Tax-aware direct indexing, in full: model, data, backtest, observations

Tax-aware direct indexing is the load-bearing strategy on the platform. It does what an index ETF does — track a benchmark — and adds the one thing the ETF wrapper structurally can't: harvest the embedded losses that show up, name by name, every year a market exists. This post is the long version: model, data, ten vintages of backtests, and the observations we keep coming back to.

A US large-cap (100-name) universe had ten down names in a typical year of the last decade — ten constituents that finished the year underwater, often by 20% or more. Inside an index ETF those losses are invisible to the holder; the fund sees a single basis and the holder sees a single capital gain or loss only on sale. Direct indexing inverts that. Each constituent is held in the holder's name, with its own basis. Every name that drops is a candidate for harvest against the holder's other realised gains — interest income from a year-end bond sale, an exit from a private position, the sale of an outside concentrated stock. The economic value of that ongoing harvest stream is what the literature calls tax alpha.

An ETF holds the index opaquely. Direct indexing holds the same names transparently — so every name that drops can be sold for a loss without changing what you're tracking.

The optimizer minimises a weighted sum of two penalties: distance from the benchmark in the risk-model metric, and realised tax cost net of harvested loss. The tracking-error penalty has the risk model's covariance matrix Σ inside it, so distance is measured in factor space, not raw weight space. The tax penalty looks at every lot the optimizer might touch on the sell side, scores it under the jurisdiction's lot-identification rule (HIFO by default in the US), and accumulates short-term and long-term realised gain or loss into a single dollar number.

min   λ_te · (w − w_b)ᵀ Σ (w − w_b)   +   λ_tax · τ(w)
 w

s.t.  Σ w = 1                       (budget)
      0 ≤ w_i ≤ c_max                (long-only, single-name cap)
      TE(w) ≤ TE_max                 (hard tracking-error ceiling)
      w_i = 0  for i ∈ wash_lock    (30-day wash-sale lock vector)
      lot identification: HIFO       (tax engine, jurisdictional)

Three modelling choices deserve calling out:

• TE is both penalty and constraint. λ_te penalises tracking error in the objective; TE_max caps it hard. The penalty pulls the solver toward the benchmark on quiet days; the cap stops it breaching when tax opportunities are abundant.
• Wash-sale is a vector, not a flag. The lock is per-ticker and dated. A name sold for a loss on day t is force-zero on day t+1 through t+30. Days t+31 onward the optimizer is free to repurchase. Dates carry across rebalances; a Friday loss locks Monday's solve as well.
• Lot-level, not position-level. Every position is a stack of dated lots. The HIFO heuristic identifies the highest-cost lot first when selling, minimising the realised gain (or maximising the realised loss) on each ticket. The lot ID is part of the persisted Trade record so the broker statement matches the optimizer's view.

Five datasets feed every solve:

The headline trajectory below starts each vintage on Jan 2 of its start year and runs through the end of the panel. $1M starting capital, 5% TE budget (loose by direct-indexing standards; deliberately so, to surface the harvest tail), HIFO, 30-day wash-sale lock. Marginal rates: 37% short-term, 23.8% long-term (incl. NIIT). Federal only — state treatment varies and is left out of the headline number.

Decomposing the gross-of-tax outperformance into its sources clarifies what is and isn't running. Across the eight vintages above, the median attribution looks like this:

The harvest line is the load-bearing one — three-quarters of the alpha, every vintage. Deferral matters most in years that bank a lot of long-term gains; tilt residual is small and not engineered for. Trading friction nets the strategy 2 bp; the replacement-security selection is what keeps it from being a much larger number.

Two things: alpha is concave in TE budget — diminishing returns kick in around 200 bp — and there's no alpha cliff at the low end. A 50 bp budget still delivers ~22 bp/yr, which is roughly the dispersion of an honest factor model's residual on a US large-cap (100) universe. The point of TE_max isn't to suppress tax alpha; it's to bound the active risk budget the holder agreed to.

• Cash-flow timing. Real accounts deposit and withdraw; backtested accounts don't. Net deposits give the optimizer fresh capital that's lockout-free and reset basis; net withdrawals shrink the harvestable stack.
• External gains assumed available. Tax-alpha numbers assume the holder has external gains to offset against. A holder with no offsettable gains banks the loss as a carryforward — same economic value, longer time horizon.
• Trading cost. 2 bp per trade is a defensible average across the universe, but a long-tail name on a thin day will cost more. Production runs should plug in a per-name spread curve.

For more on each: see Building a backtest you can defend, Replacement-security selection, and What "tax alpha" actually measures.

Educational illustration · numbers illustrative. Federal taxes only; state treatment varies.