Components of Transaction Costs
1. Spread
Bid-ask spread, typically 0.5-2 ticks for liquid futures.
2. Market Impact
Price moves against you as you trade.
For small trades: Linear model $\text{cost} = k \times \text{trade_size}$
For larger trades: Square-root model $\text{cost} = k \times \sqrt{\text{trade_size}}$
3. Financing
Cost of margin and collateral.
4. Slippage
Execution price worse than expected due to:
- Market volatility during execution
- Partial fills at worse prices
- Information leakage
Total Cost Estimation
Typical all-in costs for liquid futures:
- Small trades (<10 contracts): 2-5 bps
- Medium trades (10-100 contracts): 5-10 bps
- Large trades (>100 contracts): 10-20 bps
Minimizing Costs
- Trade liquid contracts - Stick to front-month or most liquid
- Time trades carefully - Avoid market open/close, news events
- Use limit orders - Accept execution risk for better prices
- Split large orders - VWAP/TWAP algorithms
- Cross internally - Match buys and sells within firm
Incorporating into Optimization
Add turnover penalty to objective:
\[\text{Objective} = \mu^T w - \lambda w^T \Sigma w - \gamma \sum_i \lvert w_i - w_{i,old} \rvert\]where $\gamma$ approximates your transaction cost per unit traded.