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We develop a deep learning framework to directly estimate tangency portfolio weights by augmenting benchmark factors with a long-short deep factor derived from high-dimensional characteristics. Guided by a Sharpe ratio maximization objective, the deep factor plays two key roles: (i) providing a natural hedge against benchmark risks, and (ii) capturing multi-market signals to enhance the performance of the benchmark. In an empirical application to U.S. corporate bonds using 132 firm-level bond, equity, and option characteristics, the deep factor achieves an out-of-sample Sharpe ratio exceeding 1, and the deep tangency portfolio benchmarked against the market factor yields a Sharpe ratio over 2, outperforming portfolios spanned by common observable or latent factors. These results demonstrate that bond risk signals are fundamentally dense, requiring the nonlinear integration of multi-market information to span the efficient frontier.

We find cross-market information expands the mean-variance efficiency in corporate bond and equity markets. Using 41 bond and 288 equity characteristics from the U.S. (2004-2022), we construct Within-Market and Cross-Market managed-portfolios optimized via a maximum Sharpe ratio framework. The Cross-Market strategy significantly outperforms Within-Market alternatives, generating robust alphas. These strategies are SDF projections onto payoff spaces; the efficiency expansion rejects complete market integration in the spanning sense, conditional on our managed-portfolio design. Crosssectional and time-series analyses reveal that the rejection is concentrated in illiquid and hard-to-arbitrage segments and attenuates when volatility is low and liquidity is high.

We argue that return predictability is a latent, asset-specific, and state-dependent characteristic. We develop an interpretable Panel Tree that endogenously partitions the U.S. equity panel into out-of-sample and persistent “mosaic” patterns, and estimate cluster-specific forecasting models. Predictability concentrates in stocks with large earnings surprises, high earnings-price ratios, and low trading volume. It is countercyclical, stronger when market dividend yields are high and liquidity is low. Accounting for predictability heterogeneity, which conventional models ignore, improves forecasts and yields portfolios with out-of-sample Sharpe ratios around 2. Across 50 years of data, the mosaic map shows where signals arise and where noise dominates.