Authors: Stephen Reid and Tony Carlton
Stephen is a partner in Deloitte’s Mergers and Acquisitions valuation team and an Adjunct Professor at Macquarie University, based in Sydney.
Tony is a corporate finance advisor and educator, formerly an Associate Professor in Macquarie University Business School
The appropriate treatment of a (small) size premium (or valuation discount) is one of the most contentious aspects of small business valuation. Some practitioners typically apply a premium to their discount rate when determining a cost of capital for a discounted cashflow valuation of a small business, or reduce the multiple applied to the earnings of a small business. Of the many studies of size premiums, some find evidence of a size premium and others not. For studies that do find evidence, the findings vary significantly. We observe valuers referring to one study or another when justifying their adjustment to a cost of capital for a size premium, but why do they choose that study and not another, or one that shows no evidence of a size premium? After 40 years of research, surveys and debates there is still no academic consensus as to whether it is appropriate to impose a higher required rate of return on a small business.
In this series of articles we consider the current treatment of the premium in the Australian market. In this first article we describe the current state of practice, and assess how it aligns with available empirical evidence. In particular we challenge the common practice of applying “rule of thumb” size premia, arguing it should be a last resort. In the second article we argue that, in the absence of clear evidence of the quantum of a size premium, perhaps it is wiser to seek to adjust the numerator, expected cashflows, instead. We will provide a framework for helping the valuer consider the incremental impact of smallness on the value of a business. In our third article, we provide more technical examples about how to introduce risk into a DCF valuation.
PART #1: CURRENT PRACTICE AND EMPIRICAL EVIDENCE
[20 minute read]
[May 2023]
1. Introduction
We review current practice in Australia on the size premium, and examine recent empirical research, including the most recent 2018 Australian study from CAANZ/Macquarie University Business School (the Macquarie Paper). We conclude that the use of rule of thumb size premia should be the last option chosen by the valuer. Our main reasons are the lack of theory to support such a premium, lack of clarity about what any reported size premium actually measures, and the lack of consistent results from empirical research. We offer suggestions about how best to evaluate external research sources.
2. The “Theory” of the Size Premium
The origin of the size premium is empirical, built on historical evidence that portfolios of small firms earned higher returns than large firms. Based on this evidence, it is argued a premium should be added to the discount rate for smaller firms, resulting in a discount in the valuation of a small business relative to a large business. There is no underlying theory to explain why a smaller business, per se, should earn a premium.
The most common rationale is small companies have higher risks due to a lack of product, industry or geographic diversity, greater exposure to economic factors, key person risk, reduced access to capital, and other factors; a larger business is better able to survive the impact of these types of adverse outcomes. Consequently, investors have higher expected returns for investing in small companies. It is important to distinguish between the systematic risk incorporated in beta and the CAPM, and idiosyncratic risk which is not picked up by the CAPM, and for which there is no real theory about how to incorporate into a discount rate. If size really is a surrogate for idiosyncratic risk, the absence of a compelling theory on how to adjust the discount rate for idiosyncratic risk suggests a size premium is on weak theoretical grounds.[2] A better approach is to focus on the actual idiosyncratic risk of the business being valued, rather than apply some overall average premium. Finance theory consistently advocates for risk adjusting the cash flows rather than the discount rate. This approach also provides better insights into the strategic and commercial attributes of a business, and we examine this approach in the second article.
If factors affecting cash flow and risk can be directly incorporated into a valuation, what other factors might explain a size premium? Common factors which can adversely impact smaller firms include information asymmetry (reporting transparency, lack of analyst coverage), illiquidity costs (transaction costs), illiquidity risks (the risk that liquidity in a market will not be available when required), concentrated ownership and undiversified investors. Most of these factors may not affect underlying value, but may affect the price of a share in a business, and are therefore valid issues to consider. The impact of these factors will vary across firms, industries and transaction contexts, so it is not obvious that the correct way to adjust for these factors is to include a market wide adjustment to the discount rate. As with any other risk impacting a company, we would argue these need to be tailored for the valuation situation.
