A Closer Look at Asset Class Returns in 2006-2008

Because adaptive markets are constantly evolving, the ability to explain what happened in the past does not guarantee an equal ability to accurately forecast the future. Yet without an understanding of the past, the future is bound to be even more surprising when it arrives. With this in mind, we have taken a closer look at the dynamics of real asset class returns over the past three years, and reached some conclusions about their implications for our future approach to asset allocation.

Our starting point is the following table, which shows the correlation of real monthly USD returns between a number of asset classes between January 2006 and December 2008.

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As you can see, the positive correlations between these asset classes were extremely strong, as was their average negative correlation with volatility. This is what people mean when they say that “correlations went to one during the crisis”, and in so doing reduced the expected downside risk protection from holding a diversified portfolio.

On the other hand, not all asset classes had such strong correlations with volatility over this period. The correlation between short term U.S. Treasuries and Volatility was positive, at .17. Correlations were essentially neutral with Swiss Francs, gold, and timber (note, however, that in this analysis we use the NCREIF Timber Index, instead of Plum Creek Timber (PCL), because the latter, in its REIT form, does not go back to 1990. However, the NCREIF series is appraisal based, and we have interpolated its values from quarterly to monthly, both of which distort its comparative meaning – e.g., by artificially reducing its standard deviation and correlation). Correlations with volatility were also reasonably low, though still opposite signed (i.e., their returns went down somewhat when volatility went up) for real return bonds (.34), domestic bonds (.25), foreign currency bonds (.24) and commodities (.25), as measured by a long position in a fund tracking the DJAIG Index.

We also checked to see if monthly returns for different asset classes were truly independent, as is usually assumed in asset allocation analyses. Our approach was to measure correlations of different asset class returns on their own one and two months prior returns. Using data covering the full 1990 to 2008 period, we found that while most returns were close to zero (as theory would lead you to expect) some clearly exhibited what is known as “autocorrelation.” For example, one month autocorrelations (and again, remember that this only captures linear relationships) were .47 for inflation, .52 for real returns on short term Treasuries, .24 for foreign commercial property, .23 for the Swiss Franc, .18 for foreign currency bonds, .17 for domestic bonds and .16 for commodities. Using a two month lag, we found that short Treasuries still exhibited a significant autocorrelation, at .21, while real return bonds had a negative autocorrelation of (.26). This has an important implication.

The usual practice in asset allocation analyses is to scale up monthly returns data to annual returns by raising them to the twelfth power. The underlying assumption is that the data are independent; however, the non-zero autocorrelations show that this isn’t the case. Hence, using the “power of time” approach introduces an estimation error into the data. The way to get around this is to calculate average annualized returns not by adjusting monthly returns, but rather directly, on a rolling basis (e.g., January to January, February to February, etc.).

We next did a principal component analysis of the rolling annual returns realized from January 2006 to December 2008. PCA is a statistical technique that reduces the variation in a given set of variables to variation in a smaller number of independent underlying factors.

For example, assume you have four variables in a data set. Variables one and two may have a very strong positive correlation with factor A (technically, principal component A), while variables three and four have a strong negative correlation with factor B. The art in this type of analysis lies in making inferences about just what those statistical factors represent in the real world. The first factor we extracted from this data set explained 49% of its variation (i.e., 49% in the variation of returns). It had very strong positive correlations with domestic property (.69), foreign property (.87), domestic equity (.84), foreign equity (.92) and emerging equity (.85). It also had moderately strong positive correlations with all other asset classes but two. Its positive correlation with short term Treasuries was only .12, and it had a very strong negative .86 correlation with volatility, as measured by the VIX Index. It doesn’t take much art to interpret the real world meaning of this factor: it was the enormous uncertainty shock that hit the world’s financial markets in 2008.

The second factor explains 18% of the variation in our returns data. It had strong negative correlations with real return bonds (.49), domestic bonds (.63), short term Treasuries (.86), and timber (.62, but again we caution about the uncertainty inherent in the NCREIF data series). It had moderately positive correlations with all equities and domestic property, and close to zero correlation with commodities and gold. After looking at a variety of economic data, this factor seems most consistent with changes in real bond yields. For example, looking back to the increase in real yields that occurred in 2006, we found that commentators generally believed this would be good for equities, as it would prevent the economy from becoming too overheated.

The third factor explains 12% of the variation in returns. It is highly correlated with returns on commodities, and to a lesser extent gold, timber, emerging market equities, real return and foreign currency bonds. It has a moderately negative correlation with domestic bonds, short term Treasuries and domestic equities and property. We interpret this factor as the commodities cycle, which peaked in July 2008, and brought with it rising fears of higher inflation, the sustainability of the U.S. current account deficit, and the future of the U.S. dollar exchange rate. Overall, these three factors – the uncertainty shock, changes in real interest rates, and the commodities cycle, account for 79% of the variation in real returns on our asset class series between 2006 and 2008. Intuitively, these explanations resonate with our memory of that period.

