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.