Is there a better approach to estimating the “cost of equity”? Some ways are precise, some are guesswork—but most are likely inaccurate. It is such a critical assumption in finance that I spent 20 minutes of a job interview arguing with my interviewer about which approach was most appropriate (I got the job).
For how few formulae we have to deal with in the finance world, it’s amazing how often we get them wrong—or at least interpret them in different ways. These range from just how to discount cash flows (middle of period? End of period?) to whether amortization is a “real” expense.
To some extent, all of these debates should serve to remind us that finance does not lend itself to tidy mathematical explanations such as those in trigonometry. Far more so than in natural sciences, humans in finance are both observers and key participants in the system (George Soros’ reflexivity theory). The result is that finance is relegated to “social science”, which, given capricious human judgment, may as well be an oxymoron.
But where we cannot measure what is important, we are often tempted to make the grave error of making important what we can measure. This is the mistake that brought us the capital asset pricing model, or CAPM.
In this post, we’ll examine the CAPM, some of its weaknesses, and offer up some alternative suggestions to estimate the cost of equity.
Where to Draw the Line?
The CAPM framework starts with a few basic assumptions:
- There is a “risk-free” asset available for purchase by all investors—generally assumed to be some form of U.S. sovereign debt—and this asset generates a certain return.
- There is a stable “market risk premium” that equity (stock) investors will demand in excess of this risk-free return.
From this: the volatility in price, expressed in standard deviation of (usually daily or monthly) returns, of any asset can be benchmarked to the volatility of the market as a whole, using a linear equation. The coefficient in this equation, called “beta”, is a relative measure of a given asset’s volatility in relation to that of the market. A beta of one equals the market’s volatility. Higher betas are more volatile, lower betas are less volatile, and a beta of zero implies no volatility of returns.
Let’s say the risk-free government bond is yielding 3% if held to maturity, and the market risk premium is historically 7%. The expected return of the equity market should therefore be 10%. A risky stock with a beta of two should be priced to yield an expected return of 17%. In other words, that stock’s cost of equity is 17%.
The CAPM is a fine hodgepodge of statistical niceties, but it fails to account for many real-world conditions. I’ll group these into two categories.
Merely Making False Equivalences & Measuring the Immeasurable
- “Things are risk-free until they aren’t,” at which point the idea of anything being risk-free seems mind-numbingly naïve. In the long-run, the United States does not have a 0% probability of defaulting on its debt obligation.
- There are many different rates at which government bonds are priced, usually based on how much time remains until they mature. It’s unclear which of these rates is the true “risk-free rate”, although the one with the closest approximation to the expected time horizon matching that of the typical equity investor is likely the best that can be done. Even this may be subject to other problems—for instance, if the risk-free rate is assumed to match the 7-year Treasury yield in a case where the 7-year Treasury is thinly traded and investors can expect to earn a premium for the poor liquidity of the bonds. In such a case, the risk-free rate is incorporating a liquidity premium in addition to the time value of money component, which is the only factor meant to be represented in the theoretical risk-free rate.
- Because U.S. government debt trades on the secondary market just as stocks do, to assume a certain, risk-free return on an investment in this debt implies a certain time horizon depending on the maturity of the risk-free benchmark used, as opposed to selling the asset before maturity at a potentially different realized return. But if this is the case, why is the volatility of the counterpart equity asset marked to market daily or weekly? To compare apples to apples, shouldn’t the framework only consider the total return on the equity asset over the same time horizon as that on the risk-free asset?
- The market risk premium is subject to serious estimation error. While it could in theory be observed (by deducting from previous equity market returns the risk-free rate prevailing at that time), such processes of observation are backward-looking and may not align with actual future conditions.
- To observe the market return, we must have some credible understanding of what “the market” actually is. In principle the CAPM is meant to encompass the entire investable universe. But this creates even more Jordan Peterson-style battles over proper nomenclature: “What do you mean by ‘the market’? What do you mean by ‘invest’?” Where do beanie babies or NFT’s enter the picture?
