The portfolio the optimiser hands you is the portfolio in a vacuum. The portfolio you actually trade is shaped by transaction costs, market impact, capacity, turnover constraints, financing, tax, regulation, and liquidity. The gap between the two — the implementation shortfall — is where many otherwise-good ideas die.
Transaction-cost models
Linear (proportional) costs
Cost = c · |w - w_0| where c is per-unit-trade cost (commissions, exchange fees, fixed bid-ask spread for small trades). Cheap, but doesn't capture price impact.
Quadratic (impact) costs
Cost = (γ/2) · (w - w_0)ᵀ M (w - w_0). M is an n × n cost matrix; typically diagonal with γ_i scaling each asset's market impact. Captures the empirical observation that costs grow super-linearly in trade size.
Almgren-Chriss (2001)
The canonical optimal-execution model. Separates costs into permanent (move the market price persistently) and temporary (price impact during the trade itself). Solves for the optimal time-trajectory of trades to minimise expected cost subject to a risk budget. The mathematical core of most agency execution algorithms.
Turnover penalty in portfolio construction
max μ_BLᵀ w - (λ/2) wᵀΣw - γ T(w, w_0)where T(w, w_0) = transaction-cost model
Adding T(w, w_0) to the Markowitz objective forces the optimiser to balance the gain from rebalancing against the cost of trading. With linear costs, only trades large enough to overcome the linear cost happen; with quadratic costs, trades smoothly trade off cost vs alpha.
Capacity
Every strategy has a capacity limit — the AUM at which alpha begins to erode due to impact costs. Empirical evidence (Berk-Green 2004, Pastor-Stambaugh 2012, AQR): for high-turnover quant strategies, capacity scales roughly with √ADV (square root of average daily volume) of the universe. A strategy generating 1bp/day on a $100bn universe has different capacity from a 10bp/day strategy on a $10bn universe.
Tracking error and active risk
Long-only mutual funds typically operate under a tracking-error constraint (e.g., σ(R_p - R_benchmark) ≤ 4%/year). This caps the active risk a PM can take, regardless of conviction. Optimisation under TE constraints is well-developed (Roll 1992) and produces qualitatively different optimal portfolios from unconstrained MV.
Tax-aware portfolio construction
Taxable accounts pay capital gains. Selling a winner triggers tax; selling a loser triggers a tax credit (tax-loss harvesting). Direct indexing and tax-loss-harvesting algorithms have grown into a $1T+ industry, with strategies typically adding 50-150bp/year of after-tax alpha to a passive benchmark — pure friction-management alpha, no factor exposure required.
Liquidity-aware construction
- Cap the share of a name's ADV that any single fund holds (Mar-Vega-Mark-Volger 2007).
- Cap the maximum days-to-liquidate any position at fund-level (10-20 days typical).
- Apply liquidity haircuts to expected returns for less-liquid assets.
- Stress-test the unwind: how much would the portfolio cost to liquidate in 1, 5, 20 days?
Other production realities
- Borrow costs: not all stocks short. Borrowing the hard-to-borrow ones costs 1-10%/year, eating into long-short alpha.
- Securities lending revenue: long-only funds can lend their shares for modest income, offsetting some fees.
- Margin and financing: levered strategies depend on prime-broker rates that change with market stress.
- Regulatory: position limits, short-sale rules (uptick), G-SIB capital surcharges, MiFID best-execution.
- Operational risk: trade failures, T+2 settlement, FX conversion, corporate actions all carry implementation overheads.
The Berk-Green decreasing-returns-to-scale model
Berk-Green (2004) argues that the marginal manager earns zero alpha after fees in equilibrium. Skilled managers attract inflows until their AUM grows large enough that impact costs erode the alpha to fee level. Empirical evidence broadly supports this: alpha decays after publication, after manager AUM doubles, after assets quintuple. The takeaway: every alpha source has finite capacity, and the size at which a strategy operates determines whether it can deliver to its investors.
Implementation shortfall
The cumulative gap between paper-portfolio returns (what the optimiser would have earned with frictionless execution) and live returns (what the fund actually earned). Decomposes into market impact, timing cost, commissions, and missed-trade cost. Top-tier execution adds 10-50bp/year over naive scheduling; bad execution can subtract 1%+.
Exercise
A long-short equity book has gross long exposure 100%, gross short 100%, net 0%. Annual turnover (gross long + gross short trades / AUM) = 800%. Average trading-cost is 10bp per trade. (1) Compute the annual cost drag. (2) The strategy's pre-cost Sharpe is 1.5; pre-cost expected return is 9%. Compute the post-cost expected return and Sharpe. (3) If costs doubled to 20bp, would the strategy still be viable?