Center for Financial Innovation and Stability

Notes from the Vault
Nikolay Gospodinov
November 2017

The prevailing view in the last few years is that of increased correlation across asset classes: stock prices went up and Treasury bond prices went down during "risk-on" periods with the reverse during "risk-off" periods. In this and other similar episodes, it is often tempting to build a narrative around the conjecture that the observed asset co-movements—within equity space, across asset classes, or across international markets—are driven by a common risk factor or a set of risk factors. However, eventually market conditions change and asset return dynamics can no longer be explained by such a simple narrative.¹ For example, the "risk-on/risk-off" story appears to have lost its appeal recently. Thus, financial economists are trying to identify a common set of risk factors that influence asset prices in a predictable manner; that is, there is a stable common factor structure. Despite a number of number of promising theoretical models, however, empirically extracting these factors has proven daunting.

In a recent Atlanta Fed working paper (see also my presentation at the 2017 Atlanta Fed Financial Markets Conference), I document and characterize the main regularities in the asset co-movements across asset classes over time. I argue that while some of the time variation in the asset correlations could be genuine, the noisy and volatile nature of the observed daily or weekly (high-frequency) returns can distort significantly the slow-moving signal coming from common factors. The analysis at longer horizons and time spans provides a more reliable platform for recovering the underlying factor structure. At this lower frequency, asset prices appear to be driven by business cycle and demographic factors. Here I summarize some of the main observations and findings.

Short-term risk factors
The analysis of asset co-movements and changing correlations is especially precarious at high frequency. At high frequency, the asset co-movements are driven primarily by short-term macro fluctuations, political events, sentiment (behavioral factors), and so on that are likely to induce movements in asset risk premia. Since the 2008 financial crisis, for example, there have been several episodes when the correlations between different asset classes were elevated but dropped off quickly afterwards and exhibited substantial variability. Is this dynamic due to fundamental (macroeconomic, geopolitical, demographic) factors that affect the long-term behavior of asset prices, or transient factors that are reflected only temporarily in the asset risk premia? Can we reliably isolate, in real time, the underlying source of risk from data and estimation noise? Is the most recent reading of an economic indicator sufficient to force any asset reallocation or policy reaction?

Over short time spans, the transient (genuine but short-lived) and spurious (completely coincidental) co-movements appear, in many cases, observationally equivalent—in the sense that they cannot be distinguished empirically. This makes it particularly difficult to determine if the time variability of these co-movements is a true feature of the data or a statistical fiction.

The problem is exacerbated by strong persistence of variables like yields, volatility, and prices, which could render the co-movement purely coincidental or completely spurious. A 2016 macroblog I cowrote with Paula Tkac and Bin Wei discussed the tenuous and elusive nature of these transient factors in the context of the observed elevated correlation between oil prices and market-based measures of inflation compensation between 2015 and mid-2016. In summary, almost all of the short-term variation in inflation compensation, inferred from bond prices, can be attributed to liquidity and inflation risk premia that appeared to drive the correlation with oil prices during this period. Other assets—such as the U.S. dollar, S&P 500, and high-yield bonds—have also exhibited a transitory co-movement with oil prices. While this episode suggests there are implications for financial stability when a highly volatile asset is the driver of the asset co-movements, the appropriate response would depend crucially on properly classifying the source of the co-movement as transitory, reflected in asset risk premia only, or as fundamental.²

Risk factors at business cycle frequency
Given the limitations of high-frequency data, it may be desirable to approach the problem of identifying a common factor structure from a long-run, low-frequency perspective. The factors that operate at low (business cycle and lower) frequency are more structural in nature and include macroeconomic, geopolitical, and demographic factors. Their slow-moving dynamics allow for a more reliable signal extraction and identification of the fundamental sources of risk.

Still, determining if macroeconomic risk is an important determinant for asset co-movements requires care. For example, in asset pricing models for equity returns—after properly accounting for estimation and model uncertainty—there is only weak evidence of priced macroeconomic risk (see, for example, Gospodinov et al., 2017). One potential reason for this puzzling result is the mismatch between the frequency for which the models are designed and the frequency at which they are empirically evaluated. Matching the frequency better—and the statistical properties of the data at this frequency—would help to isolate the common low-frequency movements in asset returns and relate them to macroeconomic and demographic factors.

One interesting question to ask is, "Is there a common factor structure in expected asset returns?" (See Cochrane, 2015.) To address this question, I consider two sets of asset returns: (1) domestic returns for four U.S. asset classes: S&P 500 index, Bloomberg Barclays Treasury total return index, Goldman Sachs commodity index, and U.S. dollar (USD) index; and (2) international stock returns for the United Kingdom index (FTSE), Japanese index (Nikkei), German index (DAX), and emerging markets index (MSCI).³ All the series have daily returns for the period January 2000–February 2017. The common factors are estimated as the first principal component of domestic and international returns, which are then transformed as in Bai and Ng (2004). This is a dimension-reduction statistical method that constructs a small number of uncorrelated variables (principal components), which explain the largest fraction of the variability of the original data. The estimated common factors for U.S. and international asset returns are plotted in chart 1.

The domestic common factor is the blue line and the global asset factor is the green line. The shaded areas represent the two National Bureau of Economic Research (NBER)-dated U.S. recessions over this period. Several interesting observations emerge from this graph. First, both the domestic and global factors exhibit pronounced business cycle variation with some higher-frequency cycles that are more difficult to identify. The largest weights in constructing the domestic factor are assigned to stocks, bonds, and commodities. For the global factor, most of the contributions to its dynamics come from FTSE, DAX, and emerging markets. On the other hand, the USD and Nikkei are characterized with a large idiosyncratic component. This is reassuring evidence for the widely held belief that macroeconomic risk drives the asset price dynamics at business cycle frequency. Another important observation is the close similarity between the domestic and global asset factors despite the heterogeneity (in terms of assets and unit of denomination) of the underlying series. Although the co-movement between the U.S. asset factor and business cycle extends back in time, the empirical commonality between domestic and global asset dynamics is a fairly recent phenomenon and it lends support to the finding of a substantial international market integration since the early 2000s (see, for example, Cotter et al., 2016).

