Equity beta and the capital asset pricing model are a fixture of equity valuation, yet both are commonly dismissed as too simplistic. Restrictive assumptions, patchy empirical support, statistical noise in beta estimates, and a difficult to pin down risk premium, all invite scepticism.
We explain why we think the criticism of CAPM is often overdone. Used with judgement, a single-factor CAPM can be more reliable than seemingly more sophisticated alternatives. We also examine an implied-return approach to valuation, and whether it can remove the need for CAPM altogether.
In an earlier article, ‘Calculating and analysing the drivers of equity beta’, we explained how best to calculate and analyse a historical equity beta and its drivers. That article includes a downloadable interactive model that can be used to derive an equity beta for any stock, using price data available in Excel. The model is specifically focused on the volatility and correlation components of equity beta that we discuss below.
In this article we step back and ask a different question: how much of the criticism levelled at beta and CAPM is actually justified, and what should investors do when the criticism is justified? Our focus is on beta as a measure of risk and as a factor that determines the required equity return and discount rate in valuation models. Of course, the other key component of CAPM – the equity risk premium – is also problematic, but because it is difficult to estimate rather than because its relevance is in doubt.
Risk affects value in two ways – expected cash flows and the discount rate
Risk affects equity value through both the cash flows being valued and the rate at which those cash flows are discounted. Building risk separately into both components is not double counting; the two adjustments capture different things.
Future cash flows should, in principle, be probability-weighted across possible outcomes rather than based on a single ‘most likely’ outcome. We explored this distinction, and why it mattered during the disruption caused by Covid-19, in our article ‘The most likely profit may not be the most relevant profit’. Getting the cash flow forecast right (and ensuring it is unbiased) matters, but our focus for the remainder of this article is how risk should be reflected in the discount rate.
Why CAPM still matters
It is generally accepted that investors are risk averse and require a higher return from riskier investments, which for equity valuation translates into a higher discount rate or a lower valuation multiple. The best-known method for deriving a risk-adjusted discount rate is the capital asset pricing model, which expresses the required return as the risk-free rate (rf) plus an equity risk premium (ERP), scaled by a beta coefficient:
Required return = rf + ERP × β
The theoretical foundations of CAPM rest on some fairly restrictive assumptions: that risk can be measured by return volatility, that returns are normally distributed, and that markets are frictionless enough for a single ‘market portfolio’ to apply to all investors. We set out these assumptions, and how beta itself is calculated, in our companion article; here we are more interested in whether the framework holds up in practice than in restating the mechanics.
CAPM endures because the alternatives are not obviously better
These assumptions, and the difficulty of finding conclusive empirical support for the model, have prompted many attempts to extend or replace it. The most common extensions are multi-factor models, which add further risk factors, such as size, value or momentum, to the market factor. First, it is worth testing whether the two building blocks of beta – volatility and correlation – actually affect investor behaviour in the way CAPM assumes.
Testing the building blocks of beta
Beta combines two separate measures: the volatility of a stock’s own periodic returns, and the correlation of these returns with those of the market. Both are questioned in isolation. If neither drives stock pricing in practice, the case for CAPM would be weak; if both demonstrably do, that is a reasonable basis for retaining beta and CAPM, at least as a starting point.
Equity beta = Stock volatility / Market volatility × correlation of stock and market returns
Does volatility matter?
The risk measure underlying CAPM is volatility, with beta (through the correlation component) capturing how a stock contributes to the volatility of a diversified portfolio. Critics argue that other risk measures matter more to investors, particularly downside risk or the probability of a large loss, and that volatility alone is too blunt a tool.
Changes in volatility are strongly negatively correlated with market returns
We think this criticism is overstated and that volatility is clearly a factor driving investor behaviour. Furthermore, even if investors focus on other risk factors, these are generally a variation on (and correlated with) volatility anyway.
The relationship is easy to observe by comparing the VIX index, which measures the US market’s implied 30-day volatility, with the level of the S&P 500 itself. Changes in the VIX are strongly negatively correlated with changes in the index – a coefficient of around -0.77 over the past decade, when calculated using our own model, with a VIX futures ETF as a proxy for changes in implied volatility. A correlation of that size implies that roughly 60% of daily variation in the S&P 500 can be linked to shifts in investors’ perception of risk.
Daily change in S&P 500 index volatility versus change in S&P 500 index
The Footnotes Analyst equity beta model
VIX is a short-term measure and may not fully capture longer-term risk expectations, but we think an increase in short-term implied volatility is likely to be linked to the same underlying risk factors that matter over longer horizons. If volatility clearly matters for pricing an index, it is difficult to argue it is irrelevant for pricing the individual stocks that make it up.
Does correlation matter?