Entirely Missing the Point
- The entire premise of CAPM equates the volatility of a stock’s price fluctuations with the actual risk in the underlying business. By doing so, the model forgets what being an equity investor actually means: owning a real claim on the profits of a real business. Companies face risk when key employees leave, products fail, or competitors innovate faster than they do. Companies do not face risk when the stock price fluctuates. This is the CAPM’s most fundamental error—incorrectly using observable volatility as a proxy for unobservable risk.
- If we take for granted that the “fair” price of a stock is the intrinsic value of the future cash flows generated by the underlying business, we realize that CAPM also assumes this intrinsic value changes based on non-economic factors such as the market risk premium and risk-free rate. For instance, a 1% lower market risk premium should reduce the cost of equity for a one-beta stock by 1%, raising its stock price even though nothing about the company’s actual position changed. The CAPM postulates that such changes should be reflected in the discount rates used to determine the present value of the business’ future earnings. This is the argument you could use to justify worshipping at the Federal Reserve altar to re-value every stock in your portfolio. In theory, it is plausible due to reflected opportunity costs of owning equity as opposed to other assets, but this is only relevant if you actually invest in those different asset classes.
But for all that—as my interviewer continued to insist—one should demand a higher expected return when the volatility of that return is expected to be high. And this is something that CAPM recognizes: for the most part, risk and return should be positively correlated. Thus, the CAPM should output a higher cost of equity for companies that truly are riskier, and vice versa. The best alternative approach will be one that reflects this idea.
Potential Alternatives
We’ll explore four ideas—some more comprehensive than others—to consider in thinking about the cost of equity.
1: No Overthinking Allowed
The approach that I recommended in my job interview was the simplest one possible. Just pick a number. If you think 10% cost of equity feels right, use 10%. If 12%, use that.
It’s useless to argue that this is a quantitative or intensely thought-out method, because it isn’t—and that’s the point. This is a heuristic designed to save time and focus on other parts analyzing & valuing a business that are both more amenable to analysis and relevant to the business.
The key advantage of the “pick a number” approach is consistently—for instance, use 10% for every company you look at. Of course, this presupposes that the general level of risk is consistent in the market you’re looking in. Maybe you use one number as a benchmark for U.S. stocks but add a few hundred basis points when considering companies in China, Mexico, India, or other emerging markets.
Another advantage of this method is that between similar companies in the same region of the world, costs of equity shouldn’t be significantly different. It makes no sense that Amazon trades more expensively than General Motors because Amazon investors are content with a lower threshold return—it’s because they place higher value on Amazon’s economic profits and growth prospects. A fixed cost of equity will therefore place these two companies on the same footing in terms of that one crucial variable, allowing you to isolate other components of intrinsic value to compare against the stock price. If your thesis on GM is that its “implied” cost of equity will converge to that of Amazon, this is madness.
The disadvantage of this approach is one common to consistent practices: it can be inflexible. Further, depending on how punitive it is, it can create periods where few equities look attractive. For instance, insisting on a 12% cost of equity during a tech bubble is a great way to not find any margin of safety.
Such a handicap needn’t be fatal, although this depends in part on what assets comprise your investable universe. If you’re a dedicated long-only equity investor, you have to own stocks, even if many of them are expensive. In such cases, a fixed cost of equity could create environments where you have to hold many names at less attractive valuations. Worse still: at the security level, research analysts may be tempted to “fudge” meaningful assumptions on revenue and margins to make a margin of safety appear higher—all to try and compensate for an inflexible and conservative cost of equity. Therefore, removing a source of error adds potential for new errors.
2: Stocks are Basically Bonds, Right?
We could, in theory, price stocks as if they were bonds. That is, build a full schedule of the expected value and timing of cash flows between today and the maturity of the security. We can do this without any reliance at all on the “cost of equity”. Then, we calculate the yield-to-maturity as with a bond: the discount rate at which the present value of our projected cash flow stream equals the current stock price.
