Let $W^b_i$ denote the weight of stock i in the existing portfolio and $W^a_i$ denote the weight of stock i in the new portfolio to be created. Let $c_i$ denote the transaction cost of stock $i$.
If $m_i$ is the expected return of stock $i$, what is the transaction cost-adjusted expected return of the stock $i$. Please help me with this question. Thanks in advance!
The cost-adjusted expected return is the expected return, minus the transaction costs. The total size of your trade is $|W_i^b - W_i^a|$ and the cost per unit is $c_i$. The transaction cost adjusted return is the expected return, minus the total cost of doing the trade.