Our next step was to perform the same analysis on rolling 12 months returns data from 1991 to 2005 to see if these same factors were present. We admit to feeling somewhat akin to the 9-11 Commissions, going back to see what dots were present in the past that we had failed to properly connect. Sure enough, we found the same factors present in the data. The real interest rate cycle explained 19% of the observed returns, though the correlations were somewhat different (e.g., more strongly positive for domestic and emerging market equities, and more negative for volatility). The commodities cycle again explained 12% of return variation, with quite similar asset class correlations. However, uncertainty shocks had a much smaller impact in the earlier period, explaining 27% of variation, compared to 49% in 2006 – 2008. Moreover, in the earlier period, the correlation of volatility with this factor was about half as strong as in the later period, and the correlation with property and equity markets was also lower, though not by as much. Also, in the earlier period, commodities, gold, timber, and real return bonds had low correlations with the factor, while in the later period these were largely replaced by short term Treasuries, and to a lesser extent, timber. In sum, in the 1991 – 2005 data we see some indications of the impact of uncertainty shocks on asset class returns, but not to the degree that we saw in 2006 – 2008. The fact that the top three factors explain 79% of variation in the later period, but only 58% in the earlier period reinforces this point – there were clearly more factors with a relatively stronger effect on returns in the earlier period than there were over the past three years, which were dominated by the uncertainty shock.

In broad terms, however, the results of both PCA analyses are consistent with a view that asset class returns can be segmented into three different regimes. One is characterized by the normal business cycle, exemplified by rising and falling real interest rates. We would expect the supply and demand for returns on different asset classes to be relatively well balanced during this regime, which is most consistent with idealized markets that are in equilibrium and characterized by efficient pricing. The other two regimes represent departures from this equilibrium, in which we would expect to see less efficient pricing and wider gaps between the expected supply of and demand for returns on different asset classes. The dominant characteristic of the first disequilibrium regime is elevated uncertainty. The dominant characteristic of the second is elevated inflation. To test these ideas, we divided monthly real returns from 1990 to 2008 into three groups. Fifty high volatility months had changes (either positive or negative) in volatility of 20% or more. Fifty four high inflation months had a change in the CPI of .4% or more (i.e., almost 5% per year). The remaining months were deemed to be in the normal regime. The following table shows the average monthly return and standard deviation for each asset class under each regime, as well as within regime rankings of relative returns and risks.

This table illustrates a number of interesting points. First, the difference between the regimes is clear. Second, there are obvious benefits to hedging against the downside risks represented by the high uncertainty and high inflation regimes. Third, an allocation to volatility represents a potentially powerful way to limit tail risks, though at the cost of lower returns during the normal regime. In the past, we have noted that investable volatility products are based not on the VIX index, but rather on futures contracts on the VIX, which usually have much lower price fluctuations, which reduce their potential value as a hedging investment.

However, this analysis has refined our views on these products. Even if you assume that the returns on VIX futures (which are now available to retail investors via Barclays VXX exchange traded note) equal only 33% of the returns on the underlying index, the above table suggests they may still be a good hedging investment in some portfolios. While further analysis will be needed to determine when that will be the case, we are encouraged by what appears to be a real opportunity for reducing the potential return impact of tail risk in portfolios.

Fourth, gold (which is now more easily accessed via ETFs) also has attractive hedging benefits. However, as an asset class (as opposed to a liquid store of value, in the case of gold coins), gold apparently provides fewer hedging benefits than volatility. Again, more analysis will be needed to determine if this applies to all portfolios, or whether gold as a financial asset class distinct from commodities may in some cases have a permanent role. Fifth, and consistent with many other studies, the table also shows that relative risk rankings are much more consistent across regimes than relative return rankings.

Finally, while we have not shown them, our analysis of the correlations between asset class returns under the three regimes found what many readers would expect: correlations are lowest under the normal regime, highest when volatility is high, and in the middle under the inflation regime.

As we noted at the outset, because adaptive markets are constantly evolving, the ability to explain what happened in the past does not guarantee an equal ability to accurately forecast the future. Yet an understanding of the past can surely help us to better prepare for the future, even if we cannot accurately forecast the exact form it will take. In our case, we have for some time been working on a new portfolio construction methodology that will be based, in part, on an expanded regime switching methodology that incorporates the lessons we have just reviewed. Where we used good and bad regimes in the past, we will be moving to a three regime model, with more significant differences in the risk, return and correlation assumptions under each regime.

In addition, because estimation errors are inescapable in any asset allocation analysis, we will also continue to employ shrinkage methodologies to limit their potential impact. We believe that these changes will further improve a portfolio construction methodology that has already proved its mettle under some very challenging circumstances.

That said, we also reiterate two key points: all asset allocation methodologies contain inescapable shortcomings. For that reason, they must always be complemented with ongoing asset class valuation analyses (based on a mix of approaches, like our fundamental and scenario based methodologies), as well as a willingness to occasionally move beyond relatively passive risk management techniques like diversification and automatic rebalancing, and employ more active hedging measures like moving to cash or buying options.