Size premium

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When Eq. First, the empirical evidence that followed the seminal work by Banz provides contradictory evidence on the existence of a size premium. For example:. In spite of this evidence, proponents of adding a size premium typically cite Banz , Reinganum , and Fama and French as support for the existence of the size premium. For example, Ang explains:. Given the above, there is no basis to assume that a size premium exists, let alone assume that we have to augment the CAPM to account for it. We would be hard pressed to find a valuation conducted by a practitioner in which the beta is estimated using monthly returns from to the valuation date.

Instead, practitioners often use estimation periods between two to five years preceding the valuation date when calculating beta. Note that the CAPM is a one period model that describes the way investors form expectations one period ahead. Even if we were convinced that a size premium is warranted to augment the CAPM cost of equity, we still have to correct the Ibbotson methodology to account for the last two issues described above.

Obtain 10 size-based value-weighted portfolio returns, ERP, and risk-free rate data. First, the data is freely available and is updated regularly, so practitioners can use up-to-date data through the valuation date. Second, using an independent data source avoids any potential criticism in the construction of the size-based portfolios and the choice of inputs.

Ultimately, a reliable and robust size premium should not be dependent on the data source used. The use of a three-year estimation period is in the middle of the two- to five-year estimation period typically used by practitioners and it is the method used by Yahoo Finance for the betas it reports on its website. Estimate the ERP using at least 35 years of data, which means that we would have an estimate of the ERP each month beginning in June i. The interquartile range i. Table 1 reports the Practitioner-Consistent Size Premium averaged over the last 5, 15, 25, 35, and 53 years.

Averaging over the last five years, we observe that Decile 10 smallest stocks values are marginally significant while Decile 1 largest stocks values are statistically significant. For example, averaging over the last 35 years, only Deciles 2 and 4 have statistically significant Practitioner-Consistent Size Premiums. As Table 2 confirms, for the most part, the interquartile range of each decile ranges from large negative values to large positive values. As a consequence, there is substantial overlap in the interquartile ranges of the different deciles.

Such a huge overlap between the interquartile ranges of Decile 1 and Decile 10 make it difficult to reliably distinguish a Practitioner-Consistent Size Premium that should be in Decile 1 from a Practitioner-Consistent Size Premium that should be in Decile Even if we ignore the lack of statistical significance of the Practitioner-Consistent Size Premiums, the calculated values still generate inconsistent and unreliable results.

Table 1 also shows that Decile 10 has a Practitioner-Consistent Size Premium smaller than most of the other deciles over an investment lifetime of 35 years. Indeed, only during the year and year averages does Decile 10 smallest stocks have the largest Practitioner-Consistent Size Premium and Decile 1 largest stocks have the smallest Practitioner-Consistent Size Premium.

However, even during those scenarios, the Practitioner-Consistent Size Premium for the deciles in between Deciles 1 and 10 are not increasing as firm size is decreasing. Notes: Data is from July to November The data can be arranged in a table giving you a measure of additional size premium for a given company market capitalization. So far so good. You can read off the company size premium and come up with a discount rate to use in your business valuation.

But what if the company you are valuing is smaller than the smallest publicly traded companies? Since it is not easy to find reliable data on returns for very small private companies, you can try using the data you have to estimate the size premium for your target firm. One way to do this is to use extrapolation.

You base your estimate on the known numbers then use the so-called linear regression calculation, available in a typical spreadsheet program, to estimate the size premium for your size company. For example, in Excel this calculation is performed using the Forecast formula. You specify the company market cap, presumably smaller than the range of capitalizations you have available from existing data.

The desired number is calculated for you using the known values of company size premia and market capitalizations. Here is the result:. How much difference can this make to your business valuation result? Consider the following scenario of future cash flows for the business over the next 5 years:. See an example of how to value a company of any size by discounting its cash flow while forecasting size premium to properly account for business risk.

You seem to be rather confused about the data analysis results. Consult the Valuation Handbook for details on the CRSP Deciles Size Premia study and note the market capitalization ranges for the deciles and the size premia indicated.

I believe you will find that ValuAdder numbers are pretty close. Also, the interpolation by linear regression across the entire range of market capitalization will get you in trouble as the relationship is highly nonlinear.

You would need to resort to a piece wise interpolation to capture the actual relationship. This is especially true for the tiny companies within or below the 10th Decile sizes. You should note that there are two distinct methodologies used to calculate the size risk premia:.

These studies differ in methodology. I suggest that you review the methodologies before jumping to conclusions. You may also choose to use the results of both size risk premium studies in your analysis.

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