We develop a Sharpe ratio–maximizing decision framework for environments in which binary approval rules endogenously determine the investable set. In conventional portfolio theory, investors optimize weights within an exogenously given asset universe; in credit screening, however, the approval threshold τ simultaneously governs both the number and the quality of admitted assets. This endogeneity renders diversification a function of τ, causing idiosyncratic risk to re-emerge at the portfolio level. Because each loan generates only a single realized outcome, its idiosyncratic variance cannot be directly estimated. We compute expected returns using decile-specific conditional returns of predicted default probabilities and construct a risk proxy from the cross-sectional variance within expected-return intervals. Using LendingClub data from 2007 to 2020 with 50 repeated cross-validation runs, we obtain an average Sharpe ratio of 0.0919 and an average approval rate of 26.9% under the optimal threshold τ*. The Sharpe ratio exhibits an inverted U-shaped pattern with respect to τ, confirming a trade-off in which stricter screening improves the quality of the approved loan pool while concentrating it on fewer loans. Whereas indiscriminate approval of all loans yields a negative Sharpe ratio, the proposed model achieves a positive one. A portfolio that underperforms Treasury securities when evaluated solely on expected returns can outperform them once risk information is incorporated. The findings demonstrate that when the investment set is endogenously determined by the screening rule, explicit incorporation of asset-level risk information – rather than expected return alone – is essential for investment decisions.
Park et al. (2026) studied this question.