The idea behind CAPM: only undiversifiable risk is paid for
CAPM starts from an observation about diversification. Hold one stock and you carry two kinds of risk: whatever happens to that company specifically, and whatever happens to the market as a whole. Hold thirty stocks and the company-specific risks largely cancel — one firm's factory fire is offset by another's good quarter. The market risk does not cancel, because every holding moves with it.
From that, the model draws a sharp conclusion: you should not be paid for risk you could have diversified away for free. Only the exposure that survives diversification — systematic risk — earns a return. Beta measures precisely that exposure. It is the slope from regressing the asset's returns on the market's, so a beta of 1.15 says that, historically, the asset moved 1.15% for each 1% move in the index.
The formula then reads as a price list. Start at the risk-free rate, which you can earn without taking any market risk at all. Add the market risk premium, which is the extra return investors demand for holding the market rather than Treasuries. Scale that premium by beta, because you are taking beta times as much market risk as the index does. That is the whole model: E(Ri) = Rf + β × [E(Rm) − Rf].
The result is a required return, not a forecast. It is the hurdle. A stock whose expected cash flows imply a lower return than this is overpriced for its risk; one that implies a higher return is a candidate. That framing is why CAPM appears in three places at once: in valuation as the discount rate on equity, in corporate finance as the cost of equity inside WACC, and in performance measurement as the benchmark for alpha.
Choosing the three inputs, where all the disagreement lives
The arithmetic is trivial and the inputs are contested. Practitioners using the same model on the same company routinely land two or three percentage points apart, and every point of that gap comes from these choices.
Risk-free rate. Match the maturity to the horizon of what you are discounting. For a company valuation with cash flows running decades out, the 10-year Treasury yield is the near-universal convention; for a one-year holding-period question, a one-year bill is the coherent choice. Use the nominal yield with nominal cash flows and a real yield with real cash flows — mixing them is the single most common structural error.
Beta. Published betas differ because the estimation choices differ: five years of monthly returns against a broad index is the most common recipe, but two years of weekly data against a different index gives a materially different number for the same stock. Many providers also apply the Blume adjustment, shrinking the raw estimate two thirds of the way toward 1.0 on the empirical finding that betas revert. For a private company or a division, you cannot regress anything — you take a peer group's betas, strip out their leverage, average, and relever at your own capital structure, which is what our unlevered beta calculator does.
Market risk premium. This is the least observable and the most argued-about number in finance. The two approaches are historical — the realised excess return of equities over government bonds across a long sample — and implied, which backs the premium out of current index prices and forecast cash flows. They disagree, they both move with the sample and the method, and neither is authoritative. Because beta multiplies this number, an error here scales directly into your answer: a stock with a beta of 1.5 turns a one-point difference in the premium into 1.5 points of required return.
Enter the premium directly if you have a house figure; enter an expected market return if you would rather reason about the level. The calculator treats both routes identically, since the premium is just the market return minus the risk-free rate.
Worked example: a beta 1.15 stock with a 4.3% risk-free rate
You are valuing a stock with a published beta of 1.15. The 10-year Treasury yields 4.30% and your house view is that a broad equity index will return 9.50% over the same horizon. The stock actually returned 11.00% last year.
- Market risk premium. 9.50% − 4.30% = 5.20%. This is the reward for holding the market instead of Treasuries.
- Scale it by beta. 1.15 × 5.20% = 5.98%. The stock carries 15% more systematic risk than the index, so it must earn 15% more premium.
- Add the risk-free rate. 4.30% + 5.98% = 10.28%. That is the required return, and it is the discount rate you would apply to this company's equity cash flows.
- Compute alpha. 11.00% − 10.28% = +0.72 percentage points. The stock beat what its systematic risk demanded, by a margin that is well inside the noise of a single year.
Now test the sensitivity that matters. Keep everything else fixed and move the market risk premium from 5.20% to 6.20% — one point, easily within the disagreement between two reputable estimates. The required return becomes 4.30 + 1.15 × 6.20 = 4.30 + 7.13 = 11.43%, and the alpha flips from +0.72 to −0.43 points. The stock did not change. Your view of the equity premium did, and it moved the verdict by 1.15 points — exactly beta times the change, which is the model telling you where its own fragility is.
Reading the result, and reading the security market line
Plot required return against beta and you get a straight line: intercept at the risk-free rate, slope equal to the market risk premium. This is the security market line, and every correctly priced asset sits on it. An asset plotting above the line is offering more return than its beta requires — that vertical distance is Jensen's alpha, and it is what active managers are paid to produce.
