By Erik Kobayashi-Solomon, Managing Director – Framework Investing
The first rule of modern finance – that a dollar today is worth more than a dollar tomorrow – is an elegant first principle that underlies project financing as well as bond and equity investing.
This industry is projected to double in size from $22 billion to an estimated $44 billion
However, in equity investing, the tactical implementation of this elegant principle – the rate used in discounted cash flow analyses – is contentious because of the subjectivity of choosing an appropriate rate. This subjectivity is born from the fact that, unlike bonds, stocks have no nominal coupon rate or face value from which to calculate the current market rate. Equity discount rates are, in other words, unobservable, so subject to differences in opinion and methodology.
Corsair Capital was down by about 3.5% net for the third quarter, bringing its year-to-date return to 13.3% net. Corsair Select lost 9.1% net, bringing its year-to-date performance to 15.3% net. The HFRI – EHI was down 0.5% for the third quarter but is up 11.5% year to date, while the S&P 500 returned 0.6% Read More
Our position is that the traditional method of assigning an equity discount rate – boosting a fixed income reference rate by a “risk premium” – is fundamentally flawed because it fails to take into consideration the very different types of risk borne by fixed income and equity investors. We believe that the risks borne by fixed income and equity investors cannot be directly compared, so basing equity rates on fixed income rates is invalid.
Because we see conceptual problems in combining and comparing fixed income and equity rates, it follows that we also reject the commonly-used measure of Weighted Average Cost of Capital (WACC). Our position is that talking about a “weighted average” of two fundamentally different quantities makes as little sense as averaging apples and oranges.
The Capital Asset Pricing Model (CAPM) is the academically-accepted framework for assigning appropriate discount rates. There are a multitude of theoretical issues with using CAPM to determine equity discount rates, a good summary of which listed here. From an empirical standpoint, Fama and French, as well as others, have shown that CAPM simply has limited or no predictive power in the real world.
Despite the demonstrated weaknesses in the CAPM formulation, the methodology that it represents – namely, “start with a fixed income rate and add something to account for added risk” – persists as the go-to method for thinking about determining cost of equity.
In natural language, the CAPM tells us that the appropriate discount rate for an equity investment is directly related to the risk-free rate and to the asset’s price variance compared to that of the market.
Let’s pull apart the CAPM, see why it is inappropriate for determining a company’s cost of equity, and build a model for a more effective, sensible way of performing this vital task.
Low-Hanging Fruit: Discard Beta
The first thing that sufficiently capitalized principal investors can do to improve the CAPM equation is to discard the beta term – representing covariance of the asset vis-à-vis the market, normalized by the asset’s own variance. An unlevered principal investor need not worry about market price fluctuations over an arbitrarily short time frame; investment returns are not path dependent, but rely only upon the start and end points and whatever cash flows were realized during the interim period.
Levered and agent investors are concerned with path dependency and market price fluctuations, but the reasons are much less related to discount rates and the value of the asset – the topics of our discussion – and much more to market and career risk, respectively.
Levered investors may have to re-collateralize a margin account, so should acknowledge up front that valuation risk is less important to them than the level and type of leverage used (i.e., margin account or options). Agent investors must acknowledge the time-dependent nature of returns of stocks under their management because underperformance for any one year might affect their fund’s assets under management and / or career prospects. Again, these issues do not pertain to the question at hand, so we will just say that the concept of beta, a formalization of the “risk” associated with path dependency, should be ignored when considering an appropriate discount rate for principal investors.
The Crux of Our Argument: Risk is Vector, not Scalar, and Different Types of Risk Cannot Be Summed
The more important reason to invalidate the CAPM and its back-of-the-envelope cousins is that the risk incurred by a bond investor is different in nature from the risk incurred by a stock investor and, in our view cannot and should not be compared or “weighted.”
Let’s look at two investors – one, an investor in a fixed-rate bond of an economically mature, stable company; the other, an investor in the stock of that same company.
The credit investor accepts the risk that the investee company will fail. In exchange for accepting this risk, the credit investor receives a fixed, periodic fee, and may also hold legal rights to ownership of the firm’s assets if the equity value of the company collapses to zero.
Note that the bond investor is not betting on the firm’s success – its future growth and prosperity – but rather betting against its failure. If the company can generate enough cash to pay interest and principal payments over the life of the bond, the bond investor is satisfied.
In contrast to a bond investor, an investor in the equity of the company is betting for its success relative to alternatives. Equity is a residual claim on future economic growth, so if a company in which one holds an investment fails to boost its economic value as fast as alternative investments do, the investment will not be successful on a relative basis.
Put simply, equity risk represents an opportunity cost because of the nature of equity itself.
Anyone who has had to make practical investing decisions knows full well that the risk associated with not failing is very different than the risk associated with not succeeding. In the parlance we use at Framework Investing, a bond investor accepts exposure to a company’s failure (on an absolute basis) while an equity investor gains exposure to a company’s success (on a relative basis).
Clearly, the two risks are connected, especially at a specific and fairly rare point: the point at or near which the book value of equity of a company goes to zero. We would submit, however, that for most companies, most of the time, the relationship between absolute failure (bankruptcy) and relative success are tenuous at best, and cannot and should not be connected theoretically or mathematically.
The CAPM and similar methods treat rates as scalar quantities. However, as is clear from our examples, risk is not a scalar, but a vector term, that is intimately tied to directionality of outcomes. Three percent payment in exchange for accepting downside risk simply cannot be added or compared to opportunity costs related to gaining exposure to upside potential.
