The expected return is the predicted return. It can, for example, be deduced from a model such as a factor model ($\approx$ regression).

Portfolio

The expected return of a portfolio is the weighted average of the expected returns for each asset in the portfolio.

\[\mathbb{E}[R_p] = \Sigma_{i=1}^d \omega_i \mathbb{E}[R_i]\]

Indeed: \(R_p = \sum_{i=1}^N \omega_i R_i\)

Warning if continuous returns:

\[r_p = ln(1+R_p) \color{red}{\neq} \sum_{i=1}^N \omega_i r_i\] \[r_p = ln \big( \sum_{i=1}^N \omega_i e^{r_i} \big)\]

Algorithmic trading

The expected return is a common metric in algorithmic trading. See the relevant section.