From the standpoint of traditional finance, small stocks are riskier than large stocks and thus contain a risk premium, which should translate into higher expected returns.
In 1981, Rolf Banz’s study, “The Relationship Between Return and Market Value of Common Stocks,” found market beta doesn’t fully explain the higher average return of small stocks. From July 1926 through 1981, the monthly size premium averaged 30 basis points. However, from January 1982 through November 2014, the monthly premium has averaged just 10 basis points. As a result, the premium has been called into question. Has it shrunk, or even disappeared?
Today, it’s both much easier and less costly to diversify the risks of small stocks, through mutual funds and ETFs, than it was during the period Banz studied. In addition, trading costs, in the form of commissions and bid-offer spreads, have come way down. Thus, we shouldn’t be surprised that the size premium may have shrunk over time.
The size premium issue is complicated by a well-known anomaly. While small value stocks have provided higher returns than large value stocks, small growth stocks have provided lower returns than large growth stocks. Using the Fama-French research indexes, the annualized returns from July 1926 through November 2014 for each of the four asset classes are:
- Small Value: 14.9 percent
- Large Value: 12.0 percent
- Large Growth: 9.6 percent
- Small Growth: 8.7 percent
While they produced lower annualized returns than large growth stocks, small growth equities exhibited higher volatility. The annualized standard deviation of returns over this period was 18.5 percent for large growth and 26.5 percent for small growth. Note that the standard deviations for small value and large value were 24.7 percent and 28.5 percent.
Thus, from a traditional finance viewpoint, the returns and volatility of large growth, large value and small value stocks line up as they should. Higher returns are positively correlated with higher volatility. Returns and volatility of small growth stocks, however, don’t. This is why small growth stocks have been referred to as the “black hole” of investing, and why they present an anomaly.
The field of behavioral finance supplies us with an explanation for this anomaly. It exists because investors seem to have a preference for “lottery tickets.” Nicholas Barberis and Ming Huang, authors of the NBER working paper “Stocks as Lotteries: The Implications of Probability Weighting for Security Prices,” found that:
- Investors have a preference for securities that exhibit positive skewness, which occurs when values to the right of (more than) the mean are fewer but farther from it than the values to the left of the mean. Such investments offer a small chance of a huge payoff (winning the lottery). Investors find this small possibility attractive. The result is that positively skewed securities tend to be “overpriced,” meaning they earn negative average excess returns.
- Investors’ preference for positively skewed assets explains the existence of several anomalies (deviations from the norm) to the efficient market hypothesis, including the low average return on IPOs, private equity and distressed stocks, despite their high risks.
In theory, we would expect anomalies to be arbitraged away by investors who don’t have a preference for positive skewness. They should be willing to accept the risks of a large loss for the higher expected return that shorting overvalued assets can provide.
However, in the real world, anomalies can persist because there are limits to arbitrage. First, many institutional investors, such as pension plans, endowments and mutual funds, are prohibited by their charters from taking short positions. Second, the cost of borrowing a stock in order to short it can be expensive, and there can also be a limited supply available to short. Third, investors are unwilling to accept the risks of shorting because of the potential for unlimited losses.
This is prospect theory at work. The pain of a loss is much larger than the joy of an equal gain. Fourth, short sellers run the risk that borrowed securities will be recalled before the strategy pays off, as well as the risk that the strategy performs poorly in the short run, triggering early liquidation. Together, these factors suggest that investors may be unwilling to trade against the overpricing of skewed securities, allowing the anomaly to continue.
The conclusion we can draw is that the disappearing size premium issue may be a function of this “black hole,” rather than one that impacts the asset class in its entirety. If you screened out the “black hole” stocks, there would be a size premium possible to capture. Said another way, it’s the higher-quality small stocks that explain the size premium.
Controlling For Quality
Cliff Asness, Andrea Frazzini, Ronen Israel, Tobias Moskowitz and Lasse Pedersen, authors of the January 2015 paper “Size Matters, If You Control Your Junk,” examined the problem of the disappearing size premium by controlling for the quality factor. They observe: “Stocks with very poor quality (i.e., “junk”) are typically very small, have low average returns, and are typically distressed and illiquid securities. These characteristics drive the strong negative relation between size and quality and the returns of these junk stocks chiefly explain the sporadic performance of the size premium and the challenges that have been hurled at it.”
On the other hand, high-quality stocks have the following characteristics: low earnings volatility, high margins, high asset turnover, low idiosyncratic risk and low financial and operating leverage. The research shows these stocks, the kind of stocks Benjamin Graham and Warren Buffett have long advocated, outperform low-quality stocks with the opposite characteristics (“lottery-ticket” equities).
And the authors found that “small quality stocks outperform large quality stocks and small junk stocks outperform large junk stocks, but the standard size effect suffers from a size-quality composition effect.” In other words, controlling for quality restores the size premium.
The authors thus concluded that challenges to the size premium “are dismantled when controlling for the quality, or the inverse ‘junk,’ of a firm. A significant size premium emerges, which is stable through time, robust to the specification, more consistent across seasons and markets, not concentrated in microcaps, robust to non-price based measures of size, and not captured by an illiquidity premium. Controlling for quality/junk (the QMJ factor) also explains interactions between size and other return characteristics such as value and momentum.”
They further discovered that “controlling for junk produces a robust size premium that is present in all time periods, with no reliably detectable differences across time from July 1957 to December 2012, in all months of the year, across all industries, across nearly two dozen international equity markets, and across five different measures of size not based on market prices.” They also note: “When adding QMJ as a factor, not only is a very large difference in average returns between the smallest and largest size deciles observed, but, perhaps more interestingly, there is an almost perfect monotonic relationship between the size deciles and the alphas. As we move from small to big stocks, the alphas steadily decline and eventually become negative for the largest stocks.”
Another important finding was that the higher-quality stocks were more liquid, which has important implications for portfolio construction and implementation.
Controlling For Low Beta
In addition, the authors found similar results when, instead of controlling for the quality factor, they controlled for the low-beta factor. Recall that high-beta stocks (those lottery tickets) have very poor historical returns. High-beta stocks tend to be the same low-quality stocks. They found that small stocks have negative exposure to the two relatively new factors of profitability: RMW (robust minus weak) and CMA (conservative minus aggressive) or investment. High-profitability firms tend to outperform low-profitability firms and low-investment firms outperform high-investment ones.
As a final note of interest, the new Q-factor model (which includes the four factors of beta, size, profitability and investment) is able to explain almost all of the anomalies that plague the prior workhorse model, the Fama-French four-factor model (beta, size, value and momentum). The sole, albeit large, exception is the poor performance of small growth stocks with low profitability.
In summary, the authors concluded that “size matters—and in a much bigger way than previously thought—but only when controlling for junk. Controlling for junk, a much stronger and more stable size premium emerges that is robust across time, including those periods where the size effect seems to fail; monotonic in size and not concentrated in the extremes; robust across months of the year; robust across non-market price based measures of size; not subsumed by illiquidity premia; and robust internationally. These results are robust across a variety of quality measures as well.”
Today, there are various small-cap mutual funds that include screens to minimize exposure to small junk stocks and overweight quality ones. There are also multi-style funds that incorporate profitability into their construction rules so that investors can benefit from the latest academic research.
Larry Swedroe is the director of research for the BAM Alliance, a community of more than 150 independent registered investment advisors throughout the country.