What we as mechanical investors need is an optimal stock switching strategy. We have a screen which is stock rating system that each period has determined that there are N held stocks that are less likely to outperform than N new stocks. The algorithm should optimally create a set of sell then buy orders that accomplish this with a minimum slippage. I can’t believe that the brokerages that have this same problem in their internal mutual funds management. Pairs trading sometimes use a rule based on the available shares at a spread and the z-score. I asked Claude for advice on this problem and this was part of the reply:

This is a well-studied problem that touches several areas of quantitative finance. Here's the landscape:
The Core Problem
You're solving a portfolio transition optimization problem — minimizing cost (market impact, spread, timing risk) while moving from portfolio A to portfolio B.

Multi-Leg Execution Algorithms
Brokers and execution systems (e.g., ITG, Virtu, Bloomberg EMSX) solve this as a constrained optimization:
minimize: Σ spread_cost_i + Σ market_impact_i + timing_risk
subject to:
- available_quantity_i at each price level (LOB depth)
- cash-neutrality or delta-neutrality constraints
- position limits
- correlated execution timing across legs
Cross-Impact & Correlation Effects
The hard part for N > 2 is cross-asset market impact — selling stock A moves the price of correlated stock B before you buy it. Research papers by:
• Mastromatteo et al. on cross-impact
• Schneider & Lillo — "Cross-impact and no-dynamic-arbitrage"
These show that naive leg-by-leg execution is suboptimal; you need to jointly optimize the execution schedule.

>>> The point is that all the major brokers know about this problem and most likely are already using internal algorithms for this. And this type of portfolio exchange isn’t just used by mechanical investors. Or perhaps they don’t want to offer a black box system that obviously like any system like this make some poor trades.