The myth of CAPM as a measure of cost of equity
CAPM is the standard methodology used in financial academia to calculate the cost of equity. But value investors like Warren Buffett have been outspoken in the past about its imperfections. So why shouldn’t we use CAPM to measure the cost of equity?
CAPM (as shown in the formula above) is simply a 'y=mx+c' formula adapted for financial inputs. At it's heart, it is a regression model that seeks to find a trend from multiple dispersed data points, and attempt to extrapolate that trend to determine a future data point.
What this means in layman's terms is that CAPM is simply a historical average of past stock prices. Since you're drawing an average from multiple independent stock prices, there will be a variance from the derived average trend, and from that variance a standard deviation can be procured. That standard deviation can be interpreted as volatility, because it represents the possibility of that derived average trend deviating from the "actual" trend - which could lead to a wrong extrapolation. Hence, it represents the risk that the derived average trend is wrong.
If we can find an accurate trend with a high R-squared, that means stock prices (y-axis) will tend to follow that trend over time (x-axis). Which also means that we can to some extent plot where stock prices will eventually land in the future, because if it has a high R-squared it means that future events trend with those of the past.
Notice that nowhere in this extremely sound statistical thesis does it involve inputs from the future. It only uses past inputs, and assumes the future will follow a historical trend. But it ignores the fact that some of those past inputs may themselves have been low-probability inputs (e.g. Trump winning in 2016). It just overlays a trend based on what happened in the past - even if that past event is unlikely to ever repeat again. So you can't exactly draw a high-probability trend when your inputs themselves are low-probability inputs. Furthermore, even within the statistical framework of the bell curve itself, simply relying on a trend to determine future outcomes completely ignores the existence of black swan events (e.g. coronavirus).
As you can see, the CAPM formula in the context of the cost of equity ('y' = Ri) is simply calculating the trend ('m' = Bi) multiplied by the excess return from risk taken when investing in equities ('x' = (Rm - Rf)) plus the return when no risk is taken ('c' = Rf). By default, this should result in a calculation of return on equity (ROE); but since your cost of equity is simply the opportunity cost of not investing in an alternative investment, you can take the ROE of that alternative investment as your cost of equity.
That's the theory, at least. In reality? It makes so many assumptions that it can at best be described as a flawed attempt to represent risk. 1) It assumes that the historical trend will hold in the future. 2) It presumes that low-probability risk events (i.e. tail risk) are so unlikely to occur that their impact is negligible. 3) It assumes that the possibility of a deviation from the average trend represents Risk! This is so totally untrue it beggars belief.
Let me explain why. Risk does not mean a deviation from a share price trend. Risk can exist in all kinds of forms. Does a company's historical share price (HSP) capture the possibility that a fire might break out in its main factory, therefore affecting earnings (i.e. business risk)? Does a company's HSP capture the possibility of who might win in the next election, and the subsequent impact on future stock prices (i.e. political risk)? Does the company's HSP tell you what determines future interest rates, and therefore a company's cost of capital (i.e. macro risk)? No! The company's HSP does none of that. You can draw absolutely zero conclusion about the company's future stock price by extrapolating a trend from its historical stock price. Like, literally, there is no relationship. It is that bad.
So how should you approach the assessment of risk to future stock prices? Ideally, you should be familiar enough with all the moving parts of the business to estimate potential losses from each one of those risk events occurring. Then calculate the possibility of those risk events occurring, and apply them to the magnitude of those loss outcomes. This is a basic version of how every CEO and insurance company in the world calculates risk, and is more easily recognized by its standard terminology: Expected Value.
In conclusion, you will not suffer any disadvantage by completely discounting the accurate estimation of CAPM in arriving at the cost of equity. Simply use other methods of calculating the cost of equity, e.g. the earnings yield (1/PE) of an alternative investment (representing your opportunity cost of investing in the target company). This could simply be the earnings yield (1/PE) of an index fund, or that of your favorite stock in your existing portfolio.
(Some readers were asking why the ‘earnings yield of an alternative investment’ should be used as a proxy for cost of equity. I’ll address it below.)
The definition of cost of equity (COE) is actually not much different from cost of debt. Cost of debt is the interest rate, because if I issue $1 worth of debt to to you, I'm getting $1 from you in exchange for a promise to pay you x% interest annually. Hence my cost of debt is x%
Similarly, if I issue $1 worth of equity to you, I'm getting $1 from you in exchange for a promise to pay you y% annually. Let's assume y% = 10%. Therefore my COE is 10%.
So how do you arrive at y% for a particular stock? It's simply the stock's average return on equity (ROE). Since the ROE = annual profit/total equity, shareholders in aggregate are getting the average annual profit as y% of total equity (their cumulative investment in the company’s shares). Which meets the above definition of COE.
Hence a company's ROE (from an investor’s perspective) = its COE (from the company’s perspective). But what would be your personal COE? It's simply the opportunity cost of investing in the target company instead of another investment. Because if you invest in the target company, you can no longer invest in that other investment; hence it becomes a cost of equity to you.
So what would that other investment be? For many, it's likely to be an index fund. That's why many fund managers use an index fund's earnings yield (1/PE) as their cost of equity. Why use earnings yield instead of ROE? Because the earnings yield represents the investor’s ROE in the secondary market - since you are acquiring those shares at the current market price, not the primary IPO price.
For me personally, I assume my COE is the earnings yield of my favorite stock in my portfolio; because if I didn't invest in the target company, I would most likely be investing in my favorite stock.
Hence, the calculation of COE can be reduced to the earnings yield of your favorite stock or index fund. No need to spend time dredging data to calculate beta.