Alpha Subtracts, Treynor Divides

The lecturer stops the class to correct his own board. Jensen's alpha is a subtraction - the moment you divide by beta you have written the Treynor ratio instead. 1. Jensen's alpha = Ra − Rf − beta × (Rm − Rf). The fund's excess return, less the share of the market's excess return that its beta entitles it to. 2. Percent or decimal, either is fine: 5.5% = 0.055 and 4% = 0.04. What is not fine is one of each on the two sides of the subtraction. 3. Fund A's excess return: 0.055 − 0.04 = 0.015. 4. The market's own excess return: 0.025 − 0.04 = −0.015. Negative. 5. Fund A only carries 0.277 of it: 0.277 × (−0.015) = −0.004155. 6. 0.015 is greater than −0.015, so fund A beat the market. That is the sign answered before any subtraction. 7. The size of the gap: alpha = 0.015 − (−0.004155). Minus a minus is a plus, so the two pieces add. 8. alpha = +0.019155, which is the 1.9155 percentage points of the previous part, divided by a hundred. 9. The wrong move: (Ra − Rf) / beta = 0.015 / 0.277 = 0.054. That is a real number and a useful one - it is fund A's TREYNOR ratio. It is not the alpha. 10. Same three ingredients, two measures. Treynor divides by beta; Jensen multiplies the market term by it and subtracts. English narration and presentation.