CAPM: Expected Return and Beta

Reading-order note. Numbered #2 and drafted third, after the risk-free rate and the equity risk premium, because CAPM assembles both and inherits every uncertainty in each. All figures come from the hub's canonical parameter set and are illustrative teaching values, not forecasts; no beta or required return here describes any real company, and no number of holdings is recommended.

Its answer is a single line: the risk-free rate, plus a premium scaled by how much the asset moves with the market. It is the most influential model in finance and it does not survive contact with the data. Both halves of that sentence are true and both matter, because the idea underneath it is durable even where its predictions fail, and it remains the shared vocabulary in which cost of equity is discussed everywhere.

The insight that survives: only some risk gets paid for

Start with the observation the whole model is built on: risk splits into two kinds, and only one of them is compensated. Unsystematic (diversifiable) risk is specific to a company: a factory fire, a failed product, a fraud. Systematic (market) risk is common to everything: recessions, rate shocks, the general state of the world. The reason this matters is economic rather than mathematical: diversifiable risk can be removed at almost no cost simply by holding more things, so nobody has to be paid to bear it, and in a competitive market nobody is. Only the risk that cannot be diversified away commands a premium. That is the deepest idea in the model and it stands independently of any of CAPM's later problems. The arithmetic of diversification makes the split visible. Take individual holdings with 30% annual volatility and an average correlation of 0.25 between them. One holding carries 30.0%. Five carry 19.0%. Ten carry 17.1%. Thirty carry 15.7%. A thousand carry 15.0%. The decline stops at 15.0% and no amount of further diversification moves it; that floor is the systematic component, the risk that remains after every idiosyncratic exposure has been averaged away. Most of the benefit arrives early: going from one holding to ten removes about six-sevenths of the removable risk, and going from thirty to a thousand removes almost nothing.

The model, and what beta actually is

CAPM says the expected return on an asset is the risk-free rate plus its beta times the equity risk premium. On canonical inputs, 4.0% risk-free and a 5.0% premium, that gives β 0.60 → 7.0%, β 1.00 → 9.0%, β 1.40 → 11.0%. Beta measures sensitivity to market movements: 1.00 means the asset has historically moved with the market, above 1.00 means it amplified market moves, below means it damped them. Now four things beta is not, each of which is misunderstood routinely. Beta is not volatility. A wildly volatile asset whose movements are unrelated to the market has a low beta, because the model only counts the part of its movement that travels with everything else. Beta is not risk in the ordinary sense. It says nothing about the chance of permanent loss, fraud, obsolescence, or a business model quietly failing; a stable company sliding into irrelevance can carry a comfortable beta the entire way down. Beta is not a forecast. It is a regression coefficient fitted to past returns, and it is used as though the relationship it measured will persist. And beta is not a single number. It depends on choices, the estimation window, the return frequency, and which index stands in for "the market", and different defensible choices produce materially different betas for the same company, which is the practical problem the worked example below quantifies.

Where the model fails, and why it is still everywhere

The empirical record is genuinely unkind, and an honest treatment states it plainly. The relationship between beta and return is flatter than the model predicts. Research examining long periods has repeatedly found that low-beta assets earned more than CAPM says they should and high-beta assets less; the pattern is documented well enough to have its own literature and its own strategies built to exploit it, which is roughly the opposite of what a working model looks like. Beta alone does not explain the cross-section of returns. The multi-factor research tradition established that characteristics such as company size and valuation ratios carried explanatory power beta did not, which is why factor models exist at all; that work belongs to Pillar 28. And there is a foundational objection. The model's "market" means every risky asset in existence, equities everywhere, property, private businesses, arguably human capital, which is not observable. Every test therefore substitutes an index, so what gets tested is the index rather than the theory, and a critique along these lines has stood since the 1970s without a satisfying answer. The assumptions are also plainly false: a single holding period, all investors sharing the same expectations, no taxes or transaction costs, and unlimited borrowing and lending at the risk-free rate. So why does it persist? Three honest reasons. It gives a shared language: cost of equity is quoted in CAPM terms across the profession, so the model is the common ground on which disagreements are stated. It enforces a discipline, requiring that a required return be justified by something rather than asserted. And its central insight remains correct: compensation attaches to non-diversifiable risk. The useful posture is to treat CAPM as a structured way of asking the question rather than a machine for producing the answer, which is also how the honest practitioners who use it daily treat it.