The formula to calculate Jensen's Alpha is:
\[ \alpha = \text{Rp} - (\text{Rf} + \beta_p \times (\text{Rm} - \text{Rf})) \]
Where:
Jensen's Alpha is used to measure the risk-adjusted performance of a security or portfolio in relation to the expected market return.
Let's assume the following values:
Using the formula:
\[ \alpha = 12 - (0.5 + 0.85 \times (0.4 - 0.5)) \]
Evaluating:
\[ \alpha = 12 - (0.5 + 0.85 \times -0.1) \]
\[ \alpha = 12 - (0.5 - 0.085) \]
\[ \alpha = 12 - 0.415 \]
\[ \alpha = 11.585 \]
Jensen's Alpha is 11.585%.
| Annual Return on Investment (%) | Risk Free Interest Rate (%) | Beta of the Portfolio | Annual Return of the Market Benchmark (%) | Jensen's Alpha (%) |
|---|---|---|---|---|
| 10 | 0.5 | 0.5 | 0.5 | 9.500000000000 |
| 10 | 0.5 | 0.5 | 1 | 9.250000000000 |
| 10 | 0.5 | 0.5 | 1.5 | 9.000000000000 |
| 10 | 0.5 | 1 | 0.5 | 9.500000000000 |
| 10 | 0.5 | 1 | 1 | 9.000000000000 |
| 10 | 0.5 | 1 | 1.5 | 8.500000000000 |
| 10 | 0.5 | 1.5 | 0.5 | 9.500000000000 |
| 10 | 0.5 | 1.5 | 1 | 8.750000000000 |
| 10 | 0.5 | 1.5 | 1.5 | 8.000000000000 |
| 10 | 1 | 0.5 | 0.5 | 9.250000000000 |
| 10 | 1 | 0.5 | 1 | 9.000000000000 |
| 10 | 1 | 0.5 | 1.5 | 8.750000000000 |
| 10 | 1 | 1 | 0.5 | 9.500000000000 |
| 10 | 1 | 1 | 1 | 9.000000000000 |
| 10 | 1 | 1 | 1.5 | 8.500000000000 |
| 10 | 1 | 1.5 | 0.5 | 9.750000000000 |
| 10 | 1 | 1.5 | 1 | 9.000000000000 |
| 10 | 1 | 1.5 | 1.5 | 8.250000000000 |
| 10 | 1.5 | 0.5 | 0.5 | 9.000000000000 |
| 10 | 1.5 | 0.5 | 1 | 8.750000000000 |
| 10 | 1.5 | 0.5 | 1.5 | 8.500000000000 |
| 10 | 1.5 | 1 | 0.5 | 9.500000000000 |
| 10 | 1.5 | 1 | 1 | 9.000000000000 |
| 10 | 1.5 | 1 | 1.5 | 8.500000000000 |
| 10 | 1.5 | 1.5 | 0.5 | 10.000000000000 |
| 10 | 1.5 | 1.5 | 1 | 9.250000000000 |
| 10 | 1.5 | 1.5 | 1.5 | 8.500000000000 |
| 12 | 0.5 | 0.5 | 0.5 | 11.500000000000 |
| 12 | 0.5 | 0.5 | 1 | 11.250000000000 |
| 12 | 0.5 | 0.5 | 1.5 | 11.000000000000 |
| 12 | 0.5 | 1 | 0.5 | 11.500000000000 |
| 12 | 0.5 | 1 | 1 | 11.000000000000 |
| 12 | 0.5 | 1 | 1.5 | 10.500000000000 |
| 12 | 0.5 | 1.5 | 0.5 | 11.500000000000 |
| 12 | 0.5 | 1.5 | 1 | 10.750000000000 |
| 12 | 0.5 | 1.5 | 1.5 | 10.000000000000 |
| 12 | 1 | 0.5 | 0.5 | 11.250000000000 |
| 12 | 1 | 0.5 | 1 | 11.000000000000 |
| 12 | 1 | 0.5 | 1.5 | 10.750000000000 |
| 12 | 1 | 1 | 0.5 | 11.500000000000 |
| 12 | 1 | 1 | 1 | 11.000000000000 |
| 12 | 1 | 1 | 1.5 | 10.500000000000 |
| 12 | 1 | 1.5 | 0.5 | 11.750000000000 |
