The literature of portfolio optimization is extensive and covers several important aspects of the asset allocation problem. However, previous works consider simplified linear borrowing cost functions that leads to suboptimal allocations. This paper aims at efficiently solving the leveraged portfolio selection problem with a thorough borrowing cost representation comprising a number lenders with different rates and credit limits. We propose a two-stage stochastic programming model for asset and debt allocation considering a CVaR-based risk constraint and a convex piecewise-linear borrowing cost function. We compare our model to its counterpart with the fixed borrowing rate approximation used in literature. Numerical results show our model significantly improves performance in terms of risk-return trade-off.