One of the main counter arguments against a size premium is the more recent empirical research which suggests the size premium has disappeared since the mid 1980’s when it was first “discovered”.[3] One obvious explanation is that as soon as a so-called pricing anomaly is discovered market behaviour will lead to its elimination as investors chase the additional returns. The existence of roll-up aggregators in pharmacies, funeral homes, dentists and garden centres, and targeted small cap funds suggests there are mechanisms for capturing any pricing discrepancy between large and small firms. The extreme version of this argument is that, if small firms suffer a valuation discount, then arbitrage profits can be earned by simply aggregating a group of small businesses, resulting in the disappearance of small businesses. The fact that nearly 50% of firms on the ASX have market capitalisation less than $42m counters this conclusion.
3. Current State of Size Premium Research
The size premium debate continues to attract research interest, so we briefly examine recent research to provide context. Much of this research is directed at portfolio investment management, so it is important to assess the implications for the valuation practitioner.
There are three broad strands of research:
[1] There is no size premium
An excellent summary of this line of argument is presented by Alquist, Israel and Moskowitz[4]. They argue that the size premium is not a material source of additional expected returns. Factors explaining the apparent appearance of a size premium include: adjustments to US databases to adjust for the incorrect treatment of delisted firms in the original studies, the strong influence of the “January effect”, and the fact that most of any reported premium is attributable to micro stocks (less than US18.8m). They particularly emphasise the need to adjust for market betas when calculating “excess” return. Recent research[5] also confirms the primacy of the market factor in the Australian market. Hoang et al used statistical testing which directly addressed the potential impact of data mining. Using Australian data for the period 1992 – 2017 they tested for 91 pricing factors (including size), finding the only significant factor that explains returns is the market factor (which drives the CAPM).
[2] There is a size premium but it takes some digging[6]
The simplest calculation of a size premium takes the difference between returns of large capitalisation stocks and small capitalisation stocks, to give a so-called excess return. This is a raw or unadjusted return. Statistically it is an unconditional return. It is this type of calculation that shows the size premium has “disappeared”. However, what if any size premium is being masked by other characteristics, such as lower quality profits, higher risk or some other factor[7]. To test whether there is a “pure” size premium the impact of these other factors needs to be removed. This usually requires statistical procedures, such as regression, to “remove” the effects of the targeted factors. The resulting excess returns are usually described as conditional because they relate to adjusted returns or to a subset of the data. In order to attempt to explain the disappearance of the size premium researchers have identified a number of factors to adjust for when estimating a size premium. The general argument is that these other factors have masked the true size premium since the 1980’s but, once adjustments are made, there is an underlying pure size premium. This type of research is more complex and prone to greater subjectivity but, done well, should assist our understanding when there are multiple factors impacting returns.
The main examples include:
- Asness et al[8] found the estimated unconditional size premium to be highly volatile over different sample periods. When they adjust returns by removing the effect of asset quality, defined as profitability, growth, stability and safety, they find a consistent size premium. These results were based on data for the US and 24 other countries, including Australia. Similarly, Alquist et al (discussed above) also find a size effect when they adjust for asset quality. This is the main statistical test used in the Macquarie Paper as well. Valuation Implication: These sorts of results need to be considered, but still require further exploration. If the size premium exists after allowing for asset quality, it is less likely the size premium serves as a surrogate for risk – so what is it measuring?
- Estimates of size premia assume that realised (excess) returns are a good estimate of expected (or required) returns. This is a heroic assumption. Expected returns reflect expectations of cash flow; if actual cash flows differ from expected cash flows, then actual returns will differ from expected returns. Hou and van Dijk[9] studied returns for US companies over two periods: 1963-1982 (when size premia are commonly found) and 1983- 2014 (when many studies report no size premia). In the second period actual cash flows were lower than expected, leading to share price underperformance and lower than expected returns. Larger firms exceeded expectations, leading to higher than expected returns. As a result, there was no outperformance by smaller stocks in this second period. After adjusting for this expectations effect, they argue the size effect in the second period is in excess of 8% per annum, much larger than most studies of this period. Valuation Implication: This analysis concludes that simple reliance on realised returns leads to unreliable estimates of excess returns or size premia, and allowance needs to be made for the impact of differences between actual results and expectations. Another approach may be to directly use expected returns to measure differences between large and small firms. The use of multiples is one way to respond to this problem.
