The Size Effect Continues to be Relevant
Considerations in Applying a Size Premium (Part III of III)
In this third and final article, as displayed in Exhibits 1 through 4 in Part 1 of this three-part article, the size effect has been observed even when looking at recent periods starting in 1981 and 1990. If one holds that you should not apply the SP in the MCAPM and that beta should be the only measure of risk, one is supporting using the pure or textbook CAPM to estimate expected returns. But that cannot be correct as the literature clearly demonstrates. Though the pure CAPM is a good tool to teach the relationship of risk and return, pure CAPM is not an effective model for estimating expected returns. Despite the empirical evidence, there are some who blindly support the pure CAPM. This author disagrees and concludes that until we have better models for pricing risk, one should consider using the MCAPM instead of the pure CAPM in developing discount rates.
As displayed in Exhibits 1 through 4 in Part I of this article series, the size effect has been observed even when looking at recent periods starting in 1981 and 1990. If one holds that you should not apply the SP in the MCAPM and that beta should be the only measure of risk, one is supporting using the pure or textbook CAPM to estimate expected returns. But that cannot be correct as the literature clearly demonstrates. Though the pure CAPM is a good tool to teach the relationship of risk and return, pure CAPM is not an effective model for estimating expected returns. Despite the empirical evidence, there are some who blindly support the pure CAPM. This author disagrees and concludes that until we have better models for pricing risk, one should consider using the MCAPM instead of the pure CAPM in developing discount rates. Applying the SP is based on observed returns, not a theoretical ideal. Therefore, one can match the subject companyâs characteristics to the companies that had similar characteristics over time and then use the observed returns for the latter as proxy to what expected returns might be for the subject company.
However, when applying the SP in estimating the cost of equity capital for a small company, one should not simply apply SP by rote. One should be matching the characteristics of the subject company with those of the companies used in arriving at the SP whether one is replying on the CRSP Size Premia or the Risk Premium ReportâSize Study SP data.
For example, some practitioners gravitate to using the SP observed for subdecile 10z without comparing the characteristics of the subject company for which they are estimating the cost of capital with those of the companies that comprise subdecile 10z.
We publish the fundamental characteristics of the companies comprising subdecile10z annually in the Cost of Capital Navigator (in Exhibit 4.10 in the reference section). Year after year, one finds that subdecile 10z is partially populated with troubled companies.
One way to correct for the underestimation of beta is by using sum beta method instead of the OLS method. Stocks of smaller companies generally trade less frequently and exhibit more of a lagged price reaction (relative to the market benchmark index) than do large cap stocks. The sum beta estimates are generally greater for smaller companies than the betas derived using non-lagged market benchmark data, therefore, resulting in size premia of smaller magnitude. Though using the sum beta estimate increases the beta for smaller market cap companies, we still observe premia in excess of that predicted by beta for smaller companies comprising subdecile 10z.
Even using sum beta over a look-back period may underestimate a forward-looking beta for a troubled company. The market price of the troubled company stock likely is readjusting downward to the troubled nature of the subject company even during periods when the general stock market returns are increasing. One also observes that beta estimates of the companies comprising the 10z subdecile are less than the beta estimates of the subdecile 10a (the largest 50% of companies comprising decile 10) which is comprised of fewer troubled companies.
From these data we can conclude the following:
- Using the OLS method of estimating betas for calculating the SP for subdecile 10z likely understates betas, and therefore may overstate the SP.
- Subdecile10z is populated by many large companies as measured by total assets (but highly leveraged) companies with small market capitalizations that probably do not match the characteristics of financially healthy but small companies (as indicated by the percentage of equity to total assets of the 95th percentile of companies, the largest companies, comprising the subdecile).
- Stocks of troubled companies included in the data may have had their stock prices so diminished that they are likely trading like call options (unlimited upside, limited downside) (as indicated by the negative latest fiscal year return on book equity of the 25th percentile and fifth percentile of companies comprising the subdecile). Even if one uses the sum beta method, the beta estimates are likely under-estimated and the SP
Let us contrast the composition of companies in subdecile 10z with those that comprise the 25th portfolio (comprised of the smallest companies) of the Risk Premium ReportâSize Study.
The Risk Premium Report studies use the sum beta method (using monthly returns over a look-back period) to measure the SP because we observe that the betas of small companies in the data set are underestimated if one uses the OLS method of estimating betas because of the low liquidity of small company stocks.
The characteristics of the companies comprising the portfolio of the smallest companies (Portfolio 25) can be thought of as financially healthy (not troubled), but simply small.
The information and data in the Risk Premium Report studies are primarily designed to be used to develop cost of equity capital estimates for many companies that are fundamentally healthy, and for which a âgoing concernâ assumption is appropriate.
One can further refine the appropriate SP by comparing risk characteristics of the subject firm with those of the companies comprising the portfolio of companies reported in the Size Study. Exhibits 5, 6, 7, and 8 displayed in Part I of this article series, display the fundamental risk characteristics that match the relative portfolio based on size. Note that the differences in debt do not cause the differences in risk. Also note that the unlevered betas of the portfolios comprising smaller companies are greater than those of larger companies; the average operating margins of the companies comprising the portfolios of smaller companies are less than the average operating margins of those of the larger companies; and the coefficient of variation of operating margins of the companies comprising the portfolios of smaller companies are greater than the coefficient of variation of operating margins of those of the larger companies. These fundamental risk measures support the position that smaller companies are, on average, riskier than larger companies. The SP may be a proxy of an operational risk difference between large and small stocks.
