Stuck in the Middle (with Who?) Reviewed by Momizat on . Unsystematic Risk Premia in Privately Held Companies How does a valuation professional quantify and defend the unsystematic risk premia (URP)? Is the latter a f Unsystematic Risk Premia in Privately Held Companies How does a valuation professional quantify and defend the unsystematic risk premia (URP)? Is the latter a f Rating: 0
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Stuck in the Middle (with Who?)

Unsystematic Risk Premia in Privately Held Companies

How does a valuation professional quantify and defend the unsystematic risk premia (URP)? Is the latter a factor that helps explain why CAPM is less frequently used valuing a privately held company? As for Total Beta, is that any better than the use of Beta? In this article, the author suggests if one accepts that imperfect diversification (ID) explains the risk premia, he suspects that the risk level is a function of the buyer pool or market participant pool and that characteristic will validate whether the base URP should be adjusted up or down in a valuation engagement.

It is generally accepted that the capital asset pricing model (CAPM) framework is suboptimal in isolation for estimating compensable risk in privately held companies (PHCs).  The “imperfection” might be best summarized as an inability to account for the company-specific risk that, in some meaningful measure, routinely results in incremental return requirements on PHC investments.  However, the process of formulating a company-specific risk premium (otherwise known as an unsystematic risk premium, or URP) for PHCs in any given circumstance has historically been relegated to the realm of guesstimates and conjecture.  In fact, PHC analysts have often been left to decide for themselves on the matter of URP magnitude, speculating not only on where they are on the URP playing field, but also what the boundaries of the URP playing field are (or should be) in the first place.

Stuck in the middle…

If we hold ourselves to strictest avoidance of controversial, non-persistent “anomalies”, as well as adjustments that are best applied elsewhere to address either cash flow risk or liquidity risk, the area that appears to be most worthy of deeper consideration is the notion of imperfect diversification (ID).  ID suggests that PHC market participants are stuck somewhere between two opposing extremes, the notions of “perfect diversification” and “perfect non-diversification”.  Although something of an unexplored area, this middle ground of ID is not really that unfamiliar a place to be, as each bookend is not only considered to be “quantifiable” as it pertains to URP inferences, but also appears to reflect some familiar and fairly sensible arguments on compensable risk.  Representing one end is Beta, coolly advising the PHC market participant that substantially all company-specific risks can be eliminated through maintenance of a well-diversified portfolio (i.e., minimum URP).  Representing the other end is Total Beta, frantically reminding the PHC market participant that any particular investment in isolation is, in fact, wholly exposed to all company-specific risks (i.e., maximum URP).  Market participants are obviously advised not to put “all of their eggs in one basket”, so Beta’s argument seems to have something to offer in terms of compensable risk expectations on PHC investments.  On the other hand, the substantially-higher risk aversion represented by Total Beta is understandable not only in terms of the less-than-perfect diversification that often results from such investments, but also in terms of the phenomenon of “behavioral finance” in general.

If one can accept a premise that a “tug-of-war” of sorts is going on between these two regarding incremental compensable risk expectations (stemming virtually solely from ID), then the relative strength of the “players” might be the next logical inquiry.  Practitioners typically agree that Beta is “weak” for capturing, in isolation, compensable URP in PHCs.  What may be somewhat less apparent, however, is why Total Beta might be considered “weak” for that purpose as well.  First, Total Beta assumes that compensable risk can readily be expressed as a function of just Beta and correlation.  In other words, Total Beta assumes that, all else (namely Beta) equal, the lower the company or industry correlation with broader market returns the higher the compensable risk expectations of that same industry or company.  The suggestion that all sources of “unexplained” price changes for a company or industry represent, collectively, one big bucket of additional compensable risk appears, in common-sense terms, to be a significant overstatement.  Secondly, and related to the prior point, deployment of Total Beta inside of the otherwise-standard CAPM framework routinely results in annual equity return expectations well in excess of 20.0%, certain magnitudes of which might arguably be appropriate on an ex-ante basis for certain relatively “riskier” investment opportunities over finite holding periods (e.g., certain venture investments over short-to-medium term holding periods), but which do not reasonably represent annual return expectations into perpetuity.  So, “advantage, Beta”?  Perhaps one should expect the center flag in this hypothetical tug-of-war to move materially in Beta’s direction, if not fully across its end line?  It does seem plausible that a “baseline” URP for PHCs may manifest in this tug-of-war way, by necessity somewhere in between those implied by these two bookend notions, and by intuition somewhat closer to minimum URP than maximum URP.

It is also likely worth considering that seasoned professionals, who have routinely had the opportunity to observe and derive URP from actual PHC deal prices given reasonable (i.e., expected value, weighted average) forecasts over a multitude of industries, are probably readily able to estimate what their “baseline” observation of URP has been in such situations.  Perhaps, similar to existing surveys on the equity risk premium that are periodically conducted, a survey on URP involving PHC analysts would prove enlightening on this issue by providing a “consensus” estimate of URP for PHCs and facilitating further research on that consensus estimate within the aforementioned tug-of-war range defined by Beta and Total Beta.

Finally, if one is prepared to accept the notion that ID is the primary driver of URP, then it follows that the magnitude of URP for any PHC investment might reasonably be expressed as a function of the relative severity of ID in that particular market participant pool for that particular investment.  For example, in the case of a local, family-owned business where one has reason to believe that the market participant pool may, on average, ultimately have a relatively higher portion of their wealth tied up in the PHC investment, then one might reasonably advocate for a relatively higher (i.e., “above baseline”) URP.  Alternatively, in the case of a regional/national firm having a larger, more diverse ownership base where one has reason to believe that the market participant pool may, on average, ultimately have a relatively lower portion of their wealth ultimately tied up in the PHC investment, one might reasonably advocate for a relatively lower (i.e., “below baseline”) URP.

…between a rock and a head case

The philosophical and quantitative gap that exists between the theoretical “rock” that is Beta and Henny-Penny’ish Total Beta may be helpful in explaining the existence and magnitude of a baseline estimate for URP in PHCs.  Furthermore, one can envision adjustments to such a baseline URP estimate for any particular PHC investment opportunity given the relative severity of ID that is envisioned to manifest in that particular market participant pool for that PHC investment.


Jim Kelley, CFA, is a director in the Southwest Region of CBIZ Valuation Group. He has conducted valuations of both closely held businesses and public companies in a number of industries, including: technology and software, consumer products manufacturing, industrial manufacturing, pharmaceuticals, financial and business services, and natural resources. His analyses have been performed in a variety of contexts, including: litigation and economic damage assignments, M&A advisory and arbitration, domestic and international transfer pricing studies, fairness and solvency opinions, tax, financial reporting, and other management requirements.
Mr. Kelley can be reached at (972) 406-6917 or by e-mail to JAKelley@cbiz.com.

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