Jensen's Alpha Calculator

1. What is the Jensen's Alpha Calculator?

Definition: The Jensen's Alpha Calculator computes Jensen's Alpha, a risk-adjusted performance metric that measures a portfolio's excess return compared to the expected return predicted by the Capital Asset Pricing Model (CAPM).

Purpose: It helps investors determine whether a portfolio outperforms the market on a risk-adjusted basis, providing insight into a portfolio manager's skill.

2. How Does the Calculator Work?

The calculator uses the following formula:

$ \text{Jensen's Alpha} = R_p - [R_f + \beta (R_m - R_f)] $

Where:

$ R_p $: Portfolio Return (%), calculated as $ \frac{\text{Ending Value} - \text{Beginning Value}}{\text{Beginning Value}} \times 100 $;
$ R_f $: Risk-Free Rate (%);
$ \beta $: Portfolio Beta (systematic risk relative to the market);
$ R_m $: Market Return (%).

Steps:

Enter the beginning portfolio value in dollars.
Enter the ending portfolio value in dollars.
Enter the risk-free rate as a percentage (e.g., U.S. Treasury bill rate).
Enter the portfolio beta (a measure of market risk).
Enter the market return as a percentage (e.g., S&P 500 average return).
Calculate the portfolio return using the formula above.
Calculate the expected return using CAPM: $ R_f + \beta (R_m - R_f) $.
Subtract the expected return from the portfolio return to get Jensen's Alpha.
Display the portfolio return and Jensen's Alpha as percentages, formatted in scientific notation if the absolute value is less than 0.001, otherwise with 4 decimal places.

3. Importance of Jensen's Alpha Calculation

Calculating Jensen's Alpha is essential for:

Risk-Adjusted Performance: Assesses whether excess returns are due to skill or risk.
Manager Evaluation: Helps identify portfolio managers who consistently outperform the market.
Investment Decisions: Guides investors in selecting funds with positive alpha.

4. Using the Calculator

Example 1: Calculate Jensen's Alpha for a portfolio with a beginning value of $10,000, ending value of $12,000, 2% risk-free rate, beta of 1.2, and 11% market return:

Beginning Value: $10,000;
Ending Value: $12,000;
Portfolio Return: $ \frac{12,000 - 10,000}{10,000} \times 100 = 20\% $;
Risk-Free Rate: 2%;
Beta: 1.2;
Market Return: 11%;
Expected Return: $ 2 + 1.2 \times (11 - 2) = 12.6\% $;
Jensen's Alpha: $ 20 - 12.6 = 7.4\% $.

Example 2: Calculate for a portfolio with a beginning value of $5,000, ending value of $5,250, 1% risk-free rate, beta of 0.8, and 10% market return:

Beginning Value: $5,000;
Ending Value: $5,250;
Portfolio Return: $ \frac{5,250 - 5,000}{5,000} \times 100 = 5\% $;
Risk-Free Rate: 1%;
Beta: 0.8;
Market Return: 10%;
Expected Return: $ 1 + 0.8 \times (10 - 1) = 8.2\% $;
Jensen's Alpha: $ 5 - 8.2 = -3.2\% $.

5. Frequently Asked Questions (FAQ)

Q: What does a positive Jensen's Alpha mean?
A: A positive value indicates the portfolio has outperformed the market on a risk-adjusted basis.

Q: Can Jensen's Alpha be negative?
A: Yes, a negative value means the portfolio underperformed the market, adjusted for risk.

Q: Why is beta important in this calculation?
A: Beta measures the portfolio's sensitivity to market movements, ensuring the return is adjusted for systematic risk.