Can total beta really be used to measure risk for a single (undiversified) private company?


Academics and appraisers vary in their opinion as to whether total cost of equity, derived from capital market theory, can be extended to cover a single asset—particularly a private company.  Damodaran says that while he’s not particularly attached to total beta, he’s true to the idea that we care about risk, and we recognize the need to bring the risk of being undiversified into the discount rate.  “If we lived in a fully diversified world,” he points out,” there’s be no private company owners, no small cap discount, etc.”  But these things exist; “if we own only five mutual funds, we’re already in violation of CAPM.”  Every private company owner has already chosen to be a “rebel” and take on both the additional danger, and the additional opportunity of reducing diversification.   At that point, the owner has left the market portfolio world of CAPM, and entered the standard deviation world of total beta, Damodaran argues.  “We don’t have to throw out CAPM; each of it’s assumptions have statistical support.”

Damodaran also argues that the cost of equity changes over time.   Take a startup with an owner fully invested in the business.  The cost of equity might be 25%--but a couple of years later when venture capital is brought in, the owner becomes less undiversified, and perhaps 15% is a better number.   Meanwhile, a terminal value at the time of going public would represent further diversification, and lower COE.  Risk and expected return are no longer linear relations, and CAPM’s relationship with a fully diversified portfolio or asset class becomes more problematic.  Total beta adds a standard deviation for a single stock, at least as used in approaches like the Butler Pinkerton Calculator.  “Either you’re comfortable with this, or not, and you need to decide how to work around your discomfort,” says Damodaran.  

William Sharpe, in his Nobel Prize winning work in “Capital asset prices: a Theory of Market Equilibrium Under Conditions of Risk” (1964), did argue that individual single assets are related to risk and return for diversified holdings, “typically...will lie above the capital market line.”


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