Though ‘Size’ is the most important factor explaining stock market returns, the possibility of size being a proxy was first mentioned in Banz (1978). Even after forty years of factor investing the industry is still looking for answers. This paper chronologically lists the research on ‘Size’ and why the question regarding ‘The Size Proxy’ has never been so relevant.
History of Size
After Ball and Brown (1968) work on information content in earnings, researchers looked for further confirmation in financial data relevance. Basu (1977) suggested that Price Earnings had information content. Although it was not clear, size seemed to subsume other variables. Rosenberg and Marathe (1976) observed that macroeconomic events on individual securities could be captured through microeconomic characteristics essentially common factors. While confirmation regarding information relevance continued, it was Bawa and Klien (1977) who suggested that P/E could also fail as an indicator i.e. information content could fail or be insufficient. This was followed by Banz (1978) who discussed fundamental value as a predictive indicator and questioned whether size is just a proxy. He also highlighted the lack of theoretical foundation regarding size. Statmann (1980) observed that Book Value was a key factor while Kiem (1980) suggested that Book Value was a proxy for size. Arbel and Strebel (1983) suggested that small size could be a special case of neglect effect. Since size and book value were still debated, Fama’s argument regarding the ineffectiveness of Beta was challenged by Lakshinok (1993). Beta was not redundant. In 1996 Fama and French accepted that they have stumbled on the factors and do not know why the factors work but continued to highlight the importance of size. Dividend policy irrelevant but driven by size, Fama and French (2000).
‘Investment performance of common stocks in relation to their P/E ratios, Basu, 1977’
“Contrary to the growing belief that publicly available information is instantaneously impounded in security prices, there seems to be lags and frictionsin the adjustment process. As a result publicly available P/E ratios seem to possess information content and may warrant and investor’s attention at the time of portfolio formation or revision…Although it is not clear that the anomalous returns derive explicitly from the failure of the CAPM to account for firm size, several studies have shown that anomalous return behavior associated with firm-specific variables is largely subsumed under the ‘size effect’.”
The research focussed on outperforming low P/E strategy vs. high P/E strategy. P/E was considered to have information content. This seemed in line with the Ball and Brown (1968) work on information content in earnings. For example, Reinganum (1981) finds that the relation between abnormal returns and P/E ratios reported by Basu (1977) appears to vanish after controlling for size.
‘Common Factors in Security Returns: Microeconomic Determinants and Macroeconomic Correlates, Barr Rosenberg and Vinay Marathe 1976’
The research developed the theory that the effects of macroeconomic events on individual securities could be captured through microeconomic characteristics essentially common factors, such as industry membership, financial structure, or growth orientation.
‘The Effect of Limited Information and Estimation Risk on Optimal Portfolio Diversification, Bawa and Klein 1977’
“If insufficient information is available about a subset of securities, investors will not hold these securities because of estimation risk, i.e. uncertainty about the true parameters of the return distribution. If the amount of information is generated on small firms is smaller, many investors will choose not to hold such firms. There is inconsistency in the functioning of P/E. Over time measures are known to lose their predictive strength. There is enough literature on the failure of P/E as a predictive tool and as a factor”
‘The relationship between return and market value of common stocks, Banz, 1978’
“The securities held by only a subset of the investors have higher risk-adjusted returns than those considered by all investors. Why are small firms less risky than the large firms in UK, while the opposite is true in US. The size effect has been in existence for at least forty years and is evidence that the capital asset pricing model is misspecified. The size effect is not linear in market value; the main effect occurs for very small firms while there is little difference in return between average sized and large firms. It is not known whether size per se is responsible for the effect or whether size is just a proxy for one or more true unknown factors correlated with size.There is no theoretical foundation for such an effect…offer some conjectures and even discuss some factors for which size is suspected to proxy. P/E effect a proxy for size. the P/E-ratio effect is a proxy for the size effect and not vice versa.”
‘Book values and stock returns, Stattman D., 1980’
The research finds a positive relationship between average return and BTM for U.S. stocks, as do Rosenberg, Reid, and Lanstein (1985). Chan, Hamao, and Lakonishok (1992) find that BTM is useful in explaining Japanese stock returns.
