Spanning the Achievable Stochastic Discount Factor with Asset Pricing Trees

Abstract

Risk factors price a cross-section of test assets if they span their joint investment opportunities that can be realized in the presence of transaction costs. This study introduces the Achievable Asset Pricing Trees approach, which extends the Asset Pricing Trees of Bryzgalova et al. (2020) by incorporating transaction costs directly into the Sharpe ratio optimization procedure. Empirical analysis shows that neglecting transaction costs in the test asset construction underestimates the optimal scale of shrinkage parameters and introduces bias toward cross-sections that favor more frequent rebalancing. Our method delivers test assets with greater realizable investment opportunities.