This suggestion, though an interesting thought experiment, has several impediments to practicality:
- Stocks don’t mature. There’s no fixed due date like with bonds. These instruments live as long as the company lives—which is, in theory, forever. Of course, most companies do not survive indefinitely; the past is littered with the graves of immortal corporations from Enron and Lehman Brothers to Standard Oil and the East India Company. And we could probably capture most of a perpetuity’s value by assuming a life of, say, 50 years. But this is imperfect and prone to error.
- Equities are not “fixed-income” instruments. To be fair, neither are bonds. Every bond has some component of credit risk and bond prices have to incorporate some expectation of returns falling short of the fixed cash flows promised. But stocks are far more variable, because the financial performance of the companies they represent are variable. Yet to price stocks the same way we price bonds, we’d have to use a single schedule of estimated future cash flows. The only solution to this is to overlay these estimates with a probability distribution of some kind to reflect different potential outcomes. But this rigorous quantification is still likely to miss the true future path of the company’s results.
3: “My Time is Too Valuable”
Just a thought, especially for personal investing. If you as an individual are insistent on picking your own stocks, you have both to consider risk (which CAPM tries to do) and the opportunity cost of your time. There are thousands and thousands of stocks you might consider buying, but there are only twenty-four hours each day to evaluate them. All else equal, the more valuable your time (or the more time-constrained your investment process is), the lower your cost of equity should be. If you have more time to spend, you should demand a higher return on your investments in compensation for your investment of time and effort.
4: Infuse the CAPM with Meaning
There are some building blocks of the CAPM that need not be rejected out of hand—for instance, the concept that stocks with less predictable returns should compensate buyers with higher expected, or average, returns. Where the CAPM gets this messed up is by using a poor proxy for risk (volatility of stock returns).
In theory, we can take a step in the right direction by replacing the stock’s return in the CAPM formula with a different variable—either the company’s earnings yield (net income divided by the market cap, or inverse of the P/E ratio), or the company’s free cash flow yield (FCF as a % of market cap, or inverse of P/FCF ratio).
Let’s say (making up numbers) the total cash flows and total market cap of the S&P 500 (assuming this is a market proxy) are such that the index has yielded a 5% free cash flow yield in the past, and that the standard deviation of this yield is 1.5%. We can now benchmark any given company’s cash flow yield against that of the index over a given time period, and calculate beta in just the same way as we would if we were using stock price returns. This analysis is well within the realm of what’s possible with existing fundamental data providers. We’re still comparing the volatility of a security’s performance with that of the market, but we’re using a metric that seems more closely tied to the long-term success of an investment in that company.
This type of modification wouldn’t absolve the CAPM of all of its failings. We would still be using a backward-looking method based on volatility to price forward-looking risks. Even worse, we’re introducing a potential sample-size bias. We can get stock returns every day, but free cash flow and earnings are generally reported only once per quarter, and therefore even a daily calculation of the relevant yields would only update one of the two variables in each ratio: the market prices. We can mitigate this somewhat by using last-12-month cash flows and earnings—but over a ten-year horizon there will only be 37 such twelve-month periods to evaluate.
This analysis also fails to account for a company’s growth: some companies have lower cash flows because of investments they’re making for future growth. In some cases, this growth may be already occurring; in others, it might not be. Adding the cumulative growth rate in FCF over the forecast period may not be the appropriate adjustment—but some adjustment is necessary to give credit for a company’s expected growth.
Any replacement of the CAPM with a more relevant formula is bound to run into some such hurdles regarding implementation. For our purposes here, we simply suggest that some such formula is likely to be discoverable, one which can improve on the original model by focusing on metrics more meaningful for long-term value investing. Of course, the ultimate test (as with the original) is whether or not such implementation is amenable to making serious investors any money—if not, the improvement would be simply theorizing for its own sake.
Such theorizing, however, is sufficient to afford some key understanding of what the cost of equity is. It is both intangible and indispensable, both vital and subjective. It’s a factor that investors and companies must grapple with—but when they do, they must remember that “not everything that counts can be counted”, and vice versa.
If readers are interested, we’ll take some time to experiment with some replacement formulas for CAPM, and really explore the numbers.