Fans of boxing history (or those with enough gray hair) will remember the “Thrilla in
Manila”, the third and final heavyweight boxing match between Muhammad Ali and Joe Frazier.  Frazier had won the first match, and Ali the second.  The run-up to the third fight was nasty, with Ali calling Frazier a “gorilla”, and Frazier responding that he “wanted to take [Ali’s] heart out”.  The actual boxing match was an epic battle, with Frazier pounded so badly his eyes were swollen shut for days afterward, and Ali fainting after the match ended.  Ali reportedly said the match was the “closest to dying” that he had ever been.

Imagine the surprise when a “Thrilla in
Manila” erupted in the normally genteel world of business valuation.  The challengers to the status quo were Peter Butler and Keith Pinkerton.  In Round One[1], they claimed that “Total Beta” (“Tβ”) provides a better measure of risk for valuing privately-held companies than the traditional beta in the Capital Asset Pricing Model (“CAPM”).  Tβ is defined as the (standard deviation of an individual stock’s return) / (standard deviation of the market’s return).  In contrast, β in the CAPM is defined as the (covariance of the individual stock to the market) / (variance of the market).  According to it proponents, Tβ in the Butler-Pinkerton Model (“BPM”) is claiming to look at the total risk and return to the stock, while the β in the CAPM looks at the nondiversifiable market risk.

Butler and Pinkerton followed this with a one-two combination directed at the gut of the BV profession.  They claimed that (1) privately-held companies are not valued as part of a diversified portfolio, therefore Tβ is the best measure to determine the cost of equity, and (2) using Tβ, one could precisely calculate specific company risk.

The latter claim was based on a reworking of the modified CAPM traditionally used by BV experts.  In the modified CAPM,

Cost of Equity = R_f + β (R_m - R_f) + SP + CSRP

where

R_f  = the risk-free rate

β = beta

(R_m - R_f)  = the market risk premium

SP = the size premium, and

CSRP = the company specific risk premium.

Using Tβ, the BPM’s Cost of Equity = R_f +Tβ (R_m - R_f).

By equating the BPM with the modified CAPM, one can solve for the company specific risk premium, CSRP = (Tβ – β) (R_m - R_f) – SP.

Butler and Pinkerton claimed to have found a precise quantitative way to determine the CSRP.  This quantitative approach has a certain appeal to BV experts,  as traditionally the market risk premium was a matter of the BV expert’s professional judgment based on a qualitative analysis of the company.  Moreover,
Butler and Pinkerton got into the corner of the BV expert by developing proprietary computer software to calculate total beta.

The champion of the business valuation orthodoxy was Larry Kasper, who fought back in Round Two[2] using several strategies.  First, Kasper gave
Butler and Pinkerton a punch to the head by attacking the logic of the model.   Specifically, he pointed out that the buyer of a public stock is not compensated if he chooses not to diversify away specific risk, and asked why an investor in a private company should be compensated for making the same decision.  He followed with an uppercut by saying that in an efficient economy, the prices people pay for goods would not be higher if the company were privately-owned rather than public, hence there should be no difference in the companies’ returns.

Kasper then let loose a fusillade of jabs to the Butler Pinkerton model, saying among other things that it lacked peer-reviewed academic support, had inconsistent definitions of risk, broke down if an investment had zero correlation with the market, and produced different results for the CSRP depending upon whether the size premium was from Ibbotson or Duff & Phelps.

In Round Three[3],
Butler and Pinkerton threw some jabs of their own.  They stated that most companies are valued as stand-alone assets, hence Tβ is the appropriate risk measure.  They said some small company betas may have a lagged response to market forces, while Tβ would not be affected.  The reiterated their claim that Tβ captures 100% of a stock’s systematic risk, size risk and company specific risk.

Butler and Pinkerton then used a bit of Muhammad Ali’s “rope a dope” strategy, backing away from calculating the CSRP, and saying instead that Tβ made the calculation of size premiums and CSRPs unnecessary, as the Butler Pinkerton model’s basic equation where the Cost of Equity = R_f +Tβ (R_m - R_f) was all that was needed.

Kasper for his part displayed more statistical muscle in Round Four[4].  He pounded away at the underlying logic of Tβ and the BPM, first by stating that the definition of β in the CAPM is not the “risk” of the security, it is the proportion of the market return received by investors in a particular stock.  Thus the underlying correlation between an individual stock and the market return would be unchanged whether it was measured by β or Tβ.  Kasper then threw an uppercut to the jaw, asking how a measure like Tβ, which is being multiplied by a measure of systematic risk (the market return) in the BPM, can measure specific risk, which is supposed to be independent of the market?  Kasper said the BPM was trying incorrectly to convert the regression “alpha” and unexplained error term, which are uncorrelated with the market return, into a Tβ measure that is a function of the market return.

So how do we score this sparring match?  First, one needs to examine the logic of the BPM and the arguments of its critics.  Is the BPM correct or not?  Read the articles listed in the endnotes and decide.

Second, understand the concept of nondiversifiable risk.  This is the risk that cannot be removed by balancing out a portfolio with other assets, and finance theory says that only nondiversifiable risk is compensated with a higher return.  In the basic CAPM, this is accounted for by adjusting the market return using β.  In the modified CAPM, it can also be accounted for in the CSRP.   Business valuation experts consider this intuitively when they consider factors making up the CSRP.  For example, if a small company has so much dependence on the owner that it might not survive if the owner were hit by a bus, then the CSRP would be high, as no other assets could balance out this risk.  Is the BPM including diversifiable risk, or just the nondiversifiable risk?

In the end, the winner of BV’s Thrilla in
Manila will be decided in the mind of every valuation expert, with support from the academic community and court decisions.  But no one will argue it is one heck of a fight.

 **Please note when reading the comments to this blog that they are listed in order of most recent first.  So start at the bottom if you want to read them in chronological order.**