Expected Return Calculator

Expected Return Calculator – Probability, Portfolio, CAPM and Multi-Period Returns

The Expected Return Calculator helps you analyze the potential performance of investments using different frameworks. Instead of focusing on a single scenario, expected return brings together multiple possible outcomes, their probabilities, portfolio weights, or risk factor exposures and summarizes them into a single central estimate.

Expected return does not guarantee future results, but it is a fundamental concept in portfolio construction, risk management and valuation. This calculator lets you work with probability-weighted scenarios, portfolio weights, the Capital Asset Pricing Model (CAPM), holding period returns and the difference between geometric and arithmetic averages in one place.

How the Expected Return Calculator Works

The tool is organized into five modes that reflect common real-world use cases:

• Expected Return (Probabilities): Compute probability-weighted expected return and volatility from discrete scenarios.
• Portfolio Expected Return: Calculate the expected return of a portfolio from asset-level returns and allocation weights.
• CAPM Expected Return: Estimate expected return for a risky asset using the Capital Asset Pricing Model.
• Holding Period Return: Evaluate realized or expected return over a specific holding period, including income.
• Geometric vs Arithmetic Returns: Compare long-run compounded growth to the simple average of period returns.

Each mode is based on transparent formulas that you can use to test scenarios, compare strategies and understand how assumptions affect expected outcomes.

Mode 1: Expected Return from Probabilities

The probability-based mode is most useful when you have a small number of clearly defined outcomes and estimated likelihoods. For example, you might think a stock has a 40% chance of returning 15%, a 40% chance of returning 5% and a 20% chance of losing 10%.

Probability-Weighted Expected Return

Probabilities can be entered as percentages and will be normalized if they do not sum to exactly 100%. The calculator also estimates variance and standard deviation of returns:

This gives you both a central expectation and a simple risk measure based on your scenario assumptions.

Mode 2: Portfolio Expected Return

The portfolio mode calculates expected return using asset-level returns and allocation weights. This is a direct application of the idea that portfolio return is a weighted average of component returns.

Portfolio Return Formula

Weights are typically based on market value or allocation percentages. If your weight inputs do not sum to exactly 100%, the calculator normalizes them by dividing each weight by the total. This is useful when you are experimenting with allocations or working with rough weight estimates.

For example, if you allocate 60% to a stock with 8% expected return and 40% to bonds with 3% expected return, the expected portfolio return is (0.6 × 8%) + (0.4 × 3%) = 6%. You can experiment with adding more assets and shifting weights to see how the portfolio expectation changes.

Mode 3: CAPM Expected Return

The Capital Asset Pricing Model (CAPM) is a one-factor model that links expected return to market risk. It assumes investors can diversify idiosyncratic risk and will only be rewarded for bearing systematic risk, captured by beta.

CAPM Expected Return Formula

Here, R_f is the risk-free rate, β is the asset’s beta (sensitivity to market movements), and (R_m − R_f) is the equity market risk premium. The calculator also lets you enter an optional alpha, which is an incremental return above CAPM expectations:

This lets you compare model-based expectations to your own view of a manager’s skill or a security’s mispricing.

Mode 4: Holding Period Return (HPR)

Holding Period Return measures total return on an investment over a defined time interval. It includes both price change and income, such as dividends, interest or distributions.

Holding Period Return Formula

Expressed as a percentage:

If you provide the holding period in years, the calculator also estimates an annualized rate of return:

This helps you compare investments with different holding periods on a consistent yearly basis and see how much of the total return came from income versus price appreciation.

Mode 5: Geometric vs Arithmetic Returns

The final mode highlights the difference between the simple average of periodic returns and the compounded growth rate over time. This is important when evaluating long-term investment performance and projecting future outcomes.

Arithmetic and Geometric Average Formulas

Because negative returns hurt compounded wealth more than positive returns of the same magnitude help it, geometric averages are usually lower than arithmetic averages when returns are volatile. The difference between them is sometimes called volatility drag and can be significant over long horizons.

Why Expected Return Matters

Expected return is central to many financial decisions. Investors use it to decide between asset classes, assess whether compensation is fair for the risk taken, build strategic allocations and evaluate managers. However, expected return is always based on assumptions; the future may differ from any estimate.

By using a calculator that supports multiple frameworks, you can:

• Quantify your views about scenarios and probabilities.
• See how shifting portfolio weights changes expected outcomes.
• Compare simple expectations with factor-based models like CAPM.
• Review realized holding period returns against expectations.
• Understand how volatility impacts long-term growth through geometric returns.

Examples of Expected Return Calculations

Example 1: Scenario-Based Expected Return

Assume you are considering an investment with three scenarios: a 30% chance of a 15% gain, a 50% chance of a 6% gain and a 20% chance of a 10% loss. Expected return is (0.3×15%) + (0.5×6%) + (0.2×−10%) = 4.3%. The calculator also shows variance and standard deviation based on this distribution.

Example 2: Portfolio Expected Return

Suppose your portfolio holds 50% in a broad equity index with expected return of 7%, 30% in investment-grade bonds with 3% expected return and 20% in cash at 1%. Portfolio expected return is (0.5×7%) + (0.3×3%) + (0.2×1%) = 4.4%.

Example 3: CAPM Expected Return

Consider a stock with beta of 1.3. If the risk-free rate is 2% and expected market return is 9%, the market risk premium is 7%. CAPM expected return is 2% + 1.3×7% = 11.1%. If you believe the stock will outperform by 2% per year due to company-specific factors, you could enter alpha of 2% to see an adjusted expectation of 13.1%.

Example 4: Holding Period Return

Imagine you invest $10,000 in a fund, receive $400 in distributions and later sell for $10,800. Total value plus income is $11,200, so HPR is ($11,200 − $10,000) ÷ $10,000 = 12%. If the holding period is two years, annualized return is approximately (1.12)^1/2 − 1 ≈ 5.83% per year.

Example 5: Geometric vs Arithmetic Returns

Consider yearly returns of +20%, −10%, +15% and +5%. The arithmetic average is (20 − 10 + 15 + 5) ÷ 4 = 7.5%. Geometric average is [(1.20 × 0.90 × 1.15 × 1.05)^1/4 − 1], which is lower because of volatility. The calculator shows both values and the difference, illustrating how volatility drag reduces long-term growth relative to the simple average.

How to Use This Tool Effectively

• Start with the Expected Return (Probabilities) tab when you have discrete scenarios and subjective probabilities.
• Use the Portfolio Expected Return tab to test allocations and rebalancing ideas.
• Apply the CAPM tab to connect expected return with beta and market assumptions.
• Use the Holding Period Return tab to evaluate realized or hypothetical past investments.
• Explore the Geometric vs Arithmetic tab to understand how volatility affects long-term growth.
• Combine multiple modes for a fuller picture, for example using CAPM to estimate asset returns and then feeding them into the portfolio tab.

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