We came across an interesting paper on size premium by Clifford Ang, where Ang argues against adjusting a cost of capital for the size premium, citing empirical evidence and inconsistencies that challenge its validity.
Ang is an author of several finance textbooks and articles, contributing significantly to the field of valuation and economic analysis – his publications can be found here.
The Historical Context
We have discussed the size premium extensively in earlier posts. Ang notes that the concept of a size premium was first introduced by Banz in 1981. Since then, the existence of the small firm effect is challenged (if it ever existed).
Kroll (formerly Morningstar and Ibbotson Associates) and Duff & Phelps publish annual figures on the Size Premium in Excess of CAPM. Many practitioners have since been incorporating these premiums, which include pre and post 1981 data into their CAPM calculations to estimate the cost of equity.
Challenging the Size Premium
Ang’s primary contention is that the empirical evidence post-Banz does not substantiate the existence of a size premium. While some studies indicate a size premium, they could be the result of data mining or conducted by parties with vested interests.
Building on the data mining point, Ang explains … “One telling outcome of data mining is that an effect appears significant in sample, where the models are originally estimated, but it fails out of sample, where the models are tested after their discovery.”
We noted another explanation for the disappearance of the size premium in our earlier posts … as soon as a so-called pricing anomaly is discovered, market behavior will lead to its elimination as investors chase the additional returns. It is also worth noting that not all studies of size premiums follow the approach adopted by Kroll and Duff & Phelps.
The Practitioner’s Dilemma
Even if a size premium is valid, Ang argues that the premiums calculated by Ibbotson and Duff & Phelps are inconsistent with those employed by valuation practitioners, rendering the premium essentially arbitrary.
The crux of the problem for practitioners lies in the inconsistency between the calculated Size Premium in excess of CAPM and the way practitioners estimate the CAPM cost of equity. For instance, the beta calculation in the Ibbotson methodology, which is based on data dating back to 1926, starkly contrasts with the two to five-year estimation period typically used by practitioners. This disparity means that adding the published size premium to a practitioner’s CAPM cost of equity is akin to appending a random number.
A Proposed Solution
Ang attempts to bridge this gap by developing a Practitioner-Consistent Size Premium, aligning the size premium calculation with the way practitioners select inputs to their CAPM cost of equity. However, his analysis reveals that this approach yields unreliable and statistically insignificant results, with inconsistency and overlap in the calculated premiums across different firm sizes.
Conclusion
Ang concludes that the empirical evidence does not support the addition of a size premium to the CAPM cost of equity.
Further, even if it was valid to adjust for size, the current methods of calculating this premium are flawed and inconsistent with practitioner valuation approaches. He suggests that instead of modifying the CAPM cost of equity, practitioners should consider adjusting the expected cash flows in their DCF analyses to account for the risks the size premium is purported to reflect.
In our previous posts we gave detailed guidance about how practitioners might do this.
What do you think about the arguments made by Ang?