- Ahn, Min and Duo[10] studied the impact of business cycles on returns over 1950 – 2012. They found that small firms only earned excess returns during the trough stage of a business cycle, which lasted on average for seven months. They argue that the limited number of Troughs since the 1980’s explains the lack of observed size premiums. Using US data over July 1963 to September 2018, Cho[11] finds a small size premium exists only in times of macro-economic uncertainty, presumably related to changes in credit market conditions. Valuation Implication: If a size premium only emerges in times of economic uncertainty, or the trough of a business cycle, what does this mean for a valuation which should account for the full range of economic conditions?
[3] Even if there is a size effect, what does it mean?
Even if there is a genuine size premium, there needs to be clarity about what it represents, to at least avoid any double counting with other valuation adjustments. For example, if there is still a size premium after adjusting for risk what exactly does it represent? The most popular candidate is (il)liquidity – any reported size premium is really a surrogate for the costs and risks of liquidity. For example: Alquist et al conclude “any detectable size premium is well captured by a liquidity premium”. Using international data, Asness et al conclude: “These liquidity level and risk effects can help explain most, or perhaps even all, of the size effect, even when controlling for quality”. For Australia this question was examined by Bettman, Ng and Sault[12]. For the period 1990 – 2008 they find evidence of a size premium. However, after allowing for transaction costs and the actual trading volumes in small stocks, they find that the dollar amount of profits earned by investing in portfolios of small stocks are no different from zero. More than half the companies listed on the ASX have a market capitalisation less than $42m[13], and are therefore liquid to varying degrees.
4. Common practice in Australia (which is not necessarily best practice)
The CAANZ Business Valuation Surveys of 2021 and 2022 asked respondents about the size premium. In the 2022 survey, 93% of respondents adjusted their selected earnings multiple or discount rate for the size of the business (90% for 2021). 60% of respondents based their adjustment on subjective information, while others used the Macquarie CAANZ paper (33%), Ibbotson (25%) and Duff & Phelps (20%).
The basis for the subjective adjustments made by respondents to the 2021 survey included:
- “Balanced assessment of scale, depth of management, reliance on key customers and overall future prospects”
- “Alpha from Duff & Phelps, but tempered by Damodaran’s approach that there has to be benefit from control”
- “Depth of management, spread of customers and engagement and quality of balance sheet”
- “Experience and market assessments”
- “Judgement”
- “Market data”
- “Past research and market transactions”
- “Risk premium applied and scaled based on size of target”
Neither survey asked respondents to quantify the adjustments they make.
The 2017 KPMG Business Valuation Survey “For all it’s worth” also asked respondents about size premiums[14]. For those respondents who applied a size premium the majority said they applied a size premium in the CAPM formula or apply an alpha factor.
Figure 1
Source: extract from “For all it’s worth”
The median discount applied by practitioners when valuing equity <$50m was 5%, and 3% when the equity value was between $51-100m. From Figure 2 we can conjecture that size premiums are commonly applied by survey respondents for businesses at an equity value less than $50m but less so for larger businesses.
Figure 2
Source: extract from “For all it’s worth”
These adjustments imply significant impacts on valuations. Table 1 shows the value impact of the premiums arising from the KPMG survey to value businesses in the different KPMG survey size buckets. Using the median results from the KPMG survey generates valuation discounts up to 33.3%, within typical market levels. Using the higher values for reported size premiums results in valuation discounts in excess of 50%.
Table 1: Multiple Discounts implied by common size premiums in Australia
5. Australian Evidence
In determining by how much to adjust the discount rate, some valuers refer to data from Kroll (previously Duff & Phelps and Ibbotson/Morningstar), which is based on a data series of returns by company size, or decile, from 1926 onwards[15]. At face value, this data suggests a significant adjustment would be required:
Table 2
Source: extracted from the Macquarie Paper
The Size groups reported by Duff & Phelps (as is was at the time the Macquarie Paper was prepared) are hardly relevant in the Australian context, where the median market capitalisation is around $42 million, and more than 80% of the companies listed in Australia would be considered micro-cap in the Duff & Phelps study.
