Since Rolf W. Banz first posited the size effect of equity returns in a 1981 study published in the Journal of Financial Economics, the relative outperformance of small-capitalization (small-cap) stocks compared to large-capitalization (large-cap) stocks has remained a steady point of debate within the investment management literature.
Even a cursory review of the annualized returns since the inception of the S&P SmallCap 600 index shows that the small-cap index has produced a higher cumulative return than the large-cap S&P 500 index (209.02% versus 188.13%).
The nature of this outperformance has been one of the central points of discussion within the literature. Of primary concern is the variability over time of this outperformance, as discussed in a 1983 Journal of Financial Economics study by Philip Brown, Allan W. Kleidon, and Terry A. Marsh. Sherman Hanna and Peng Chen found that small-cap equities were riskier equity investments relative to large-cap equities for holding periods of less than 15 years, while they were less risky for holding periods of longer than 15 years in their July 1999 AAII Journal article, “Small Stocks vs. Large: It’s How Long You Hold That Counts.”
A review of Eugene Fama’s and Kenneth French’s small-versus-big index series shows that in monthly returns between July 1926 and February 2012, small-cap stocks outperformed roughly 51% of the time. During that time, small-cap stocks also delivered a cumulative excess return of 253% relative to large-company stocks.
Given the variability of relative returns of small-cap equities versus large-cap equities, the question for investors is which environments or economic conditions are most conducive to small-cap stocks outperforming large-cap stocks. This article explores this very question. We explore several hypothesized scenarios that conceptually make sense as to producing favorable environments for small-cap stocks.
Modern portfolio theory as espoused by Harry Markowitz suggests that assets that demonstrate higher levels of risk, as defined by standard deviation (“volatility”), would require higher levels of returns to investors for assuming the additional relative risks versus other assets. Therefore, for investors who have higher tolerances for risk, higher standard deviation assets, over time, should produce higher returns. Investors often assess the value of underlying organizations via some form of discounted cash flow. Equity prices then reflect the perceived value of these discounted cash flows, as suggested by Jonathan Berk in a 1997 Financial Analysts Journal study.
More precisely, equity prices, more often than not, attempt to reflect the visibility of these discounted cash flows. Small-cap stocks tend to have three primary characteristics that diminish the visibility of future cash flows. First, small-cap stocks will often have shorter track records upon which to build cash flow assumptions. Second, small-capitalization companies may be less widely followed by Wall Street analysts. Lastly, investors may perceive small-capitalization stocks as more economically sensitive assets. All of the above factors may have implications as to when small-cap stocks should theoretically outperform less risky equity assets.
As Zaugang Liu and Jia Wang surmised in a 2010 Financial Services Review article, large-cap growth stocks appear to be the safest equity investment for investors with short time horizons, while small-cap equities are the most profitable for long-term investment horizons. However, these findings consider only time horizon and do not sufficiently explore the variability of returns across changing macroeconomic conditions. With respect to the economic sensitivity and visibility of future cash flows, it would intuitively follow that higher risk assets that are more economically sensitive may outperform in time of improving macroeconomic conditions and conversely underperform in times of deteriorating economic conditions. This leads us to hypothesis #1 and hypothesis #2:
Our third hypothesis is born out of observations by LeRoy Brooks and Gary Porter, in their 2012 Financial Services Review study. They found that there is a growing body of literature that suggests investors can extract portions of stock market returns by exploiting various information signals related to size, style and other subsets of the broad market. Sector rotation strategies have long been a method for investors to attempt to extract such portions of equity returns. However, the literature has not given ample attention to examining the size effect of sector rotation. Within sector rotation strategies, investors posit that by making the appropriate sector allocation at the various points in the economic cycle, they can add excess returns to the broad market. If we extend this argument beyond just the sector allocation to include a size allocation as well, the question arises as to whether the presumably higher-risk and thus higher-reward small-cap equities within those specific sectors will perform better. Therefore, our third hypothesis is presented:
Our two hypotheses attempt to address small-cap equity performance relative to that of their large-cap counterparts. In this study, we are attempting to address how small-cap equities perform under various conditions:
To explore our first premise, we have gathered quarterly U.S. economic data via GDP and U.S. unemployment rates as provided by the U.S. Bureau of Labor Statistics. We have also gathered small-cap equity returns relative to large-cap equity returns. For this, we have used the Fama and French small-versus-big index returns. This data series extracts the excess returns of small U.S. equities versus large U.S. equities as defined by market capitalization. The intent is to determine whether these points of economic data can be used as predictive measures of when to favor large-cap equities versus small-cap equities in investment portfolios.
With these data sets we then cross-referenced the excess returns of small-cap equities against various time periods within the GDP and unemployment series.
To examine the concept of a size effect on equity sector rotation strategies, we gathered monthly investment index returns of the large-cap S&P 500 index, the S&P SmallCap 600 index and each of their respective sector indexes. We then calculated periods of positive equity returns as found within the broad market index (S&P 500). We then calculated excess returns of each sector of the S&P 500 relative to the S&P 500 itself, which would then indicate favorable conditions to allocate additional assets to that sector. Lastly, we calculated the excess returns of the small-cap sector to the broad market.
The findings suggest that there are certain economic conditions that are more favorable for small-cap excess returns relative to large-cap equities.
