What is portfolio beta?

Beta measures how sensitive a portfolio is to movements in a benchmark index. A beta of 1 means the portfolio tends to move in line with the market; a beta above 1 indicates higher volatility, and below 1 indicates lower volatility.

What is portfolio alpha?

Alpha is the difference between a portfolio’s actual return and the return predicted by the CAPM model. Positive alpha suggests outperformance relative to risk, while negative alpha suggests underperformance.

How does this calculator compute expected return?

The calculator uses the CAPM formula: Expected return = Risk‑free rate + Beta × (Market return − Risk‑free rate). It then compares this expected return to your portfolio’s actual return.

Do I need precise beta estimates?

For education, approximate beta values from fund providers or research reports are sufficient. More precise estimates require regression analysis on historical returns.

Is this a full performance attribution model?

No. This tool focuses on CAPM‑style alpha and beta. Full performance attribution may include multiple factors, timing effects, and more advanced analytics.

Can I export the alpha & beta breakdown?

Yes. Use the Export CSV button to download the breakdown table and analyze it in a spreadsheet or share with an advisor.

Investment Alpha & Beta Calculator

Estimate your portfolio’s alpha and beta using the CAPM framework. Compare expected return to actual return and see performance relative to your benchmark.

Risk‑free rate (% per year) Market return (% per year) Portfolio return (% per year)

Portfolio beta Benchmark name Analysis horizon (years)

Risk‑free compounding Notes (optional) Target alpha (% per year)

Tip: Use consistent annualized returns for the risk‑free rate, market, and portfolio.

Important: This calculator uses a simplified CAPM framework. Real‑world performance analysis may include multiple factors, time‑varying risk, and more advanced attribution methods.

Alpha & beta calculation formulas

Alpha and beta are core concepts in modern portfolio theory. Beta measures how sensitive your portfolio is to market movements, while alpha measures performance relative to the risk implied by beta. This calculator focuses on the CAPM relationship between risk and return.

1. CAPM expected return

Expected return (CAPM) = Rf + β × (Rm − Rf)

Where:
Rf = Risk‑free rate
Rm = Market (benchmark) return
β  = Portfolio beta

This formula estimates the return your portfolio should earn given its beta and the difference between market and risk‑free returns.

2. Portfolio alpha

Alpha = Rp − [Rf + β × (Rm − Rf)]

Where:
Rp = Portfolio actual return

Alpha is the difference between your actual return and the CAPM expected return. Positive alpha suggests outperformance relative to risk; negative alpha suggests underperformance.

3. Risk‑free compounding (approximate)

If monthly compounding is selected:
Effective annual Rf ≈ (1 + Rf/12)¹² − 1

This approximation adjusts the risk‑free rate when you choose monthly compounding, helping align the rate with your return horizon.

These formulas provide a clear, intuitive way to connect risk and return. While real‑world models may include multiple factors and dynamic risk, CAPM remains a useful starting point for understanding alpha and beta.

How to interpret alpha and beta in your portfolio

Alpha and beta are two of the most widely used metrics in portfolio analysis. They help you understand how your portfolio behaves relative to a benchmark and whether your returns are consistent with the risk you are taking. This tool is designed to make those concepts concrete by connecting them directly to your inputs.

What beta tells you about risk

Beta measures sensitivity to market movements. A beta of 1 means your portfolio tends to move in line with the benchmark. A beta above 1 indicates higher volatility—your portfolio may rise more in bull markets but fall more in bear markets. A beta below 1 suggests lower volatility and potentially more defensive behavior.

For example, a portfolio with beta 1.2 is expected to move 20% more than the market on average. If the market rises 10%, the portfolio might rise around 12%; if the market falls 10%, the portfolio might fall around 12%. This is a simplification, but it captures the core idea.

What alpha tells you about performance

Alpha measures performance relative to the risk implied by beta. If your portfolio has a beta of 1.2, the CAPM model predicts a certain expected return given the risk‑free rate and market return. If your actual return exceeds that expected return, you have positive alpha; if it falls short, you have negative alpha.

Positive alpha can indicate skill, effective strategy, or favorable conditions. Negative alpha may suggest that fees, timing decisions, or poor security selection are dragging performance below what your level of risk would justify.

How this calculator models your situation

This tool asks for four key inputs: risk‑free rate, market return, portfolio return, and portfolio beta. It then computes the CAPM expected return and alpha. You can also specify a target alpha to see whether your current results meet your goals.

If you choose monthly compounding for the risk‑free rate, the tool approximates an effective annual rate. This helps align the risk‑free input with the annual returns you typically use for market and portfolio performance.

Worked example

Suppose you enter the following:

Risk‑free rate: 3% per year
Market return: 8% per year
Portfolio return: 10% per year
Portfolio beta: 1.2

The CAPM expected return is:

Expected return = 3% + 1.2 × (8% − 3%) = 3% + 1.2 × 5% = 3% + 6% = 9%

Your portfolio’s actual return is 10%, so alpha is:

Alpha = 10% − 9% = 1%

This means your portfolio outperformed the CAPM expectation by 1 percentage point per year, given its level of market risk.

Practical tips

Use consistent time horizons for all inputs (e.g., annualized returns).
Check whether your alpha is net or gross of fees—fees can significantly affect results.
Compare alpha across multiple periods to see whether outperformance is persistent or episodic.
Use the CSV export to track alpha and beta over time or share with an advisor.

Alpha and beta are not the whole story, but they provide a powerful lens for understanding how your portfolio behaves and whether your returns align with your risk. This tool gives you a clear, structured way to explore those relationships.

Frequently Asked Questions

Do I need historical data to use this tool?

No. You can use expected or realized annual returns for the risk‑free rate, market, and portfolio. For more advanced analysis, you would estimate beta from historical data, but this tool accepts any reasonable beta input.

How should I choose the benchmark?

Choose a benchmark that reflects your portfolio’s investment universe, such as a broad equity index for stock portfolios or a blended index for multi‑asset portfolios.

Can alpha be negative?

Yes. Negative alpha means your portfolio underperformed the CAPM expected return given its beta. This can happen due to fees, poor security selection, or unfavorable market conditions.

Is a higher beta always bad?

Not necessarily. Higher beta means higher sensitivity to market movements, which can be desirable if you seek more aggressive growth and can tolerate volatility. The key is aligning beta with your risk tolerance and goals.

Does this tool account for multiple factors?

No. It focuses on the single‑factor CAPM model. Multi‑factor models, such as those including value or size, require more complex inputs and estimation.

Can I export the results?

Yes. Use the Export CSV button to download the alpha & beta breakdown and store it in your own records or share with an advisor.