More recently a number of practitioners have started referring to a relatively new study by Macquarie University, “The Size Premium: Australian Evidence”, released in 2018. The Macquarie Paper summarises the prior Australian research on the topic[16] – 9 papers, with 4 concluding that a size premium exists and 5 concluding that it doesn’t. The paper draws the following conclusions from the prior literature:
- “There is some evidence that smaller firms exhibit greater returns than larger ones but this result is not pervasive across all geographies or time periods.
- It is readily demonstrated that smaller firms are riskier than larger ones based on the variability of stock prices. Whilst average returns may be higher, the incidence of small firms outperforming large ones may not be large.
- Some of this observed outperformance is coincident with other return factors such as value, profitability and price momentum or risk factors such as credit risk or illiquidity.”
The Macquarie Paper used two approaches. Firstly, it used the traditional analysis of historical returns for various sized companies. Secondly, it tested if implied size discounts were incorporated into market multiples. It also used more discrete size buckets, defining companies with a value of less than $6.15m as ‘Micro’, and those up to $17.04m as ‘Small’.
Analysing Historical Returns
Table 3 presents summary data from the Macquarie research, and is the table we have seen referred to by valuers in support of a size premium.
Table 3
The results are calculated by forming portfolios of companies in each size bucket each month so, from month to month, the actual companies in each size bucket may be different. Excess returns are simply the average monthly difference between actual returns and market returns, weighted by market values. They are not Beta adjusted. The results above are based on monthly returns, therefore if a valuer was determined to use this analysis to calculate a size premium, it would be appropriate to add a premium of 72% (6.02% x 12 months) to a discount rate for Australian Micro companies and 45.6% for Small companies[17]. These levels of premiums are far in excess of adjustments we see made for size in valuations. Where this chart is referred to by valuers, they have not adjusted the monthly excess returns to annual returns.
We caution against using this table as the primary data source for the measurement of a size premium, for the following reasons:
[1] Note the standard deviation of the excess returns for the Micro and Small firms: they are significantly larger than the other size buckets. For Micro companies, 95% of annualised returns fall between (27)% and 171%[18]. For the Biggest group of companies the range is between (31)% and 31%. The range for the Micro companies is three times that of the Biggest bucket. While the differences in average returns of each size bucket might be statistically significant, in economic terms it is arguable whether the average of the Micro and Small buckets are representative of returns for small firms, and certainly would prompt caution in using the average as a generic size premium.
[2] There is no analysis of how sensitive these results are to changes in definitions and methodology.
[3] The “quality” of businesses in each size cohort improves as firm size increases, with default risk (measured by Distance to Default, DTD), profitability (measured by Return on Assets, ROA) and asset growth (measured by growth in book assets, Growth) all improving with increases in size. Beta also reduces with increases in size. It is therefore important to extract the impact of these other characteristics, to ensure the reported size premium is not covering for these other factors.
Regression analysis was used to determine if the differences in excess returns were explained by these other factors. The results are presented in Table 4 with dummy variables representing the Micro and Small size cohorts. When using dummy variables a value of 1 is assigned if a company is in the Micro group, otherwise a zero value is assigned. The coefficient therefore represents the average additional return for members of the Micro group relative to the Mid/Large/Biggest cohort, after allowing for the other factors in the regression equation. Similarly for the Small Dummy variable.
Table 4: Selected regression results from Macquarie Paper
The coefficients for the dummy variables indicate a statistically significant premium was earned by Micro and Small firms, implying annual size premiums of 48% for Micro and 12% for Small, lower than the raw results presented earlier[19]. This is after allowing for the separate impact of company specific differences in default risk, profitability and growth, making these better estimates of the size premium than the raw results presented earlier. Because these regression estimates have adjusted for the individual impact of profitability, risk and growth arguably the use of size premia from these models assumes that underlying forecasts adjust for these factors.
The Macquarie Paper notes: ”our regression indicates that there is a micro and small firm size effect but we would not be confident in using the coefficients in a cost of capital as: (1) the quantum of implied returns will essentially discount to an exceptionally short payback period; and (2) we need to account for the option-like payoffs.” Furthermore, even if the significance tests for individual variables are significant (as measured by the t-test) the overall low R2, of around 5% or less for the returns regressions, suggests there are other factors having a significant influence on results.