‘Size Related Anomalies and Stock Return Seasonality, Kiem, 1980’
The research found a significant negative relation between abnormal returns and the degree to which market value of equity exceeds the book value of equity, and also interpret this relation as a proxy for the size effect.
‘The neglected and small firm effects, Arbel and Strebel, 1983’
The research paper argued that the small size effect is just a special case of “neglect effect”; firms that are neglected by security analysts exhibit superior market performance because intensive analyst coverage raises stock prices and hence lower returns.
‘Is beta dead or alive?, Lakshinok, 1993’
“The stock market is so noisy that, with the existing data, one cannot generally draw clear-cut conclusions as Fama and French do that Beta is dead. Unless the difference in returns is large and the period is long, no conclusive statements can be made. Noisy stock returns are a problem not only when we try to figure out if Beta works. Consider a star money manager who beats the market by 200 basis point a year with a tracking error of 5 percent a year. It would take 25 years to determine whether this manager is smart or lucky. Needless to say, plan sponsors are not so patient. We examined whether the very noisy and constantly changing environment generating stock returns permits strong statements about the importance of Beta…The noisy, dynamic environment generating stock returns clouds our ability to reach firm conclusions with respect to the compensation for beta risk….downside risk is the major concern…not found a single money manager who seems to be concerned about the various multidimensional risk measures consistent with the arbitrage pricing models. If downside is a major concern of investors, beta is a good measure of risk…The discussion thus far indicates that burying beta might be premature. An alternative explanation, is behavioral and institutional factors that are unrelated to risk play a major role in generating stock returns, thereby confounding the relationship between risk and return.”
Market noise and dynamic environment, limited testing time of 20 years, makes it hard to measure the effectiveness of Beta. This does not make it redundant. Is smart beta dumb?, Pal 2015 explained how Beta was relevant and how it is the smart beta thinking that is inaccurate and needs to evolve.
‘Multifactor explanations of Asset Pricing Anomalies, Fama, 1996’
“In other words, without knowing why, we have stumbled on explanatory portfolios that are close to three factor MMV…we don’t know without knowing a) are there new common factors b) how correlated are the new common factors.”
‘Disappearing Dividends: Changing Firm Characteristics or Lower Propensity to Pay?, Fama and French, 2000’
“Dividend policy may be irrelevant, but it’s driven by size. The evidence suggests that three fundamentals – profitability, investment opportunities, and size – are factors in the decision to pay dividends.
The potential of size to be a proxy was mentioned by Banz (1978). The industry has not moved beyond size effect. The effect exists in a certain set of market situations and vanishes in a different set of situations. The size effect is inconsistent in its expression. It is not universal, and the possibility that size is still a proxy, leaves the door open for future research. Any factor that challenges size effect consistently would resolve this debate of what is the proxy that drives size and what is more important than size. This factor would also leave the information embedded in other subfactors as unimportant. The other question is if beta is really driven by a sequence of factors, which one is more important that the other, is it size or value or both? The confusion between relevance and irrelevance of factors continued to dominate the research from Ball and Brown (1968). The factor school remains fragmented with more than a few reasons to believe that there could be a universal factor beyond the size factor and despite industry clustering behind size, the question asked by Banz (1978) has the potential to change everything we have assumed about the size factor.
 Investment performance of common stocks in relation to their P/E ratios, Basu, 1977
 Common Factors in Security Returns: Microeconomic Determinants and Macroeconomic Correlates, Barr Rosenberg and Vinay Marathe 1976
 The Effect of Limited Information and Estimation Risk on Optimal Portfolio Diversification, Bawa and Klein 1977
 The relationship between return and market value of common stocks, Banz, 1978
 Book values and stock returns, Stattman D., 1980
 Size Related Anomalies and Stock Return Seasonality, Kiem, 1980
 The neglected and small firm effects, Arbel and Strebel, 1983
 Is beta dead or alive?, Lakshinok, 1993
 Multifactor explanations of Asset Pricing Anomalies, Fama, 1996
 Disappearing Dividends: Changing Firm Characteristics or Lower Propensity to Pay?, Fama and French, 2000