Correlation determines how much of a stock’s risk can be diversified away. The portion that cannot be eliminated – the systematic or non-diversifiable risk – is what should matter to an investor holding a well-diversified portfolio. Correlation with the market varies considerably by sector and business type; we set out some of the drivers, including business mix, size and leverage, in our earlier article.
Evidence that correlation is priced directly into individual stocks is hard to pin down empirically, but there is reasonable indirect evidence from how investors behave. Gold is a familiar example: one reason investors hold this asset is its historically low, and sometimes negative, correlation with equities. Over the last ten years a physical gold ETF has shown a correlation with global equity markets of about 0.11. However, that characteristic looks more fragile over a shorter period: using a three-year window, correlation has risen to around 0.18. The latest three-year daily beta for this gold ETF has reached 0.26, driven by both higher gold price volatility and higher correlation.
Time series of physical gold ETF equity beta
Three-year rolling daily-return beta time series for the SPDR Gold Shares ETF (ARCX:GLD), the world’s largest physically backed gold ETF, derived using The Footnotes Analyst beta calculator.
Our equity beta model can produce beta, volatility and correlation data, together with this chart, for any stock or ETF where historical prices are available in Excel. Inputs for the historical period covered and return frequency can be modified. The model is free to download.
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Low correlation is used as a marketing feature by hedge funds and asset managers
Some hedge funds, particularly long-short funds, and are marketed explicitly on low or even negative correlation. The AGF US Market Neutral Anti-Beta fund (ARCX:BTAL) is an extreme example. It holds long positions in low-beta stocks against short positions in high-beta stocks, producing a fund correlation to the market of -0.63 using daily returns over three years. The return performance of this fund has been unremarkable, probably because the high-beta stocks being shorted include many of the technology stocks that have recently driven much of US market returns. This suggests investors may be buying the fund primarily for its diversification properties rather than its returns.
AGF US Market Neutral Anti-Beta fund equity beta
Three-year rolling daily-return beta time series for the AGF US Market Neutral Anti-Beta fund (ARCX:BTAL), derived using The Footnotes Analyst beta calculator.
Pension fund investment strategy statements frequently make the same point. One pension fund, for example, cited the low correlation of energy transmission assets to both equities and commodities as a reason for holding them, alongside their stable operating cash flows. If correlation is important enough to be marketed as a feature and written into pension strategy documents, it is reasonable to conclude it matters at the level of an individual stock too.
The importance of correlation is also evident from portfolio theory itself. If investors price an investment largely on the basis of how it behaves within a diversified portfolio, rather than in isolation, then correlation must logically matter alongside volatility.
Beta may not be the whole story of how investors price risk, but the evidence that differences in the two components, volatility and correlation, are reflected in investor behaviour and in market prices – and that neither is fixed over time, as the gold example shows – is, in our view, hard to dismiss.
The case against multi-factor alternatives
Commercial multi-factor risk models, such as those from BARRA, Axioma and Northfield, are widely used by portfolio managers, but their primary purpose is to construct and manage diversified portfolios, not to set the discount rate for an individual stock. These models estimate a covariance matrix across many stocks, then use it to minimise portfolio risk, or tracking error, subject to constraints. The market factor (the CAPM beta) typically still dominates.
Applying the same multi-factor logic to a single-stock discount rate is different. Multi-factor extensions to CAPM require an estimate of the stock’s beta to each additional factor, and an estimate of the risk premium attached to each factor, on top of the market beta and equity risk premium CAPM already requires. Every additional parameter is itself subject to estimation error.
More factors mean more parameters and more estimation error
For portfolio construction, where errors in individual factor exposures can partially offset across many holdings, this trade-off often makes sense. For pricing a single stock’s discount rate, we are less convinced. A well-estimated single-factor CAPM may in practice produce a more reliable discount rate than a multi-factor model that looks more sophisticated but carries more compounded estimation error.
A genuine limitation: non-normal returns
CAPM’s use of volatility as the sole measure of risk depends on returns being normally distributed, so that the mean and standard deviation fully describe the distribution of outcomes. Equity returns are not normally distributed in practice: they exhibit fatter tails and more skew than a normal distribution would predict, particularly during periods of market stress. This is a genuine limitation, not one we think CAPM’s defenders should dismiss.
We think this matters more for pricing tail risk and extreme outcomes than for setting a routine discount rate in a going-concern valuation. It is a reason to treat CAPM as an approximation and to apply judgement around it, rather than a reason to discard beta altogether. It is also a reason why judgement is required even after a well-structured DCF valuation is in place.
Beta may not be the only factor that drives discount rates, valuation multiples and stock prices, but it is certainly relevant. The two sections below look at where that judgement is most needed in practice: in interpreting a quoted beta, and in estimating the other key CAPM input, the equity risk premium.