Even after allowing for these adjustments there is a significant issue of ergodicity[20]. Studies of small company size premiums utilise time series statistics, aggregating the returns of small companies in each (monthly or annual) period. The overall average therefore does not necessarily measure the performance of the same companies. Stock returns are non-ergodic when observed past probabilities do not apply to future outcomes. In this case, can the observed performance of the small companies be expected to continue? Those that grow strongly will no longer be micro caps. Poorly performing larger companies will enter the small company “universe”. Also, small stocks are often delisted when they can no longer pay listing fees or fail and some small companies may be taken over, go private or enter administration. An alternative approach may be to track returns of individual companies over longer periods of time; this may be more compatible with the actual task facing a valuer. Gilbey, Marsh and Purchase[21] examined the long-term performance of firms that listed on the ASX via IPO over the period 1999 to 2019. They split the sample of 2,108 IPOs into three size buckets: Small/micro (<$75m), Medium ($75m -$700m) and Large (>$700m). They calculated one day returns and then subsequent returns from a “Dynamic Buy and Hold” strategy, with returns of each IPO calculated from IPO date to either delisting or the end of the sample period. Their results are summarised in Table 5.
Table 5: Summary of IPO returns for small and micro-cap stocks
Small/micro and medium cap stocks all earned positive returns relative to large stocks. The results appear to support a size premium, however the implied size premium appears to be very large. The one-day return implies an initial valuation discount for small/micro cap stocks compared to large caps of 10.58% (19.46% – 8.88%). The difference between long run annual returns for small/micro and large portfolios implies a discount rate adjustment of 16.34% per annum (18.62%-2.28%). Combining the upfront discount and the annual premium implies a valuation discount of nearly 66%[22]. The other important observation is that returns for the small and micro stocks are positively skewed, with a number of positive outliers ‘dragging up’ the average (refer to Column 5 in Table 5). Even though average returns were positive, most returns were zero or negative – is it sensible to base a size premium on historical measures of average returns, when most of small cap stocks underperform individually?
Multiples Analysis
The earlier discussion highlighted many issues with identifying the presence, or otherwise, of a size premium using historical data. Many of these issues can be addressed by using multiples which, by definition, are forward looking price observations:
- Current values should better reflect market required returns, rather than needing to assume historical returns represent future required returns;
- They are less affected by survivorship bias;
- They are less subject to many of the measurement issues involved in calculating historical returns;
- The valuer is able to incorporate private market transactions into the comparables set.
Any discount rate ‘(small) size premium’ should be reflected in lower multiples for smaller firms, resulting in valuation discounts when we use multiples. The Macquarie Paper found inconsistent evidence of any valuation discount in the P/E, EV to Revenue and Market to Book multiples. Table 6 summarises average multiples for the various size buckets. For the P/E multiple, small and micro cohorts of firms had material discounts relative to the larger groups, while the EV to Revenue multiple actually showed premia for the smaller size cohorts – counter to the size premium argument. There were no material differences between groups for the Market to Book multiple.
Table 6: Comparison of average multiples across size groups
As with the historical returns analysis, these overall averages may be covering for the impact of risk, profitability and growth. Regression analysis was again used to adjust for the impact of these variables. Table 7 summarises some of the results, where regression models for selected multiples are developed using dummy variables for the same micro and small size buckets.
Table 7 Extracts of P/E, EV to Revenue and Market to Book multiples
These results provide mixed evidence of a size impact. The P/E shows a statistically significant discount of 22% for Small stocks (between $6.15m and $17m), while the Market to Book regressions show a large discount for Micro stocks of 46%, and 30% for Small stocks. The Revenue multiple shows a positive impact, counter to the theory. The two bottom rows in the table show the implied valuation (discount)/premium. By way of contrast, the original paper using this methodology by Bradford Cornell[23] , using US data, found no evidence of size impacts across size groups.
Although the multiples analysis was exploratory, and is not common in the size discount/premiums literature, the multiples approach may offer a productive route for further research.
6. Interpreting the Evidence
While the surveys suggest the common use of discounts when valuing small companies, the evidence in favour of this adjustment is contentious. Some studies show that the size premium exists, others that it does not, some show it has been declining over time, with no size effect since the mid-1980s.
