Sharpe Ratio of an Actively Managed Portfolio

First of all, I am a bit confused with the idea that the optimal portfolio is composed of a benchmark portfolio and of an actively managed portfolio. I felt like all this time, the optimal portfolio was about combining a risky asset and risk free asset.

Second, whats the logic behind the formula of the Sharpe ratio of an actively managed portfolio? I cant seem to understand the logic behind this concept and feel stuck when I am asked to find the sharpe ratio of a combined portfolio made of the benchmark and an actively managed portfolio.

Please help

U overthinking it. Sharpe ratio is the same formula u calculated in level 1, and its the same formula you will use in level 3.

This is the formula im referring to:


I cant make sense out of it. When we use it and why its built like that

That is a version of the formula that is dervived from a few other formulas. Check the reading as they do it step by step.

the odds of using that formula in the exam is a possible 1 question but likely zero. Memorize jow to dervive the formulas.