The reported SP measure is an average of all companies within the ranked portfolio. Hence, by definition, there are companies with higher and others with lower risks characteristics. An analyst should consider using a lower or higher SP than the published portfolio SP. For example, the variation of operating margin may be less for the subject company than for the typical company of equal size as measured by, say, total assets. In that case, the analyst should most likely apply a lesser SP for the subject company. The goal is to match the SP that is appropriate given the fundamental risk characteristics of the subject company.
As discussed previously, the relative returns on small company stocks compared to returns on large company stocks are cyclical. This leads one to ask if one should apply a SP if the stock markets indicate that the multiples for small cap stocks have declined compared to large cap stocks? In other words, in a situation where the returns for small cap companies in the immediately preceding period were less than the returns for large cap stocks, should one not use a SP in estimating the cost of equity capital for a small company? We believe that the valuation professional should include SP even in these times because the cost of equity capital should be based on the expected returns. In developing a cost of equity capital estimate when valuing a non-publicly traded business, the valuation professional is not mimicking a trader. The trader is dealing with small blocks of stock and high liquidity. We are estimating an expected return over a long holding period.
Academic and empirical evidence indicate that the pure textbook CAPM is an imperfect indicator of expected returns. Until better models become more accepted and easier for the valuation professional to use, the MCAPM will likely continue to be widely used by valuation professionals. SP help the valuation professional correct the pure CAPM for the risks of smaller companies not captured by beta. In this article, I demonstrate that the methodology followed by Duff & Phelps to calculate SP reported in either the CRSP Decile Size Premia or Risk Premium ReportâSize Study, are robust and yields a consistent SP to be used for pricing a long-term project as it should be for a good measure of cost of capital.
This article was previously published in the American Society of Appraisersâ Business Valuation Review, Vol 37(3) Fall 2018, and is re-published here with permission.
Roger J. Grabowski, FASA, is a managing director with Duff & Phelps and an Accredited Senior Appraiser and Fellow (FASA) of the American Society of Appraisers (ASA) (their highest designation).
He was formerly Managing Director of the Standard & Poorâs Corporate Value Consulting practice, a partner of PricewaterhouseCoopers LLP and one of its predecessor firms, Price Waterhouse (where he founded its U.S. Valuation Services practice and managed the real estate appraisal practice).
He has directed valuations of businesses, interests in businesses, intellectual property, intangible assets, real property and machinery and equipment. Mr. Grabowski has testified in court as an expert witness on matters of solvency, the value of closely held businesses and business interests, valuation and amortization of intangible assets and other valuation issues. His testimony in U.S. District Court was referenced in the U.S. Supreme Court opinion decided in his clientâs favor in the landmark Newark Morning Ledger case.
Mr. Grabowski is co-author with Shannon Pratt of Cost of Capital: Applications and Examples, fifth edition. (John Wiley & Sons, 2014), The Lawyerâs Guide to Cost of Capital (ABA, 2014), and Cost of Capital in Litigation: Applications and Examples (John Wiley & Sons, 2010). He is a contributor to the Duff & Phelps on-line Cost of Capital Navigator platform and he is co-author of the Duff & Phelps annual books: Valuation Handbook-U.S. Industry Cost of Capital, Valuation HandbookâInternational Guide to Cost of Capital and Valuation HandbookâInternational Industry Cost of Capital.
Mr. Grabowski teaches courses for the American Society of Appraisers and is a frequent guest lecturer at NACVA Annual Conferences.
Mr. Grabowski can be contacted at (312) 697-4720 or by e-mail to Roger.Grabowski@duffandphelps.com.
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 At least, when conducting valuation analyses denominated in U.S. dollars from the perspective of a U.S. dollar investor.
 See Chapter 11, âBeta: Differing Definitions and Estimates,â Cost of Capital: Applications and Examples 5th ed. (Hoboken, New Jersey; John Wiley & Sons, Inc., 2014).
 âCost of Capital Equity Considerations,â in Chapter 17, âDistressed Businesses,â Cost of Capital: Applications and Examples 5th ed. (Hoboken, New Jersey; John Wiley & Sons, Inc., 2014).
 Ang erroneously criticized the Risk Premium Report for using annual returns in estimating beta even though the methodology is clearly explained.
6 Beginning in 2019 the characteristics of companies comprising Portfolios 23 and 24 in addition to those comprising Portfolio 25 will be published to better allow the user to match the subject company with the characteristics of the companies comprising the Portfolios.
 Data on average operating margin for each size-based portfolio is available through the Duff & Phelps Cost of Capital Navigator platform at dpcostofcapital.com.
 For example, see Eugene F. Fama and Kenneth R. French, âA Five-Factor Asset Pricing Model,â Journal of Financial Economics 116 (2015): 1â22.