๐Ÿ“Š

Alpha Calculator

Calculate excess return compared to expected return based on CAPM. Measure investment performance relative to risk.

Alpha Calculator

Portfolio Return

12%
-50%50%

Market Return

10%
-50%50%

Risk-Free Rate

2%
-5%10%

Beta

1.2
03

Beta measures the sensitivity of returns to market movements (ฮฒ = 1 means moves with market)

Alpha Formula: Portfolio Return - Expected Return

Expected Return = Risk-Free Rate + Beta ร— (Market Return - Risk-Free Rate)

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About Alpha

What is Alpha?

Alpha (ฮฑ) is a measure of excess return that an investment generates compared to its expected return based on the Capital Asset Pricing Model (CAPM). It represents the value added (or subtracted) by active portfolio management or stock selection skill.

Formula

Alpha = Portfolio Return - Expected Return

Where Expected Return = Risk-Free Rate + Beta ร— (Market Return - Risk-Free Rate)

Key Components

  • Portfolio Return: The actual return achieved by the investment
  • Expected Return: The return predicted by CAPM based on risk
  • Beta (ฮฒ): Measures the investment's sensitivity to market movements
  • Market Return: The return of the benchmark market index
  • Risk-Free Rate: The return on a risk-free investment (typically Treasury bills)

Interpretation

  • Positive Alpha: Investment outperformed expectations (good for investors)
  • Negative Alpha: Investment underperformed expectations (poor performance)
  • Zero Alpha: Investment performed exactly as expected based on its risk
  • Higher Alpha: Indicates better risk-adjusted performance relative to the market

Example: If Alpha = 2%, the investment generated 2% more return than expected based on its risk level. This suggests skilled management or superior stock selection.

Understanding Beta

  • Beta = 1: Investment moves in line with the market
  • Beta > 1: Investment is more volatile than the market (aggressive)
  • Beta < 1: Investment is less volatile than the market (defensive)
  • Beta = 0: Investment is uncorrelated with the market

Advantages of Alpha

  • Risk-Adjusted Measure: Considers the investment's risk level (beta)
  • Performance Attribution: Separates skill from market movements
  • Benchmark Comparison: Measures performance relative to expected returns
  • Active Management Evaluation: Useful for evaluating fund managers

Limitations

  • CAPM Assumptions: Relies on CAPM, which has limitations
  • Beta Instability: Beta can change over time
  • Market Efficiency: Assumes markets are efficient (may not always be true)
  • Time Period Dependent: Alpha can vary significantly across different periods
  • Benchmark Selection: Results depend on choosing the right benchmark

When to Use Alpha

  • Evaluating active fund managers and their stock selection skills
  • Comparing investments with different risk levels
  • Assessing whether active management adds value
  • Performance attribution analysis
  • Portfolio optimization and risk management

Note: Alpha is most meaningful when used alongside other metrics like Beta, Sharpe Ratio, and information ratio. A positive Alpha doesn't guarantee future outperformance, and past Alpha may not persist. Always consider Alpha in the context of the investment's risk profile and market conditions.

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Gas Fee Calculator

Calculate EVM gas fees: gas limit times effective Gwei (legacy gas price or EIP-1559 base + priority). Batch multiple transactions and estimate fiat with native token price.

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Dividend Discount Model Calculator

Calculate intrinsic stock value with the dividend discount model (DDM): zero growth perpetuity, Gordon growth, or two-stage dividends with a terminal Gordon value.

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Forex Profit / Loss Calculator

Calculate forex currency profit or loss: BASE/QUOTE pair, long or short, entry and exit price, lot size and contract size. P/L in quote currency with optional conversion to your currency.

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Real Return Calculator

Calculate inflation-adjusted investment returns. Understand your actual purchasing power gain after accounting for inflation.

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Income Tax Calculator

Calculate your tax liability, effective tax rate, and after-tax income. Plan your taxes with deductions and credits.

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Pension Calculator

Calculate retirement corpus needed, monthly pension amount, and required monthly contributions. Plan your retirement pension with inflation-adjusted calculations.

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