| 12 | 1 | 1.5 | 1 | 11.000000000000 |
| 12 | 1 | 1.5 | 1.5 | 10.250000000000 |
| 12 | 1.5 | 0.5 | 0.5 | 11.000000000000 |
| 12 | 1.5 | 0.5 | 1 | 10.750000000000 |
| 12 | 1.5 | 0.5 | 1.5 | 10.500000000000 |
| 12 | 1.5 | 1 | 0.5 | 11.500000000000 |
| 12 | 1.5 | 1 | 1 | 11.000000000000 |
| 12 | 1.5 | 1 | 1.5 | 10.500000000000 |
| 12 | 1.5 | 1.5 | 0.5 | 12.000000000000 |
| 12 | 1.5 | 1.5 | 1 | 11.250000000000 |
| 12 | 1.5 | 1.5 | 1.5 | 10.500000000000 |
| 14 | 0.5 | 0.5 | 0.5 | 13.500000000000 |
| 14 | 0.5 | 0.5 | 1 | 13.250000000000 |
| 14 | 0.5 | 0.5 | 1.5 | 13.000000000000 |
| 14 | 0.5 | 1 | 0.5 | 13.500000000000 |
| 14 | 0.5 | 1 | 1 | 13.000000000000 |
| 14 | 0.5 | 1 | 1.5 | 12.500000000000 |
| 14 | 0.5 | 1.5 | 0.5 | 13.500000000000 |
| 14 | 0.5 | 1.5 | 1 | 12.750000000000 |
| 14 | 0.5 | 1.5 | 1.5 | 12.000000000000 |
| 14 | 1 | 0.5 | 0.5 | 13.250000000000 |
| 14 | 1 | 0.5 | 1 | 13.000000000000 |
| 14 | 1 | 0.5 | 1.5 | 12.750000000000 |
| 14 | 1 | 1 | 0.5 | 13.500000000000 |
| 14 | 1 | 1 | 1 | 13.000000000000 |
| 14 | 1 | 1 | 1.5 | 12.500000000000 |
| 14 | 1 | 1.5 | 0.5 | 13.750000000000 |
| 14 | 1 | 1.5 | 1 | 13.000000000000 |
| 14 | 1 | 1.5 | 1.5 | 12.250000000000 |
| 14 | 1.5 | 0.5 | 0.5 | 13.000000000000 |
| 14 | 1.5 | 0.5 | 1 | 12.750000000000 |
| 14 | 1.5 | 0.5 | 1.5 | 12.500000000000 |
| 14 | 1.5 | 1 | 0.5 | 13.500000000000 |
| 14 | 1.5 | 1 | 1 | 13.000000000000 |
| 14 | 1.5 | 1 | 1.5 | 12.500000000000 |
| 14 | 1.5 | 1.5 | 0.5 | 14.000000000000 |
| 14 | 1.5 | 1.5 | 1 | 13.250000000000 |
| 14 | 1.5 | 1.5 | 1.5 | 12.500000000000 |
| 16 | 0.5 | 0.5 | 0.5 | 15.500000000000 |
| 16 | 0.5 | 0.5 | 1 | 15.250000000000 |
| 16 | 0.5 | 0.5 | 1.5 | 15.000000000000 |
| 16 | 0.5 | 1 | 0.5 | 15.500000000000 |
| 16 | 0.5 | 1 | 1 | 15.000000000000 |
| 16 | 0.5 | 1 | 1.5 | 14.500000000000 |
| 16 | 0.5 | 1.5 | 0.5 | 15.500000000000 |
| 16 | 0.5 | 1.5 | 1 | 14.750000000000 |
| 16 | 0.5 | 1.5 | 1.5 | 14.000000000000 |
| 16 | 1 | 0.5 | 0.5 | 15.250000000000 |
| 16 | 1 | 0.5 | 1 | 15.000000000000 |
| 16 | 1 | 0.5 | 1.5 | 14.750000000000 |
| 16 | 1 | 1 | 0.5 | 15.500000000000 |
| 16 | 1 | 1 | 1 | 15.000000000000 |
| 16 | 1 | 1 | 1.5 | 14.500000000000 |
| 16 | 1 | 1.5 | 0.5 | 15.750000000000 |
| 16 | 1 | 1.5 | 1 | 15.000000000000 |
| 16 | 1 | 1.5 | 1.5 | 14.250000000000 |
| 16 | 1.5 | 0.5 | 0.5 | 15.000000000000 |
| 16 | 1.5 | 0.5 | 1 | 14.750000000000 |
| 16 | 1.5 | 0.5 | 1.5 | 14.500000000000 |
