CAPM Formula: How to Calculate Expected Return (and What Beta Means)

The CAPM formula gives a stock's expected return: E(R) = Rf + β(Rm − Rf), the risk-free rate plus beta times the market risk premium. In plain words, you start with what a riskless Treasury pays, then add extra return that scales with how strongly the stock moves with the overall market. You need it whenever a problem asks for expected return, required return, or the cost of equity — in most intro finance courses, those phrases all point to this same calculation.

What beta actually measures

Beta is the part of the formula students most often plug in without understanding, so it is worth slowing down here. Beta measures co-movement with the market — when the market moves 1%, how much does this stock tend to move? It is estimated by regressing the stock's historical returns against the market's returns. Beta is not the same thing as volatility. A biotech stock can swing wildly on drug-trial news and still have a modest beta, because those swings have nothing to do with what the market is doing that day.

That distinction matters because of diversification. Every stock carries two kinds of risk. Firm-specific risk comes from events unique to one company — a factory fire, a failed product, a CEO scandal. Hold 40 different stocks and these surprises largely cancel out: one company's bad quarter is offset by another's good one. Market risk is different. When the whole market drops 8%, nearly everything in your portfolio drops with it, and owning more stocks does not save you. Since firm-specific risk can be diversified away for free, the market does not pay you extra for holding it. CAPM prices only the risk you cannot escape — and beta is the measure of exactly that risk.

Reading beta values:

• β > 1 — aggressive. The stock amplifies market moves. A semiconductor maker with β = 1.4 tends to rise about 1.4% when the market rises 1%, and fall harder in a selloff. More market risk, so CAPM demands a larger premium.
• β = 1 — market tracker. The stock moves in step with the market. An S&P 500 index fund is the textbook case; its expected return is simply the market's.
• β < 1 — defensive. The stock dampens market moves. Utilities and grocery chains keep selling electricity and food in a recession, so a β of 0.6 is typical. Less market risk, smaller premium.
• β < 0 — a hedge. Rare, but real: assets like gold-mining stocks or long-Treasury funds sometimes rise when the market falls. A negative beta produces an expected return below the risk-free rate — which sounds broken until you realize the asset is acting as portfolio insurance, and investors accept a lower return for protection.

What each input means

Risk-free rate (Rf). Use the yield on a US Treasury security, most commonly the 10-year note for equity valuation, since Treasuries carry effectively no default risk. In practice you look it up on the day of the analysis; on homework, the problem hands it to you.

Beta (β). For real companies, betas are published on Yahoo Finance, Bloomberg, and most data providers, typically estimated from about five years of monthly returns regressed against the S&P 500. Two cautions: published equity betas are levered — they reflect the company's debt load as well as its business risk — and estimates for the same company can differ across sources because of different estimation windows. For coursework, use the beta you are given.

Market risk premium (Rm − Rf). Historically, the US equity market has earned roughly 4–6% per year above Treasuries, and most textbooks and practitioners pick a premium in that range. Read the problem carefully: some give you the premium directly, while others give you Rm and expect you to subtract Rf yourself.

The output of CAPM has one main job downstream: it is the cost of equity (Re) that plugs into the WACC formula when you build a discount rate for valuation.

Here is the formula applied to three stocks that share the same market conditions — Rf = 4.2% and a market risk premium of 5.5% — and differ only in beta.

The pattern to notice: the risk-free 4.2% is the same for everyone, and the premium scales in direct proportion to beta. The utility earns a 3.3% premium, the semiconductor maker earns 7.7% — exactly 0.6 and 1.4 times the market's 5.5%. The index fund is a built-in sanity check: at β = 1.0 the formula returns 4.2% + 5.5% = 9.7%, which is just the expected market return itself. If your β = 1 case does not reproduce Rm, an input is wrong.

Common mistakes

Multiplying beta by Rm instead of (Rm − Rf). This is the single most common CAPM error on exams. Beta multiplies the premium, not the whole market return. Using the numbers above with Rm = 9.7%: the wrong version gives 4.2% + 1.4 × 9.7% = 17.78%, while the correct answer is 4.2% + 1.4 × 5.5% = 11.9%. When a problem gives you Rm rather than the premium, subtract Rf first.

Misreading a negative beta as an error. With β = −0.2: E(R) = 4.2% + (−0.2 × 5.5%) = 4.2% − 1.1% = 3.1%, below the risk-free rate. Students often assume they made a sign mistake. They did not — an asset that rises when the market falls reduces portfolio risk, so investors rationally accept an expected return below Rf to hold it.

Treating the output as a guaranteed return. CAPM says a stock with β = 1.4 should return 11.9% on average, given its market risk. It is the compensation the risk deserves — the discount rate you apply, or the hurdle the stock must clear — not a prediction of what the stock will do next year. Actual one-year returns scatter enormously around the CAPM number.

By the FinanceBrain Team · Last verified July 10, 2026 · How we produce and verify articles