Even though the analysis of historical returns in the Macquarie paper concludes that “we find significant evidence of smaller firms earning higher returns than larger firms” a deeper reading shows within the Macquarie Paper there is a wide range of potential values to use as a size premium. Furthermore, the Macquarie paper did not test for the influence of liquidity, but noted that “smaller firms are very thinly traded and that their security prices are more volatile. The higher return premium to small firms may therefore be attributable to liquidity in addition to other unknown or difficult to measure factors such as information quality, credit rationing.” That is, the observed size effect may not be due to size, per se.
The Macquarie paper continues the tradition of research on the existence of a size premium – it provides evidence for both sides of the argument!
Our discussion has identified a number of issues in using existing empirical research as the basis for determining a size premium. Calculating historical returns for portfolios of different sized firms might be appropriate for the needs of portfolio investors, but we question whether they replicate the needs of a valuation practitioner. To the extent the valuer uses published research as an input into their size premium we suggest the valuer needs to consider the following:
[1] No theory: if there is limited theory to explain the “why” and the “what” of a size premium then use of a size premium to adjust the discount rate is effectively a blackbox. We note the view that any reported size premium is really related to illiquidity costs and risks, so it is important for the valuer to address this factor. The valuer needs to consider how the use of published size premia contributes to transparent and robust valuations.
[2] The variation in results across papers means that relying on a particular empirical study may not provide the solid foundation you may have hoped for. If you want to add a small company premium to your discount rate (as opposed to adjusting the cashflows), which study will you select and why? It is dangerous to simply use studies that calculate differences in returns of “small” firms and “large” firms, so called “unconditional returns”. This appears to be the practice in Australia where analysts appear to be using data from Table 3 in this paper, or Tables 1, and 3 – 8 from the original Macquarie paper.
In selecting research papers, analysts might consider the following:
[i] Assess each individual piece of research in the context of the existing body of research, rather than relying on one study;
[ii] Has the research properly tested the robustness of the results? For example, has it tested the effect of outliers; how sensitive are the results to size groupings; does it address the issue of ergodicity; has it addressed the impact of micro sized firms in its estimates, as very small firms appear to have an outsized impact on results;
[iii] Is it better to utilise an estimated size premium that adjusts for firm specific factors, particularly market beta, and quality (profitability, risk and growth) of the business?
[iv] Does the estimation period provide an appropriate basis for developing a forward looking estimate; for example, in terms of macroeconomic conditions and embedded market expectations (i.e. similar questions that are asked when selecting the Market Risk Premium for the CAPM)?
[v] Do multiples provide a potentially more reliable source of valuation guidance, as they embed forward looking valuation parameters rather than historical returns, and allow for the incorporation of firm specific factors into the estimation?
[3] Does one size fit all? More fundamentally, most empirical studies effectively calculate average results and average causal relationships. The data shows a wide spread in results, and so while a conclusion using averages may be appropriate if talking about the overall market, it may not be appropriate when trying to value an individual business. If a size premium is being used as a surrogate for risk then the analyst should make the effort to individualise that premium. Adding a “one size fits all” size premium to the discount rate does not absolve the analyst of responsibility to identify cash flow and risk factors specific to the business being valued.
The surveys indicate a majority of practitioners use subjective judgement in estimating a size premium. Given we argue risk adjustments need to be individualised then we have to accept this is a step in the right direction. However, we also contend that subjective adjustments to a discount rate in the absence of a clear theory are not the best way to address the size question. Given the range of possible explanations for a size premium, the valuer needs to be clear what is being accounted for by adding a size premium: is it incremental risk, illiquidity costs and risks, concerns about information transparency and governance, concentrated ownership, or other factors. And, if it is incremental risk, exactly how is that incremental risk measured and is it best accounted for in the cash flows?
7. Conclusion
We have reviewed recent international and Australian research on the size premium. The evidence is mixed. On both theory and practical grounds, adjusting the discount rate to allow for a size effect is contentious.
The Macquarie paper notes that it “would be prudent for valuation practitioners to attempt to identify and estimate as many of the explicit costs and risks as possible rather than blindly apply a simple shortcut…”.
This is great advice. In the follow up article we provide a framework to assist in analysing the impact of size on the valuation.