| 16 | 1.5 | 1 | 0.5 | 15.500000000000 |
| 16 | 1.5 | 1 | 1 | 15.000000000000 |
| 16 | 1.5 | 1 | 1.5 | 14.500000000000 |
| 16 | 1.5 | 1.5 | 0.5 | 16.000000000000 |
| 16 | 1.5 | 1.5 | 1 | 15.250000000000 |
| 16 | 1.5 | 1.5 | 1.5 | 14.500000000000 |
| 18 | 0.5 | 0.5 | 0.5 | 17.500000000000 |
| 18 | 0.5 | 0.5 | 1 | 17.250000000000 |
| 18 | 0.5 | 0.5 | 1.5 | 17.000000000000 |
| 18 | 0.5 | 1 | 0.5 | 17.500000000000 |
| 18 | 0.5 | 1 | 1 | 17.000000000000 |
| 18 | 0.5 | 1 | 1.5 | 16.500000000000 |
| 18 | 0.5 | 1.5 | 0.5 | 17.500000000000 |
| 18 | 0.5 | 1.5 | 1 | 16.750000000000 |
| 18 | 0.5 | 1.5 | 1.5 | 16.000000000000 |
| 18 | 1 | 0.5 | 0.5 | 17.250000000000 |
| 18 | 1 | 0.5 | 1 | 17.000000000000 |
| 18 | 1 | 0.5 | 1.5 | 16.750000000000 |
| 18 | 1 | 1 | 0.5 | 17.500000000000 |
| 18 | 1 | 1 | 1 | 17.000000000000 |
| 18 | 1 | 1 | 1.5 | 16.500000000000 |
| 18 | 1 | 1.5 | 0.5 | 17.750000000000 |
| 18 | 1 | 1.5 | 1 | 17.000000000000 |
| 18 | 1 | 1.5 | 1.5 | 16.250000000000 |
| 18 | 1.5 | 0.5 | 0.5 | 17.000000000000 |
| 18 | 1.5 | 0.5 | 1 | 16.750000000000 |
| 18 | 1.5 | 0.5 | 1.5 | 16.500000000000 |
| 18 | 1.5 | 1 | 0.5 | 17.500000000000 |
| 18 | 1.5 | 1 | 1 | 17.000000000000 |
| 18 | 1.5 | 1 | 1.5 | 16.500000000000 |
| 18 | 1.5 | 1.5 | 0.5 | 18.000000000000 |
| 18 | 1.5 | 1.5 | 1 | 17.250000000000 |
| 18 | 1.5 | 1.5 | 1.5 | 16.500000000000 |
| 20 | 0.5 | 0.5 | 0.5 | 19.500000000000 |
| 20 | 0.5 | 0.5 | 1 | 19.250000000000 |
| 20 | 0.5 | 0.5 | 1.5 | 19.000000000000 |
| 20 | 0.5 | 1 | 0.5 | 19.500000000000 |
| 20 | 0.5 | 1 | 1 | 19.000000000000 |
| 20 | 0.5 | 1 | 1.5 | 18.500000000000 |
| 20 | 0.5 | 1.5 | 0.5 | 19.500000000000 |
| 20 | 0.5 | 1.5 | 1 | 18.750000000000 |
| 20 | 0.5 | 1.5 | 1.5 | 18.000000000000 |
| 20 | 1 | 0.5 | 0.5 | 19.250000000000 |
| 20 | 1 | 0.5 | 1 | 19.000000000000 |
| 20 | 1 | 0.5 | 1.5 | 18.750000000000 |
| 20 | 1 | 1 | 0.5 | 19.500000000000 |
| 20 | 1 | 1 | 1 | 19.000000000000 |
| 20 | 1 | 1 | 1.5 | 18.500000000000 |
| 20 | 1 | 1.5 | 0.5 | 19.750000000000 |
| 20 | 1 | 1.5 | 1 | 19.000000000000 |
| 20 | 1 | 1.5 | 1.5 | 18.250000000000 |
| 20 | 1.5 | 0.5 | 0.5 | 19.000000000000 |
| 20 | 1.5 | 0.5 | 1 | 18.750000000000 |
| 20 | 1.5 | 0.5 | 1.5 | 18.500000000000 |
| 20 | 1.5 | 1 | 0.5 | 19.500000000000 |
| 20 | 1.5 | 1 | 1 | 19.000000000000 |
| 20 | 1.5 | 1 | 1.5 | 18.500000000000 |
| 20 | 1.5 | 1.5 | 0.5 | 20.000000000000 |
| 20 | 1.5 | 1.5 | 1 | 19.250000000000 |
| 20 | 1.5 | 1.5 | 1.5 | 18.500000000000 |