# What is the expected return?

Computes the expected return of an investment from possible returns and their probabilities, from CAPM (risk-free rate, beta and market return), or for a portfolio from each holding’s amount and expected return.

- Page: https://www.acalculator.org/finance/expected-return-calculator
- JSON spec: https://www.acalculator.org/finance/expected-return-calculator.json
- Version: d05c39fae5cd

## Default answer

Example with the default inputs (Method Scenarios, Scenarios [Probability 30%, Return 25%; Probability 50%, Return 10%; Probability 20%, Return −15%]): The expected return is 9.5%.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| method | Method | Weigh possible returns by their probabilities, use CAPM, or average a portfolio’s holdings. |
| scenarios | Scenarios | One row per possible outcome: its probability and the return in that outcome. |
| rf | Risk-free rate | The yearly return on a riskless investment, such as a Treasury bill. |
| beta | Beta (β) | How much the investment moves with the market: 1 moves with it, 2 moves twice as much. |
| rm | Expected market return | The yearly return you expect from the market as a whole, such as a broad stock index. |
| holdings | Holdings | One row per holding: the amount in it and its expected return. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| expected | Expected return | The probability-weighted, CAPM or amount-weighted expected return, to 2 decimals. |
| sd | Standard deviation of return | Scenarios only: √(Σ probability × (return − expected return)²), the spread of the outcomes. |
| marketPremium | Market risk premium | CAPM only: expected market return − risk-free rate. |
| riskPremium | Risk premium of the investment | CAPM only: beta × market risk premium. |
| total | Total invested | Portfolio only: the amounts added up. |

## Method

Scenarios: E(R) = Σ pᵢ × Rᵢ, σ = √(Σ pᵢ × (Rᵢ − E(R))²); CAPM: E(R) = Rf + β × (Rm − Rf); portfolio: E(R) = Σ amountᵢ × E(Rᵢ) ÷ Σ amountᵢ.

## Assumptions

- Scenario probabilities add up to 100% and each return is for the same period.
- CAPM uses the rates you type for the same period, usually a year; it gives the return investors require for the investment’s market risk.
- Arithmetic is exact on the typed decimals; only the standard deviation uses a floating-point square root.

## Worked examples

1. method = scenarios, scenarios = {"p":30,"r":25} or {"p":50,"r":10} gives expected = 9.5%, sd = 13.865425%. Source: OpenStax, Introductory Statistics 2e, 4.2 Mean or Expected Value and Standard Deviation (μ = Σ x × P(x); σ = √(Σ (x − μ)² × P(x))). https://openstax.org/books/introductory-statistics-2e/pages/4-2-mean-or-expected-value-and-standard-deviation.
2. method = capm, rf = 3.36%, beta = 1.39, rm = 11.64% gives expected = 14.8692%, marketPremium = 8.28%, riskPremium = 11.5092%. Source: OpenStax, Principles of Finance, 15.3 The Capital Asset Pricing Model (CAPM) (Re = Rf + β × (Rm − Rf); Delta Air Lines: 3.36% + 1.39 × (11.64% − 3.36%) = 14.87%). https://openstax.org/books/principles-finance/pages/15-3-the-capital-asset-pricing-model-capm: 3.36% + 1.39 × 8.28% = 14.87%.
3. method = portfolio, holdings = {"amount":25,"er":3.3} or {"amount":25,"er":0.21} gives expected = 2.695%, total = $100.00. Source: OpenStax, Principles of Finance, 15.5 Using Excel to Make Investment Decisions (portfolio return = the weighted sum of the holdings’ returns, 0.25 × each of four stocks). https://openstax.org/books/principles-finance/pages/15-5-using-excel-to-make-investment-decisions: (3.30% + 0.21% + 3.80% + 3.47%) ÷ 4 = 2.695% (OpenStax writes 0.0269).
4. method = portfolio, holdings = {"amount":60000,"er":8} or {"amount":30000,"er":4} gives expected = 6.2%, total = $100,000.00. Source: OpenStax, Principles of Finance, 15.5 Using Excel to Make Investment Decisions (portfolio return = the weighted sum of the holdings’ returns, 0.25 × each of four stocks). https://openstax.org/books/principles-finance/pages/15-5-using-excel-to-make-investment-decisions.

## FAQ

### What is expected return?

The expected return is the average return you would get from an investment if you could make it many times over: each possible return weighted by how likely it is. It is a planning number, not a promise; any one year can land far from it.

### How do I calculate expected return with probabilities?

Multiply each possible return by its probability and add the results. With a 30% chance of +25%, a 50% chance of +10% and a 20% chance of −15%: 0.3 × 25% + 0.5 × 10% + 0.2 × (−15%) = 9.5%. The probabilities must add up to 100%.

### How do I calculate expected return with CAPM?

Add the risk-free rate to beta times the market risk premium (market return minus risk-free rate). With a 3.36% risk-free rate, a 1.39 beta and an 11.64% market return: 3.36% + 1.39 × 8.28% = 14.87%.

### How do I calculate the expected return of a portfolio?

Weight each holding’s expected return by its share of the money. $60,000 at 8%, $30,000 at 4% and $10,000 at 2% give (60,000 × 8% + 30,000 × 4% + 10,000 × 2%) ÷ 100,000 = 6.2%.

### What does the standard deviation tell me?

How far the possible returns spread around the expected return. Two investments with the same 9.5% expected return can differ a lot in risk: the one with the larger standard deviation has outcomes further from 9.5%, both up and down.

### Which method should I use?

Use scenarios when you can list the outcomes and their chances. Use CAPM for the return investors require for an investment’s market risk, such as a company’s cost of equity. Use the portfolio method when you already have an expected return for each holding.

## Sources

- OpenStax, Introductory Statistics 2e, 4.2 Mean or Expected Value and Standard Deviation: μ = Σ x × P(x) and σ = √(Σ (x − μ)² × P(x)) for a discrete random variable. https://openstax.org/books/introductory-statistics-2e/pages/4-2-mean-or-expected-value-and-standard-deviation (retrieved 2026-10-18)
- OpenStax, Principles of Finance, 15.3 The Capital Asset Pricing Model (CAPM): Re = Rf + β × (Rm − Rf); Delta Air Lines with a 1.39 beta, 3.36% T-bills and an 11.64% market return: 14.87%. https://openstax.org/books/principles-finance/pages/15-3-the-capital-asset-pricing-model-capm (retrieved 2026-10-18)
- OpenStax, Principles of Finance, 15.5 Using Excel to Make Investment Decisions: portfolio return = 0.25 × R(AMZN) + 0.25 × R(CVS) + 0.25 × R(AAPL) + 0.25 × R(NFLX), with average monthly returns of 3.30%, 0.21%, 3.80% and 3.47%. https://openstax.org/books/principles-finance/pages/15-5-using-excel-to-make-investment-decisions (retrieved 2026-10-18)