In their seminal study, Fama and French (1992) concluded that stock returns vary systematically across two dimensions: size and value-growth. Today, everyone uses these two dimensions.
Size: The usual measure of a firm’s size is its market capitalization. As the name implies, a firm’s market capitalization (also called market cap or, simply, cap) is the product of stock price and shares of common stock outstanding. Not surprisingly, there is no universal standard used to separate small-cap, mid-cap, and large-cap stocks in the U.S. One person’s definition of small, mid, and large will differ from another.
The widely used and respected Morningstar defines large-cap stocks as those comprising the largest 70% of the market value of all U.S. stocks. Mid-cap stocks comprise the next 20% of the market value of all U.S. stocks, while small-cap stocks comprise the smallest 10%. Naturally, using Morningstar’s system causes the separations between large- and mid-cap and between mid- and small-cap stocks to vary through time.
I have recently read multiple sources that separate large- and mid-cap U.S. stocks at $10 billion market capitalization and separate mid- and small-cap U.S. stocks at $3 billion. Although I prefer Morningstar’s approach, at least in mid-2017, a useful separation for U.S. stocks would be the following:
|U.S. small-cap stocks
||< $3 billion
|U.S. mid-cap stocks
||$3 billion to $10 billion
|U.S. large-cap stocks
||> $10 billion
Another useful separation of stocks by size is to view the Russell 1000 index as a large- and mid-cap index. The Russell 1000 is the largest 1,000 U.S. stocks and is updated annually. It represents roughly 90% of all stocks. The Russell 2000 represents the 1,001st to 3,000th largest stocks in the U.S. and it, too, is updated annually. The Russell 2000 is the most popular index of small-cap stocks. The Russell 3000 combines the Russell 1000 and Russell 2000 indexes, and thus contains the largest 3,000 stocks. The Russell 3000 is considered a total stock market index; if misses some micro-cap stocks, but is still complete enough to be considered a total U.S. stock market index.
Value-Growth: The second dimension is value-growth. There is less agreement on how to separate stocks along this dimension. Fama and French (1992) separated stocks along this dimension using a stock’s book/market ratio. That is, the ratio of book value of equity per share to stock price per share. The inverse of the book/market ratio is the price/book ratio, which is a ratio that is frequently used by investment professionals. Another ratio that is frequently used to separate stocks along this value-growth dimension is the earnings/price ratio. Investment professionals typically use its inverse, the price/earnings ratio. There can also be differences due to the measure of earnings. Some of these measures include 12 month trailing earnings and forecast year-ahead earnings. Morningstar uses a combination of book/market and projected earnings/price to separate stocks into value versus growth stocks. For more information on how Morningstar separates stocks along the value-growth dimension, see Reichenstein (2004). Moreover, there are other ways to separate stocks along the value-growth dimension. Some of these include sales/price ratio, cash flows/price ratio, and dividend yield, that is, dividends/price ratio. Value stocks tend to have high values of these ratios, while growth stocks tend to have low values of these ratios.
Let me explain why book/market and earnings/price are better measures for use in regression analyses that are used in academic studies than price/book or price/earnings. Consider the price/earnings ratio. A value stock has a low ratio. For example, a stock selling at 10 time earnings may be viewed as a bargain (a.k.a., value) stock. In contrast, a growth stock may sell for 30 times its earnings; as the name implies, since a growth stock’s earnings are expected to grow fast, investors are willing to pay more for each dollar of earnings. To understand the problem of using the price/earnings ratio in regression analyses, consider a firm with negative earnings. It is not considered a value stock. However, its price/earnings ratio would be negative, thus implying it is a value stock. Another problem with using price/earnings (PE) ratios in regression analyses is for firms with near zero earnings. Consider two stocks, each selling at $50. One has earnings of -$0.01 and the other has earnings of $0.01. Their PE ratios are extreme values of -5,000 and 5,000, which on the surface seems to imply an extremely value-oriented stock and an extremely growth-oriented stock. The earnings/price ratio avoids these mischaracterizations. Both stocks sell at earnings/price ratios of essentially zero. So, they are not value stocks. Earnings/price ratios avoid the mischaracterizations from using price/earnings ratios. The value stocks are selling at high earnings/price ratios, while growth stocks are selling a low earnings/price. In short, by having price in the denominator, the earnings/price avoids the problems of defining value versus growth stocks for firms this either negative earnings or earnings near zero.
Separately, there are a few firms that have negative or near zero book values, too. These firms may have acquired other firms at prices that were much higher than their book values. The accounting treatment of such acquisitions could cause the acquiring firm’s book value to be negative or near zero. As before, in contrast to price/book ratios, book/market ratios do not mischaracterize such firms at value stocks. That is, having market price in the denominator avoids these mischaracterization problems. Thus, Morningstar uses earnings/price, book/market (price), cash flow/price, revenue/price, and dividend/price to separate stocks along the value-growth dimension.
 Eugene Fama and Kenneth French. 1992. “The Cross Section of Expected Stock Returns,” Journal of Finance, vol. 47, no. 2, 427-465.
 William Reichenstein. 2004. “Morningstar’s New Star-Rating System: Advances and Innovations,” Journal of Financial Planning, March, 42-49.