A systematic portfolio manager uses a mean-variance optimizer enhanced with an ML-predicted alpha vector to construct a 150-stock long-only equity portfolio. The optimizer is unconstrained except for a budget constraint. The resulting portfolio allocates 45% to a single semiconductor stock with the highest predicted alpha. Which constraint addition BEST addresses the concentration risk while preserving the optimizer's ability to express high-conviction alpha views?

The 45% single-stock concentration is a classic symptom of unconstrained mean-variance optimization, which Michaud (1989) famously described as an 'error maximizer.' When alpha estimates have any uncertainty — and machine-learning-predicted alphas always do — the optimizer amplifies small errors in the return forecast into extreme portfolio weights. The equal-weight allocation across all 150 stocks approach is the nuclear option that discards all alpha information. It eliminates concentration but removes the entire purpose of the machine-learning alpha model, making the exercise pointless. The absolute single-stock weight cap plus sector neutrality relative to a benchmark approach imposes a hard absolute ceiling, such as 5% of portfolio, and forces the portfolio to match benchmark sector weights. This is overly conservative: it prevents the manager from exploiting genuine sector-level alpha and may actually create hidden tracking error if sectors are constrained to benchmark weights while individual stock weights vary within them. The maximum single-stock active weight constraint with moderately expanded tracking error is correct because it allows the semiconductor stock to hold, for example, 3% more than its 2% benchmark weight — a 5% active overweight that is meaningful without catastrophic concentration. The tracking error flexibility allows the manager to express high-conviction views across multiple stocks without being forced into artificial sector neutrality. This is consistent with how institutional long-only mandates are typically structured using commercial optimizers like Axioma or Barra. The Bayesian alpha shrinkage toward zero approach is a valid risk management technique that reduces alpha uncertainty by blending machine-learning predictions with a prior toward zero. However, run alone on an unconstrained optimizer, it would merely reduce the 45% position to, say, 30% — still catastrophically concentrated. Shrinkage addresses estimation error but does not substitute for an explicit concentration constraint. Best practice combines Bayesian shrinkage of the alpha vector with active weight constraints and a transaction cost penalty in the objective function.