# CAPM — Capital Asset Pricing Model

> Beta, risk-free rate & the price of risk

**Track:** Risk & Return  
**Read time:** 12 min

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How much return should an investment promise? Too little and no one funds it; too much and capital is wasted. The Capital Asset Pricing Model (CAPM) is finance’s answer — a one-line formula that converts risk into a required return. It prices risk with a single number, beta, that measures how an asset moves with the market.

CAPM underlies the cost of equity in every WACC calculation, the hurdle rates in every capital budgeting screen, and the risk adjustments in every portfolio decision. Despite decades of academic criticism, it remains the most used model in finance — indispensable precisely because it is simple enough to apply.

## From Risk to Required Return

Investors do not take risk for free. A riskless Treasury bill sets the floor — the reward for waiting with no uncertainty. Everything above that floor is a risk premium: compensation for bearing outcomes that could disappoint. The question is which risk earns a premium, and how much.

CAPM’s insight is that only one kind of risk earns compensation in a diversified market: risk you cannot avoid by diversifying. Company-specific disappointments can be averaged away across a portfolio, so the market pays nothing for them. What cannot be diversified away is the asset’s tendency to move with the market itself — systematic risk.

## Systematic vs Unsystematic Risk

Total risk, measured by variance or standard deviation, splits into two parts. Unsystematic (idiosyncratic) risk is specific to a company — product failures, lawsuits, key-executive departures. Systematic (market) risk is shared by all assets to varying degrees — recessions, interest rate shocks, geopolitical events.

Diversification eliminates unsystematic risk almost completely: a 30-stock portfolio already removes most of it. But no amount of diversification removes the market component. Since investors can rid themselves of one type for free, they will not pay to avoid it — only systematic risk commands a premium in equilibrium. This is the intellectual heart of CAPM.

- Unsystematic: firm-specific, diversifiable, earns no premium.
- Systematic: market-wide, undiversifiable, earns the premium.
- Diversification is "free" risk reduction — the only free lunch in finance.

## Beta — Measuring Market Sensitivity

Beta (β) measures how strongly an asset’s returns move with the market’s returns, estimated statistically by regressing asset returns on market returns. β = 1 means the asset moves one-for-one with the market; β = 2 amplifies market moves (double the systematic risk); β = 0.5 moves half as much.

Intuition by industry: utilities and consumer staples typically run beta below 1 — demand is stable regardless of the cycle. Luxury goods, airlines, and semiconductor firms run beta well above 1 — demand swings amplify the business cycle. Betas above 2 or below 0 are rare and often unstable, so practitioners "adjust" extreme betas toward 1 or use industry averages.

> **Reading a beta**
>
> A stock with β = 1.3: when the market returns +10%, expect roughly +13%; when the market falls −10%, expect roughly −13%. β measures expected co-movement, not magnitude alone — the regression filters out company-specific noise, which is exactly the risk CAPM says the market ignores.

## The CAPM Formula

The model assembles three inputs into one expected return: the risk-free rate r_f (long government bond yield in practice), the equity risk premium (ERP) — the market’s expected excess return over r_f, historically 4–6% — and beta. The formula says the required return equals the time value of money plus beta-scaled compensation for market risk.

In equilibrium every asset plots on the Security Market Line: return versus beta, slope ERP. Assets above the line are bargains (return exceeds required), below the line are overpriced. Note the elegance: a zero-beta asset earns exactly r_f, whatever its total volatility — because zero systematic risk deserves zero premium.

**Formula** — Risk-free rate + beta × equity risk premium

```
E(R_{i}) = r_{f} + β_{i} × (E(R_{m}) − r_{f})
```

> **Cost of equity in one line**
>
> r_f = 4.2%, ERP = 5.5%, β = 1.25. Expected return = 4.2% + 1.25 × 5.5% = 11.1%. This 11.1% is the return equity investors require — the number that becomes the cost of equity inside WACC and the hurdle for equity-funded projects.

## Estimating the Inputs in Practice

Each input requires judgment. The risk-free rate should match the cash flow horizon — 10-year or 20-year government yields are standard. Beta is usually estimated from 2–5 years of weekly or monthly returns, then adjusted toward 1.0 (Bloomberg-style) or borrowed from industry peers when the company’s own history is short or noisy.

The equity risk premium is the most contested input: surveys suggest 5–6%, historical averages suggest different numbers depending on the period, and implied (forward-looking) estimates move with market conditions. Small-company premiums and country risk premiums are added where relevant. Sensitivity is essential: cost of equity at ±1% ERP swings valuations dramatically, so models should show the range.

## Uses and Criticisms

CAPM’s virtues explain its endurance: it is simple, uses observable inputs, and directly answers the question corporate finance needs answered — what return does capital require? Its cost-of-equity estimate feeds WACC, project hurdle rates, and fair-value discount rates across the entire economy.

The academic record is less kind: decades of data show pure beta explaining far less of return differences than theory predicts (size, value, and momentum effects persist), and the assumed single-period framework ignores taxes, illiquidity, and human behavior. Fama-French multi-factor models improve descriptive accuracy at the cost of simplicity. Yet CAPM survives as the corporate standard — a deliberate trade of precision for usability, and a reminder that in practice the best model is the one decision-makers will actually use.

## Key takeaways

- Only systematic risk earns a premium — diversifiable risk is free to eliminate.
- Beta measures sensitivity to market moves; it is the price of systematic risk.
- E(R) = r_f + β × ERP: one line from risk to required return.
- ERP is the most contested input — always show sensitivity ranges.
- Critics abound, practitioners persist: CAPM remains the cost-of-equity workhorse.

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