Jensen's Alpha For Fund A

The third performance measure stops being a definition and becomes a number. One fund, four inputs, one subtraction. 1. Jensen's alpha = Ra − Rf − beta × (Rm − Rf). A difference, not a ratio. 2. Fund A's inputs: mean return 5.5%, beta 0.277, market index 2.5%, risk-free rate 4%. 3. The market term first: 0.277 × (2.5 − 4) = 0.277 × (−1.5) = −0.4155. 4. It is negative because the market's own excess return is negative: 2.5% sits below the risk-free 4%. 5. So the CAPM says a beta of 0.277 entitles fund A to 4 − 0.4155 = 3.5845%. 6. Fund A's own excess return: 5.5 − 4 = 1.5. 7. The alpha: 1.5 − (−0.4155) = +1.9155 percentage points. Minus a minus is a plus. 8. Checked the other way round: 5.5 − 3.5845 = 1.9155. Same answer. 9. Reading the sign - alpha = 0 matched the market, above 0 beat it, below 0 missed it. The threshold is zero, not one. 10. Fund A's alpha is above zero, so fund A beat the benchmark its own beta entitles it to. Put the market itself through the formula and its alpha is exactly zero, which is the check that the measure is built right. English narration and presentation.