This dichotomy is made starker when we think back to the way the CAPM is implemented. The CAPM relates a specific company’s cost of equity, not to the company’s cost of debt, but to the rate paid by on debt issued by a sovereign government.
At a high level, investors in government bonds are betting that the overall economy of the issuing nation-state will remain robust enough and that the rule of law and administrative effectiveness of that nation-state will remain secure enough that tax receipts from the economy will continue at a sufficient level. In other words, investors in government bonds are betting that the taxation power of a state will not fail.
This nation-state level risk is clearly different from either risk mentioned in the table above. Why should the opportunity cost for owning an equity ownership in a company relative to alternative equity investments be in any way related to the power of a nation to tax its citizens?
It’s true that the compensation for accepting the extremely low risk of a nation-state losing taxing power should be low, and that that the opportunity cost of investing in an individual stock instead of some alternative will likely be higher. CAPM describes the relationships between the two risks correctly, but attempts to connect the two mathematically when they cannot and should not be. Just because the relationship between the rates set forth by the CAPM is appropriate (i.e., sovereign bond rate is lower than company-specific equity rate) does not mean that the formal description of that relationship is correct or even valid.
With this line of reasoning, we discard any reference to risk-free interest rates in CAPM, and CAPM collapses.
To build up an alternative to CAPM, let’s focus in on the topic of opportunity costs and making risky choices.
Our CAPM Alternative: Based on Long-Term Risky Choices
As equity investors, we are confronted by a plethora of choices.
The most fundamental choice, and one that has received a great deal of attention recently, is that of whether to actively invest or to make a passive investment in an index fund.
The case for active management has become more difficult. An illustration of this difficulty is the anecdote of a bet between renown value investor Warren Buffett and a hedge fund-of-funds manager that over a 10-year time horizon, an investment in a low-cost index would beat an investment in a selection of hedge funds.
Reportedly, Buffett is only months away from winning this $1 million bet as the hedge fund has generated $200,000 in profit, versus index profits of $854,000. The opportunity cost of the active investment has been significant – the principal owner of capital would have been significantly better off by investing in the index.
Over time, it has been academically demonstrated that it is difficult for agent investors to consistently construct baskets of individual investments whose aggregate price performance exceeds that of the price performance of the broad index.
We submit that, the opportunity cost of investing in an individual equity security should be measured against the expected return of the market as a whole. At the initiation of an investment in the equity of a firm, any investor can decide whether or not to invest in an individual security or in an index. If a company is unable to generate cash flows sufficient to boost its value by at least the rate at which we can reasonably assume the index will, there is clearly an opportunity cost to investing in that company and an investor would be better off investing in the index at large.
At what rate can we reasonably expect the market to compound? For that, we look back at an historical series as a base.
This series only goes back to 1950, but carrying the analysis back to the late 19th century (using Shiller’s data), generates similar return statistics. Each line represents the listed compound annual growth rate for an investor who buys the index on a particular day and sells the index on the day closest to the time period listed (i.e., 10, 20, 30, or 40 years later). Average values for CAGRs in each of the four time periods are within 41 basis points of one another and hover around 7% per year. These returns do not include reinvestment of dividends; once dividends are included, the average CAGR moves up to around 10% per year. This 10% per year level was also found by Ibbotson and Chen in research published in 2003.
As much as academics in the finance world like to think otherwise, the business of investment is a business of horseshoes and hand grenades, and any digits to the right of a decimal point should be considered for their comedic value only. The actual return of large cap stocks as measured by serious academics is probably a few basis points on one side or the other of 10%, but for simplicity’s sake, we use the 10% figure to discount future cash flows.
In other words, our rewrite of CAPM becomes:
The discount rate must be equal to the expected market return because the risk we are taking is related to opportunity costs.
Stability of Our Discount Rate
In our opinion, one of the great shortcomings of CAPM’s estimate of cost of equity is that it is continually changing. A continuously changing discount rate makes sense only if one assumes that 1) securities are efficiently priced and 2) path dependence matters. As value investors, we reject the first contention and earlier in this essay explained why path dependence should not matter to principal investors.
In general, we believe that the only important risk to owners of a company’s equity is the uncertainty surrounding its operational performance. Changing technology, shifting customer preferences, fluctuations in input prices, and other factors certainly affect the ability of a company to continue generating cash flows. However, the one constant imperative is that the company manages its response to the competitive environment and invests wisely enough to continue to generate value for its shareholders that meets or exceeds the market at large.
We believe that equity market returns are a function of economic growth and aggregate capital structure – with equity owners essentially receiving levered exposure on the growth of the underlying economy. Several recent academic papers also find this to be empirically true (Cornell (2009), Straehl and Ibbotson (2017)). We think there are good reasons to think that economic growth rates in developed markets over the next 10 years are likely to fall (e.g., demographic pressures, a return to zero-sum, nationalistic trade policies, increased outlays for maintenance capital expenditures to account for environmental degradation, etc.). If we are right about this, the broader market will likely lag its average historical rate of growth and our required hurdle rate for investment will likely fall.
Even still, we continue to use our 10% cost of equity for large capitalization firms so we do not take on idiosyncratic risks as the market resets its economic growth expectations lower.
 An “agent investor” is a professional investor working on behalf of a principal owner of capital – a professional money manager, in other words.