Many investors and advisors who implement multifactor portfolios tend to focus on capturing the value premium over the size premium, often for the simple reason that, historically, the value premium has been larger.
Others have even challenged the size premium’s very existence, citing a weak and varying historical record. In both situations, it may be that the size premium—and specifically the construction of the size factor—is not fully understood.
My colleague Sean Grover, a member of the investment strategy team at Buckingham and The BAM Alliance, put together the following analysis of size factor construction to help address and clarify this issue. He begins with some basic definitions.
Defining The Size Factor
The size factor, as defined by Eugene Fama and Kenneth French, is constructed by sorting all stocks by market capitalization, as determined by market capitalizations of NYSE stocks, into deciles and then taking the weighted average annual return of deciles 6-10 (small stocks) minus the weighted average annual return of deciles 1-5 (large stocks). In other words, it’s the top 50% of stocks ranked by size minus the bottom 50%.
Contrast this with the value factor, which is constructed by sorting stocks on book-to-market ratio and then taking the weighted average annual return from deciles 1-3 (value stocks) minus the weighted average annual return from deciles 8-10 (growth stocks). In other words, it’s the top 30% of stocks ranked by valuation metric minus the bottom 30%.
In this construct, deciles 4-7 are considered core stocks. The 30/30 construction is also used for other established risk factors, such as momentum, profitability, quality and low beta/low volatility. The size factor is the only exception.
Using data from the University of Chicago’s Center for Research in Securities Prices (CRSP), Figure 1 below presents historical returns for grouped market-capitalization deciles.
As illustrated with these market-capitalization deciles, if there’s a premium in some category of stocks over another, then that premium will be larger, the more strictly that category is defined.
As we can see with the more narrow size grouping, as stocks get smaller, their returns get higher.
In addition, the more strictly the category is defined, the more difficult it should be to capture. So in trying to understand the size premium, we ask: How does the construction of the size factor affect the amount of the premium that a portfolio can capture?
Different Perspectives On Size
Kenneth French’s data library provides returns for a variety of percentile sorts on market capitalization. Using these, we are able to build several different versions of the size factor in an attempt to answer our question.
The standard size factor—defined above as the weighted average return of the smallest 50% of stocks less that of the largest 50%—will be designated 50/50. We then construct size factors using the smallest (largest) 30%, 20% and 10% of stocks, which we’ll call 30/30, 20/20 and 10/10, respectively.
Figure 2 shows the historical annual premium for these various definitions of the size factor.
As expected, the more narrowly we define “small cap” versus “large cap,” the larger the annual premium. The standard 50/50 size factor has the smallest annual premium and, notably, the premium resulting from the 30/30 construction is actually larger than the value premium (which is 4.83%). Furthermore, all the annual premiums are statistically significant (meaning they have a t-statistic of greater than two).