Note what the vertical axis is not. The security market line prices assets against beta, not against total volatility. A stock can be enormously volatile and have a low beta if its volatility is idiosyncratic, and CAPM will demand very little extra return from it, because a diversified investor does not bear that volatility. The Sharpe ratio makes the opposite choice, dividing excess return by total standard deviation, which is the right measure when the portfolio in question is your whole portfolio rather than one holding within it.
A few sign cases are worth having straight. A beta of zero returns exactly the risk-free rate whatever the premium, because the asset carries no systematic exposure to price. A negative beta — rare, but the property people are buying when they hold long-duration government bonds or certain hedges — puts the required return below the risk-free rate, and that is not a modelling error: an asset that pays off when everything else falls is worth holding even at a poor standalone expected return, precisely because of when it pays.
Alpha over a single period tells you almost nothing. The estimate is noisy, the beta used to compute it is itself estimated, and the market risk premium is a judgement. Alpha becomes evidence only across many periods, and even then the model attributes to skill anything it cannot explain with beta — including exposures to size, value, profitability or momentum, which later multi-factor models were built to capture.
Required return by beta at a 4.3% risk-free rate
| Beta | Risk premium earned | Required return | Typical profile |
|---|---|---|---|
| 0.00 | 0.00% | 4.300% | Risk-free asset |
| 0.25 | 1.30% | 5.600% | Very defensive |
| 0.50 | 2.60% | 6.900% | Regulated utility |
| 0.75 | 3.90% | 8.200% | Consumer staples |
| 1.00 | 5.20% | 9.500% | The market itself |
| 1.25 | 6.50% | 10.800% | Broad industrials |
| 1.50 | 7.80% | 12.100% | Cyclical or levered |
| 1.75 | 9.10% | 13.400% | High-growth technology |
| 2.00 | 10.40% | 14.700% | Highly levered equity |
The profile column describes where such betas are commonly observed; it is illustrative and no substitute for the estimated beta of the specific security.
What CAPM assumes, and where it breaks
- Investors hold diversified portfolios. If your position is concentrated, idiosyncratic risk is real to you and CAPM will understate the return you should demand.
- Beta is stable. It is estimated from the past and used for the future. Betas drift with leverage, business mix and the estimation window, which is why the Blume adjustment shrinks them toward 1.0.
- One factor explains returns. Decades of evidence show that size, value, profitability and momentum carry premia CAPM does not price. Multi-factor models exist because CAPM's residual is not random.
- Borrowing and lending at the risk-free rate. No real investor can do this, which flattens the empirical relationship between beta and return relative to the theoretical line.
- The market portfolio is observable. It is not — it should include every risky asset, and every proxy is an index of listed equities. Roll's critique is that this makes the model untestable in principle.
- The horizon is a single period. Applying the output as a multi-decade discount rate assumes the risk-free rate, the premium and beta all hold flat for the whole period.
- The premium is knowable. Reasonable estimates of the equity risk premium span several percentage points, and beta multiplies that uncertainty.
CAPM for cost of equity versus CAPM for expected return
The same formula answers two questions, and it is worth keeping them separate. As an investor, the output is the return you should demand before buying — compare it with the return the price implies and you have a buy or pass. As a company, the identical number is the cost of equity: what shareholders require, and therefore the hurdle a project financed with equity has to clear. Our cost of equity calculator frames it that way and feeds the result into the weighted average cost of capital, where it sits beside the after-tax cost of debt.
What to use alongside it
CAPM gives you one number and hides the rest of the risk picture, so pair it with measures that look at different things. Standard deviation captures total volatility, including the idiosyncratic part CAPM discards. The Sharpe ratio ranks portfolios on excess return per unit of that total volatility, which is the right lens for a whole portfolio rather than a single holding. Together they answer "how much risk" and "what kind".
For company valuation, the CAPM output is an input, not a conclusion. Feed it into a dividend discount model or a discounted cash flow, and you will find the valuation moves several percent for every tenth of a point in the discount rate — which is the practical reason to run the model at a range of premia rather than a point estimate, and to say which premium you used whenever you quote a valuation.
Finally, treat a published beta as a starting point rather than a fact. Check the estimation window, the index and whether the figure is raw or adjusted before you use it, and if the company's leverage has changed materially during the window, relever the beta yourself rather than accepting a number estimated on a different balance sheet.