{
  "id": "expected-return",
  "version": "d05c39fae5cd",
  "status": "published",
  "name": "Expected Return Calculator",
  "question": "What is the expected return?",
  "summary": "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.",
  "category": "finance",
  "subcategory": "investing",
  "url": "https://www.acalculator.org/finance/expected-return-calculator",
  "markdown": "https://www.acalculator.org/finance/expected-return-calculator.md",
  "kind": "function",
  "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."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "method": {
        "title": "Method",
        "description": "Weigh possible returns by their probabilities, use CAPM, or average a portfolio’s holdings.",
        "type": "string",
        "enum": [
          "scenarios",
          "capm",
          "portfolio"
        ]
      },
      "scenarios": {
        "title": "Scenarios",
        "description": "One row per possible outcome: its probability and the return in that outcome.",
        "type": "array",
        "items": {
          "type": "object",
          "properties": {
            "p": {
              "title": "Probability",
              "description": "The chance of this outcome, from 0% to 100%.",
              "type": "number",
              "x-unit": "percent",
              "minimum": 0,
              "maximum": 100
            },
            "r": {
              "title": "Return",
              "description": "The return in this outcome. Negative for a loss.",
              "type": "number",
              "x-unit": "percent",
              "minimum": -100,
              "maximum": 10000
            }
          }
        }
      },
      "rf": {
        "title": "Risk-free rate",
        "description": "The yearly return on a riskless investment, such as a Treasury bill.",
        "type": "number",
        "x-unit": "percent",
        "minimum": -100,
        "maximum": 1000
      },
      "beta": {
        "title": "Beta (β)",
        "description": "How much the investment moves with the market: 1 moves with it, 2 moves twice as much.",
        "type": "number",
        "minimum": -100,
        "maximum": 100
      },
      "rm": {
        "title": "Expected market return",
        "description": "The yearly return you expect from the market as a whole, such as a broad stock index.",
        "type": "number",
        "x-unit": "percent",
        "minimum": -100,
        "maximum": 1000
      },
      "holdings": {
        "title": "Holdings",
        "description": "One row per holding: the amount in it and its expected return.",
        "type": "array",
        "items": {
          "type": "object",
          "properties": {
            "w": {
              "title": "Amount",
              "description": "The amount invested in this holding.",
              "type": "number",
              "x-unit": "USD",
              "minimum": 0,
              "maximum": 1000000000000000
            },
            "er": {
              "title": "Expected return",
              "description": "The expected return of this holding.",
              "type": "number",
              "x-unit": "percent",
              "minimum": -100,
              "maximum": 10000
            }
          }
        }
      }
    }
  },
  "outputs": {
    "expected": {
      "label": "Expected return",
      "description": "The probability-weighted, CAPM or amount-weighted expected return, to 2 decimals.",
      "format": "percent"
    },
    "sd": {
      "label": "Standard deviation of return",
      "description": "Scenarios only: √(Σ probability × (return − expected return)²), the spread of the outcomes.",
      "format": "percent"
    },
    "marketPremium": {
      "label": "Market risk premium",
      "description": "CAPM only: expected market return − risk-free rate.",
      "format": "percent"
    },
    "riskPremium": {
      "label": "Risk premium of the investment",
      "description": "CAPM only: beta × market risk premium.",
      "format": "percent"
    },
    "total": {
      "label": "Total invested",
      "description": "Portfolio only: the amounts added up.",
      "format": "money"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "method": "scenarios",
      "scenarios": [
        {
          "p": 30,
          "r": 25
        },
        {
          "p": 50,
          "r": 10
        },
        {
          "p": 20,
          "r": -15
        }
      ],
      "rf": 3.36,
      "beta": 1.39,
      "rm": 11.64,
      "holdings": [
        {
          "amount": 60000,
          "er": 8
        },
        {
          "amount": 30000,
          "er": 4
        },
        {
          "amount": 10000,
          "er": 2
        }
      ]
    },
    "outputs": {
      "expected": 9.5,
      "sd": 13.865424623862047
    },
    "text": "The expected return is 9.5%."
  },
  "examples": [
    {
      "given": {
        "method": "scenarios",
        "scenarios": [
          {
            "p": 30,
            "r": 25
          },
          {
            "p": 50,
            "r": 10
          },
          {
            "p": 20,
            "r": -15
          }
        ]
      },
      "expect": {
        "expected": 9.5,
        "sd": 13.865424623862047
      },
      "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; hand calculation in content.mdx: 0.3 × 25 + 0.5 × 10 + 0.2 × (−15) = 9.5; √192.25 = 13.865"
    },
    {
      "given": {
        "method": "capm",
        "rf": 3.36,
        "beta": 1.39,
        "rm": 11.64
      },
      "expect": {
        "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%"
    },
    {
      "given": {
        "method": "portfolio",
        "holdings": [
          {
            "amount": 25,
            "er": 3.3
          },
          {
            "amount": 25,
            "er": 0.21
          },
          {
            "amount": 25,
            "er": 3.8
          },
          {
            "amount": 25,
            "er": 3.47
          }
        ]
      },
      "expect": {
        "expected": 2.695,
        "total": 100
      },
      "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)"
    },
    {
      "given": {
        "method": "portfolio",
        "holdings": [
          {
            "amount": 60000,
            "er": 8
          },
          {
            "amount": 30000,
            "er": 4
          },
          {
            "amount": 10000,
            "er": 2
          }
        ]
      },
      "expect": {
        "expected": 6.2,
        "total": 100000
      },
      "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; hand calculation in content.mdx: (60,000 × 8 + 30,000 × 4 + 10,000 × 2) ÷ 100,000 = 6.2"
    }
  ],
  "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)"
  ],
  "related": [
    "beta",
    "sharpe-ratio",
    "expected-value",
    "rate-of-return",
    "wacc"
  ],
  "changelog": []
}