The common business cycle variation in asset prices warrants further inspection and validation. For that purpose, the figure superimposes (in orange line) the Atlanta Fed/New York Fed smoothed business cycle indicator that is entirely based on disaggregated labor market information. It is striking how closely this business cycle indicator underlies the common dynamics in domestic and global financial asset prices. This simple exercise provides indirect, but rather strong, evidence that macroeconomic risk matters for asset pricing.

Demographic risk factors
But is there any common variation in asset prices at even lower frequency than that of the business cycle? The recent literature⁴ has established the usefulness of low-frequency demographic variables for long-horizon stock market returns through their effect on savings rates and risk preferences over the life cycle. More specifically, slowly moving demographic trends may explain and predict some of the very persistent, low-frequency movements in stock market valuation ratios, such as the dividend- or earnings-price ratios, that have been documented in the literature. To entertain this possibility, I construct a smoothed common factor from annual data for S&P 500 returns, returns on long-term and intermediate-term U.S. government bonds, changes in S&P 500 price-dividend ratio, changes in S&P 500 dividend yield, and changes in S&P 500 earnings-price ratio for the period 1946–2016.⁵ Chart 2 plots this smoothed common factor in blue.

The long-run demographic trends are proxied by the middle-young (MY) ratio of middle-aged (40–49) and young (20–29) cohorts obtained from the U.S. Census Bureau. In addition to the historical data, the Census Bureau provides projections until 2060. Chart 2 plots the actual MY ratio for 1946–2016 as a solid green line and its projections until 2014 as a dashed green line. Again, the commonality between the long-cycle asset factor and demographics is striking. Despite the simplistic and highly stylized design of this exercise, the projected MY ratio until 2020 is expected to exert a downward pressure on stock valuation ratios and interest rates due to demographic factors, which are diminished and reversed between 2020 and 2040. While these projections reflect pure demographic information⁶ and are only suggestive about the future long-term path of U.S. asset returns, they conform to a broader set of arguments put forward in the literature regarding the effect of demographics on equilibrium real interest rates, labor productivity, and so forth (see, for example, Fed Vice Chairman Stanley Fischer's speech, 2016).

Conclusion
This post argues that attaching a risk factor interpretation to short- and medium-term co-movements is challenging given the massive amount of sampling, estimation, and model uncertainty surrounding the data analysis. However, a judiciously performed factor analysis appears to identify a common variation across domestic and international asset classes at business cycle and lower frequencies.

The issues discussed above have important implications for long-term investment decisions and policy analysis. For example, once the risk factors are properly identified, the implied dynamics of these risk factors can be mimicked with other traded assets that approximate well the underlying factor structure. Explicitly acknowledging the estimation and model uncertainty, as well as employing more general measures of dependence, would further make more robust the decision process of investors and policymakers.

References
Bai, Jushan, and Serena Ng (2004). "A PANIC Attack on Unit Roots and Cointegration." Econometrica 72 (4), 1127–1177. Available behind a paywall at http://onlinelibrary.wiley.com/doi/10.1111/j.1468-0262.2004.00528.x/full.

Favero, Carlo A., Gozluklu, Arie E., and Andrea Tamoni (2011). "Demographic Trends, the Dividend-Price Ratio, and the Predictability of Long-Run Stock Market Returns." Journal of Financial and Quantitative Analysis 46(5), 1493–1520. Available behind a paywall at https://www.cambridge.org/core/journals/journal-of-financial-and-quantitative-analysis/article/demographic-trends-the-dividendprice-ratio-and-the-predictability-of-longrun-stock-market-returns/501622627339E570B62FEFB964D2D7AB.

Nikolay Gospodinov is a financial economist and adviser at the Atlanta Fed. The author thanks Paula Tkac and Larry Wall for numerous comments and discussions that led to a significantly improved exposition. The view expressed here are the author's and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. If you wish to comment on this post, please email atl.nftv.mailbox@atl.frb.org.

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¹ The "shifting sands" in identifying global risks was the topic of this year's Atlanta Fed Financial Markets Conference. But the uncertainty surrounding popular economic concepts and policies has featured prominently in several of our most recent conference themes.

² Reliable extraction and classification of common factors is also of great importance for investment management (portfolio allocation, factor investing, and so on). The paper discusses several examples that may result in suboptimal investment strategies and mischaracterization of risk events if data and model uncertainty are not properly accounted for in the statistical procedure.

³ The source of the data is Bloomberg. The S&P 500 is intentionally omitted from the international stock returns to avoid any overlap between the domestic and international returns. The results for international stock returns in local currency and USD are very similar, but I report the results in local currency in order to avoid inducing common variation through the USD in both sets of returns.

⁴ See Geanokopolos et al. (2004), Favero et al. (2011), among others.

⁵ The data for the government bond returns are from Ibbotson Associates and the stock price data are from Robert Shiller's and Amit Goyal's websites.

⁶ The middle-young ratio could be just a convenient proxy for other slowly moving socioeconomic and political factors such as safety-net development and political polarization. Also, the demographic projections are based on assumptions about future immigration dynamics, which are influenced by policy decisions. Finally, there may be other factors, such as technological change, that could affect long-horizon asset returns.