A Jensen Measure Calculator is used to determine the risk-adjusted performance of an investment portfolio relative to a benchmark. The Jensen Measure, also known as Jensen’s Alpha, calculates the excess return of a portfolio over the expected return predicted by the Capital Asset Pricing Model (CAPM).

## Inputs

To calculate the Jensen Measure, the following inputs are required:

**Portfolio Return (Rp)**– The return of the investment portfolio (in percentage).**Risk-Free Rate (Rf)**– The return of a risk-free asset (in percentage).**Market Return (Rm)**– The return of the market benchmark (in percentage).**Portfolio Beta (β)**– The beta of the investment portfolio, which measures its volatility relative to the market.

## Formula

The formula to calculate Jensen’s Alpha (α) is:

[\alpha = Rp – \left[ Rf + \beta \times (Rm – Rf) \right]]

## Calculation Example

Let’s go through an example to understand how the Jensen Measure Calculator works.

## Example

**Inputs**:

- Portfolio Return (Rp): 12%
- Risk-Free Rate (Rf): 2%
- Market Return (Rm): 8%
- Portfolio Beta (β): 1.2

**Expected Return (ER)**using CAPM:

[ER = Rf + \beta \times (Rm – Rf)]

[ER = 2\% + 1.2 \times (8\% – 2\%) = 2\% + 1.2 \times 6\% = 2\% + 7.2\% = 9.2\%]**Jensen’s Alpha (α)**:

[\alpha = Rp – ER = 12\% – 9.2\% = 2.8\%]

So, the Jensen Measure (Alpha) for the given portfolio is 2.8%.

## Conclusion

The Jensen Measure Calculator is a valuable tool for investors and financial analysts to evaluate the performance of an investment portfolio relative to the market. By inputting the portfolio return, risk-free rate, market return, and portfolio beta, users can quickly determine Jensen’s Alpha, helping them make informed investment decisions. This calculator is particularly useful for comparing the risk-adjusted returns of different portfolios.