a great deal of additional volatility on top of U.S.-market-driven swings. A projection of future returns from these foreign markets that are consistent with the long-term reasonable risk-return balance of capital markets suggests that these markets are due for some correction, or at least are likely to deliver fairly anemic returns in some future horizon. I don’t know when the market will turn, but the returns from these assets is simply far too high compared to their risk levels to be sustainable. Quantext Portfolio Planner projections for these foreign asset classes is for considerably higher returns than domestic equities, but with an associated higher level of risk. **My bottom line (from a quantitative perspective) is that these foreign markets are an important source of growth, but they will not necessarily be a tremendous source of protection from a decline in U.S. markets over the next one to five years**.

**The caveat on all of my analysis is that it is statistics**. Markets can and do change and evolve. Perhaps the economic growth in these markets will be driven be forces that will allow them to not be dragged down if the U.S. market suffers a significant decline. The historical statistics and projections derived from them simply don’t support the idea that these foreign asset classes will insulate your portfolio from a domestic decline. The historical statistics that we use are both medium term (ten years) and near-term (three years) and when either set of historical data are used to drive forward-looking Monte Carlo simulations, the results look about the same. This does not mean that I think that investors should avoid foreign assets. All asset classes deserve due consideration in a portfolio allocation. What I am saying is that these foreign asset classes do not look like they will provide good cover from a near-to-medium term U.S. market decline. For that, I would be looking for assets that exhibit low Beta and low R-squared, as discussed in this article.