What source of size premium data have you been using? Why? (you can comment below)
[1] The Macquarie Paper
[2] One other approach to incorporating size into a discount rate is multi factor models (originated by Fama & French), which include a size factor (amongst others) in addition to a market factor. Each firm would have a ‘size beta’ just as it has a market beta, allowing a size premium to be calculated for individual firms. We do not review this approach as the multi factor models are not common in business valuation, and they suffer from the same issue as the size premium, in that they are basically empirically driven models.
[3] For a summary refer to Alquist, R., Israel, R. and Moskowitz, T. “Fact, Fiction, and the Size Effect”, The Journal of Portfolio Management, Fall, 2018, pp 34 – 51, and the Macquarie Paper.
[4] Reference in footnote 3.
[5]Hoang, K., Cannavan, D., Gaunt, C. and Huang, R. “Is that factor just lucky: Australian Evidence”, Pacific Basin Finance Journal, October 2019, Vol 57, 101191.
[6] Or you might ponder the similarities between the size premium and the Norwegian Blue parrot.
[7] The data in the Macquarie Paper which we present later certainly suggests this the case.
[8] Asness, C., Frazzini, A., Israel, R., Moskowitz, T.J., and Pedersen, L.H., “Size matters, if you control your junk”, Journal of Financial Economics, 2018, 129, pp 479 – 509.
[9] Hou, K. and van Dijk, M.A., “Resurrecting the Size Effect”, Review of Financial Studies, July 2019, Vol 32, No 7 pp 2850 – 2889.
[10] Ahn, D.H., Min, B, and Yoon, B., “Why has the size effect disappeared?”, Journal of Banking and Finance, 2019, 102, pp 256 – 276.
[11] Cho, S., “The Size premium and macrovolatilty risks: Evidence from the US and UK equity markets”, International Journal of Financial Economics, 2019, 24, pp 1271 – 1286.
[12] Bettman, J.L., Ng, W.S.K., and Sault, S.J. “The economic significance of trading based on the size effect in Australia”, Australian Journal of Management, 2010, 36(1), pp 59-73
[13] Deloitte analysis.
[14] Neither the 2019 KPMG Business Valuation survey nor 2020 CAANZ survey asked about the size premium.
[15] This data does not seek to adjust for the betas observed for companies of different sizes.
[16] Macquarie Paper, Figure 5.
[17] These are calculated by multiplying the coefficient of each Excess Return by 12 to convert to an annual return equivalent.
[18] Monthly standard deviation is annualised by multiplying by √12. For Micro companies this gives an annual standard deviation of 50.6% (14.6% x 3.46). The 95% confidence level is the expected return +/- 1.96 standard deviations. For Micro companies this gives a range of annual returns of +/- 99%.
[19] These are calculated by multiplying the coefficient of each dummy variable by 12 to convert to an annual return equivalent.
[20] Nassim Nicholas Taleb describes ergodicity in his great book Skin in the Game, Hidden Asymmetries in Daily Life (2018) in a thought experiment … Assume 100 people go into a casino with a set amount of money for a set time period, sharing their returns afterwards. The returns would reflect the odds of the games the 100 were playing. Next assume 1 person goes into a casino 100 days in a row, with a set amount of money. At some stage during the 100 days, that person is likely to run out of money and will not be able to play for the balance of the period. Finance studies are most like the former example involving 100 people observing, say, returns of companies over various periods for a size premium study. Life as a small company is more like the latter, 1 person for 100 days.
[21] Gilbey, K., Marsh, T., and S. Purchase, “ASX smallcap/microcap listings: the IPO ‘Pop’ and two decades of subsequent returns”, Accounting & Finance, 2022, 62, pp 3285-3318.
[22] Assume a business generating a level perpetuity cash flow of $100, with a discount rate of 10%. Its value is $1,000. Now assuming the discount rate is 26.34% [10% plus the ‘size premium’ of 16.34%] gives a value of $380 [$100/.2634]. Applying the issue discount of 10.58% gives an initial value of $339, a discount to the base value of 66%.
[23] Cornell, B, & Gokhale, R., “Do Valuation Multiples Reflect A Size Effect”, Journal of Business Evaluation and Economic Loss Analysis”, 2018, Volume 13, Issue 1, February, pp 1-13.