In this paper, we propose an approach to estimate parametric portfolios that accounts for transaction costs and a large number of factors. Our methodology involves first creating a portfolio that is optimized for transaction costs, while disregarding firm characteristics, but accommodating arbitrary restrictions and utilizing future information. We illustrate how transaction costs can serve as regularization over weight adjustments in this portfolio and introduce a methodology to estimate it. Subsequently, we employ this reference portfolio as a target to derive the parametric portfolio via a regression analysis on firm characteristics. Our empirical findings demonstrate that the proposed parametric portfolio method can recover a substantial portion of the initial portfolio and we observe a larger R-squared, sharpe ratio, and return when compared to conventional parametric portfolio techniques using the same factors. This outcome underscores the efficacy of our proposed approach in addressing transaction costs and arbitrary restrictions in portfolio optimization, with promising implications for investment management.