# CAPM Calculator

> Computes the expected return of an asset with the capital asset pricing model (CAPM) from the risk-free rate, the asset's beta and the expected market return, plus the equity risk premium and the beta-scaled premium.

- Calculator id: `capm` · Category: Investing & Real Estate (`investing`) · Tool name: `calculate_capm_expected_return`
- Canonical page: https://tttkmbb.com/investing/capm · This document: https://tttkmbb.com/investing/capm.md · JSON definition: https://tttkmbb.com/investing/capm.json

## Purpose

Computes the expected return of an asset with the capital asset pricing model (CAPM) from the risk-free rate, the asset's beta and the expected market return, plus the equity risk premium and the beta-scaled premium.

**Use when:** You need a required or expected return for a stock or portfolio given its beta, for example as the cost of equity in a DCF or WACC calculation.

**Do not use when:** The asset's beta is unknown or unstable, or you need a multi-factor return (Fama-French) rather than the single-factor CAPM. Informational only; not financial advice.

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `risk_free_rate_percent` | number | % per year | required | Yield on a risk-free instrument such as a government bond, in percent. (min -20, max 100) |
| `beta` | number |  | required | Sensitivity of the asset's returns to the market (1 = moves with the market, 0 = uncorrelated). (min -10, max 10) |
| `market_return_percent` | number | % per year | required | Expected annual return of the market portfolio in percent. (min -100, max 200) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `expected_return_percent` | number | % | risk_free_rate + beta × (market_return − risk_free_rate). |
| `equity_risk_premium_percent` | number | % | market_return − risk_free_rate. |
| `beta_premium_percent` | number | % | beta × equity risk premium: the return earned above the risk-free rate. |

## Formula

`expected_return_percent = risk_free_rate_percent + beta × (market_return_percent − risk_free_rate_percent)`

Single-factor CAPM (Sharpe 1964, Lintner 1965): only systematic (market) risk is rewarded; beta is usually estimated from 2–5 years of historical returns and the premium from long-run market history. Informational mathematics only; not financial advice.

## Data Sources

- Wikipedia – Capital asset pricing model — https://en.wikipedia.org/wiki/Capital_asset_pricing_model (reference, retrieved 2026-09-24)
- Wikipedia – Modern portfolio theory — https://en.wikipedia.org/wiki/Modern_portfolio_theory (reference, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/capm?risk_free_rate_percent=…&beta=…&market_return_percent=…`
- `POST https://tttkmbb.com/api/v1/calculate/capm` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/capm · OpenAPI operationId `calculate_capm_expected_return` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "capm", "inputs": {…}}`

## Example

- rf 3 %, beta 1.2, market 8 %: inputs `{"risk_free_rate_percent":3,"beta":1.2,"market_return_percent":8}` → `{"expected_return_percent":9,"equity_risk_premium_percent":5,"beta_premium_percent":6}`
- rf 4 %, beta 0.8, market 10 %: inputs `{"risk_free_rate_percent":4,"beta":0.8,"market_return_percent":10}` → `{"expected_return_percent":8.8,"equity_risk_premium_percent":6,"beta_premium_percent":4.8}`

```
GET https://tttkmbb.com/api/v1/calculate/capm?risk_free_rate_percent=3&beta=1.2&market_return_percent=8
```

## Limitations

The asset's beta is unknown or unstable, or you need a multi-factor return (Fama-French) rather than the single-factor CAPM. Informational only; not financial advice. Single-factor CAPM (Sharpe 1964, Lintner 1965): only systematic (market) risk is rewarded; beta is usually estimated from 2–5 years of historical returns and the premium from long-run market history. Informational mathematics only; not financial advice. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**What does a beta above 1 mean?**

The asset has moved more than the market: a beta of 1.2 implies returns about 20 % more volatile than the market, so CAPM demands a proportionally higher premium.

**Is the CAPM return a forecast?**

No. It is the return that compensates for systematic risk under the model's assumptions; realised returns differ, and the model ignores size, value and momentum effects.

## Related

- [WACC Calculator](https://tttkmbb.com/investing/wacc.md) — Use the CAPM return as the cost of equity in the weighted average cost of capital.
- [Sharpe Ratio Calculator](https://tttkmbb.com/investing/sharpe-ratio.md) — Risk-adjusted return of a realised portfolio.
- [DCF Valuation Calculator](https://tttkmbb.com/investing/dcf-valuation.md) — Discount cash flows at the required return.