The transition planner: a multi-period LP for moving a portfolio under a tax budget

A new tax-aware DI account rarely opens with cash. It opens with the legacy portfolio in kind — a concentrated tech sleeve, an old SMA, a self-managed book the holder grew tired of. The question the transition planner answers is the cheapest tax-by-tax path from where you are to where you want to be. This post is about the LP behind it, why the gain budget is binding, what "cumulative integrated tracking error" means, and a worked transition over eight quarters.

Selling everything to rebalance the legacy portfolio to the target benchmark in one transaction realises the entire embedded gain at once, in a single tax year, often at the short-term rate. For a portfolio that's been compounding under an LTCG-deferred regime for years, the one-shot tax bill can wipe out a meaningful fraction of NAV. The transition planner spreads that bill across quarters, opportunistically harvesting embedded losses on the way, and arrives at the target TE without the one-shot drag.

A transition isn't a rebalance. It's a sequence of budget-bound rebalances solved jointly, with the destination as a constraint and the path as the variable.

min   Σ_{t=1..T}  TE_t(w_t)                           (cumulative integrated TE)
 w_1, …, w_T

s.t.   w_t = w_{t-1} + Δ_t                              (state evolution)
       Σ Δ_t = 1                                        (full investment)
       w_t ≥ 0                                          (long-only)
       realised_gain(Δ_t)  ≤  G_t                       (per-period budget)
       wash_sale_lock(Δ_t)                              (per-period lock vector)
       w_T  →  w_target                                 (terminal target)

Three modelling choices distinguish the transition planner from the daily DI optimizer:

• It's multi-period. The objective sums TE across all periods, not just the final one. The optimizer finds a path that minimises the integrated drift, not just the endpoint drift.
• The gain budget is hard. G_t is a constraint, not a penalty. The holder picks the number — typically tied to anticipated external gains they can absorb in each period — and the LP either finds a feasible plan or returns infeasible (in which case the holder relaxes G_t or extends T).
• Embedded losses are free budget. A trade that realises a loss doesn't consume the gain budget — it expands it for future trades in the same period. So the optimizer naturally sequences harvest first, gains second, to widen the budget envelope.

A naive transition objective minimises TE at the horizon — get as close to the benchmark as possible by Q8. That can produce a plan that holds the legacy portfolio at high TE for 7 quarters and rebalances aggressively in Q8. The cumulative integrated objective penalises every quarter of TE, so the plan ramps the holder toward the benchmark monotonically.

A representative transition: account opens with $5M across 12 concentrated tech names; target is a US large-cap index at 75 bp annual TE; gain budget is $200k/year ($50k/quarter); horizon is 8 quarters.

• Future prices are unknown. The plan is computed off today's prices and a model of realised volatility; real prices will deviate. The plan is replannable on each rebalance — the holder re-runs the LP with updated holdings and the new schedule supersedes the old one.
• Future budgets are stated, not derived. The holder declares the gain budget per period. If the holder's external income changes (a bonus, an exit, a carryforward expiring) the budget should be re-stated and the plan re-run.
• No income-side optimization. The planner doesn't consider dividend yields or qualified dividend treatment. For accounts where dividend income is material to the tax bill, post-process the plan with the holder's tax adviser.

For the daily-cadence strategy that runs after the transition completes, see the tax-aware direct indexing deep-dive. For a related one-shot tool focused on year-end harvesting rather than transition, see the year-end loss harvest maximiser.

Educational illustration · numbers illustrative. Not investment, tax, or legal advice.