The importance of forecasts
Everything discussed so far relies on a well-estimated beta, but every beta coefficient you will see quoted, however it is labelled, is derived from historical price data. Data providers sometimes describe an adjusted beta as a ‘forecast’, but the adjustment is simply a statistical technique, such as pulling the historical estimate towards 1.0 to remove assumed bias; it is not a genuine forecast of future risk. We explain this adjustment, and why we are sceptical of it, in our companion article and in the downloadable interactive model for calculating and testing your own beta estimates.
A backward-looking beta is not a forecast of risk
A discount rate needs to reflect risk over the period being discounted, not simply whatever a data provider last calculated. That means treating a quoted historical beta as a starting point rather than an answer. Focus on understanding the volatility and correlation components and their trends over time, the margin of error, and whether the business or its financial leverage has changed since the estimation period. Then apply judgement to arrive at a figure you are willing to defend, in exactly the same way you already apply judgement in forecasting profit and cash flows.
The equity risk premium is just as hard to pin down
Beta is not the only CAPM input for which precise measurement is impossible. The equity risk premium – the extra return investors require for holding equities rather than risk-free government bonds – is at least as contested as beta, and arguably more consequential. Estimates of the ERP vary considerably depending on whether they are derived from long-run historical returns, survey evidence, or a market-implied approach.
We do not think this uncertainty invalidates CAPM any more than beta’s margin of error does. A CAPM-derived discount rate is not a single, precise number waiting to be looked up: it depends on two separately estimated inputs, both requiring judgement and both capable of moving a valuation materially.
We set out our own approach to estimating the equity risk premium in our article ‘Intrinsic value and the equity risk premium’. Taken together, beta and the equity risk premium illustrate a wider truth about equity valuation: even a theoretically sound framework such as CAPM only produces useful answers when investors bring judgement to its inputs, rather than treating either of them as a fixed fact.
Deferring the need for a required return
Valuing a stock with a discounted cash flow model inevitably requires a discount rate to be set before a value can be calculated. This article has, so far, addressed how that rate should be derived, with qualified support for the application of beta and CAPM. However, some approaches to equity analysis instead defer the consideration of risk and required return to later in the process.
Valuation multiples are one example. It is in the interpretation of a multiple, not its calculation, that risk and required return become relevant: a higher risk and higher required return deserve a lower multiple. This consideration is often a subjective overlay rather than a CAPM-style analysis, but it is still a step that should not be ignored.
For relative valuation, DCF-based implied returns may be more useful than simple multiples
An alternative way of deferring the required-return question is a reverse DCF: deriving the return implied by a stock’s current market valuation. Applied to enterprise value and enterprise cash flows this gives an implied unlevered return; applied to equity flows, as in a dividend discount model, an implied levered return. We think comparing these implied returns across stocks can be a highly effective approach to valuation.
While the application of implied returns is similar to the relative comparison of investments using valuation multiples, implied returns have the advantage of being based on a more comprehensive underlying DCF methodology. They are cash flow based and reflect multiple forecast years rather than the single-period profit, such as that used in the commonly quoted EV/EBITDA or price-earnings ratio. However, the challenge of implied returns is dealing with the need for longer-term forecasts, particularly those beyond the typical forecast horizon seen in consensus estimates. Implied returns are arguably more subjective and prone to model error than a simple multiple.
Implied returns also have some similarity with the forward-priced multiples1See our article ‘Why you should ‘forward price’ valuation multiples’. that we have previously highlighted. A forward multiple is the result of a partial DCF approach, although unlike implied returns, this methodology does require a discount rate to be set before the forward multiple can be calculated.
An implied return must still be judged against the risk of the investment. A high implied return may simply be compensation for genuinely higher risk, not an indication that a stock is cheap. We think a reverse DCF approach, used alongside a conventional CAPM-based analysis of risk rather than as a replacement for it, is a useful way to compare stocks and cross-check a valuation. It does not remove the need for judgement about risk, but it does move that judgement to later in the analysis, where risk can be assessed either subjectively or through beta and CAPM.
Insights for investors
- Simplicity is not necessarily a limitation. For a single stock’s discount rate, a well-estimated single-factor CAPM may be more reliable than a multi-factor model that adds parameters, and estimation error, without a clear offsetting benefit.
- Both components of beta are demonstrably priced by the market, but neither is fixed – volatility and correlation can both shift significantly over time.
- Non-normal returns are a genuine limitation of CAPM, particularly for pricing tail risk, but this is arguably better addressed through judgement than through abandoning beta altogether.
- Remember that quoted betas are backward-looking, even those labelled as ‘forecast’. Valuation requires current and forecast risk – use judgement to adjust for what has changed.
- Consider using a reverse DCF approach to derive an implied return. It does not eliminate the need to consider beta and required return, but it allows that assessment later in the analysis.