An examination of the GDP data series suggests that in a period of expanding economic activity—i.e., when GDP is increasing—small-cap stocks tend to outperform large-cap equities. Further, the data suggests that for the four quarters following the official end of a period of contracting economic activity, small-cap equities outperform large-cap equities. In our data series going back to 1948, we identified 10 periods of prolonged contracting economic activity sufficient enough to be labeled a recession. Following the end of those recessionary periods, small-cap equities outperformed in nine of the 10 recessions in the ensuing four quarters. These recessions are listed in Table 1 along with the cumulative excess return of small caps in the following four quarters.
These periods of excess returns were analyzed and found to be statistically significant. Further, small-cap equities produced cumulative excess returns of 89.5% for all these periods, inclusive of the 1953 recession when small-cap stocks delivered negative excess returns.
|Post 12 Mo.|
We also ran correlations of the small-cap excess returns to periods of rising and falling GDP and found that small-cap excess returns were negatively correlated to falling GDP and the results were statistically significant. Small-cap excess returns were only slightly positively correlated to the entire data series. Therefore, Hypothesis 1 is accepted.
We conducted a similar analysis of small-cap excess returns against U.S. unemployment rates, again using quarterly data going back to the first quarter of 1948 through the fourth quarter of 2012. Small-cap excess returns were found to be only slightly negatively correlated (–0.14) to unemployment rates and the results were not statistically significant. Therefore hypothesis #2 is not accepted.
|Recession/Falling||Post 12 Mos.|
However, we did cross-reference periods of expanding GDP following a recession, which also corresponded to a cumulative drop in unemployment rates during the same four-quarter period. Examining the four quarters following a recession where unemployment rates were also falling, we identified seven time periods. As shown in Table 2, small-cap equities delivered excess returns in six of those seven periods, a success ratio of 86%. During these seven periods, small caps delivered excess returns of 38.48% relative to large caps.
This analysis was performed under specific assumptions. First, we determined periods of favorable equity returns as measured by positive monthly returns of the S&P 500 index, also referred to as the broad market. We also then identified periods in which each of the 10 respective S&P 500 sectors outperformed the broad market. Operating from the premise that higher-risk assets in times of favorable equity environments should produce higher returns, we then calculated whether the small-cap sector counterpart (S&P SmallCap 600) outperformed their large-cap counterpart.
The results demonstrated high percentages of outperformance for each of the respective small-cap sector indexes. There were 220 monthly periods observed in our data set. Table 3 demonstrates how often each of the respective large-cap sectors outperformed within the 220 monthly periods. Further, the table demonstrates how often the small-cap sectors outperformed when the large-cap sector was in favor. Additionally, the table illustrates the cumulative excess returns of the small-cap sectors versus the S&P 500 during the periods of outperformance of the large-cap sectors relative to the broad market.
|# Times||# Times||Outper-||Small-Cap Sector|
|Large-Cap Sector||Small-Cap Sector||formance||Excess Returns|
The results show that all small-cap sectors added excess return when the large-cap sectors were in favor. Additionally, all of the small-cap sectors added excess returns more than 50% of the time. Utilities, materials, information technology, healthcare, energy and consumer staples all outperformed 70% or more of the time. The excess returns of each small-cap sector, with the exception of the utilities sector, were statistically significant, providing a relatively high level of confidence in providing excess returns via a small-cap sector usage in a sector rotation strategy. The least-consistent small-cap sectors were consumer discretionary and financials, only outperforming 57% and 61% of the time, respectively. However, the excess returns of the consumer discretionary sector were statistically significant.
Excess returns of small-cap equities versus large-cap equities within the examination of post-recessionary periods and periods of falling unemployment were conducted relying on underlying index methodology as presented by Fama and French’s definitions of small stocks versus large stocks.
Excess returns at the sector level were conducted with the index construction methodology of Standard & Poor’s, using the S&P SmallCap 600 as the definition of small-cap equities and the S&P 500 as the definition of large-cap equities. This was done given the prevailing popular acceptance of the S&P sector definitions within the practicing investment profession.
Results of this study may be influenced by the reliance on these distinct methods of index construction. There are numerous readily accepted means of index construction (index providers, market-cap weighted, fundamentally weighted, etc.) that may vary the meaningful contribution of excess returns of small caps versus large caps as defined by those varying methodologies. Future research may look to aggregate excess returns from various index methodologies.
Our analysis of excess sector returns assumes that an investor demonstrates a high level of proficiency at making the appropriate sector ‘bet’ at the appropriate time. The value of these findings may be limited by investor proficiency. The discussion as to whether investors can, with any proficiency, correctly identify and allocate assets to the appropriate sectors relative to the broad market is a separate discussion for another research effort.
This study attempted to examine the nature of the variability of excess returns of small-cap equities relative to large-cap equities. Given Markowitz’s assertion that higher-risk stocks should deliver higher returns to investors, it is presumed that small-cap stocks with their higher standard deviation would need to deliver excess returns to investors for that additional risk. The variability of these excess small-cap returns is a problem that has been noted throughout the investment management literature.
This study sought to examine specific assumptions as to whether there are identifiable economic periods where these excess returns are more likely to occur. Our findings suggest that investors have higher probabilities of capturing small-cap excess returns in times of economic expansion immediately following recessionary periods. Further, we found that investors can also capture relative excess returns at the sector level by investing in the small-cap sector when the accompanying large-cap sector is outperforming the broad market. While the findings are not meant to be a definitive approach to any specific investment process, it does help provide some direction in the further exploration of the variability of small-cap excess returns over time.