Transaction costs are a direct deduction from alpha — and unlike alpha, they are certain. This note brings them inside the optimiser. The measurement framework (implementation shortfall and its components) leads to two tractable cost models — linear for spread/brokerage, quadratic for market impact — and each produces a clean, memorable optimal-trading result in the single-asset case: quadratic costs shrink every trade toward the current position, while linear costs create a no-trade zone around the costless optimum, inside which the alpha gain cannot pay the toll. These two results are L14's analytical core and reliable exam material; the note ends with the execution problem (how to schedule the trades you do make) and the practical caveats.
Learning objectives. By the end of this note you should be able to:
- define implementation shortfall and list the cost components, knowing brokerage is often not the largest;
- write the linear and quadratic cost models and say what each represents;
- derive the optimal single-asset weight under quadratic costs and interpret the shrinkage;
- derive the no-trade-zone solution under linear costs via the case analysis;
- describe the multi-asset extensions and the trade-scheduling trade-off (impact vs risk);
- connect cost-aware optimisation back to turnover and the alpha-model mix.
In this lesson
- 8.1 Measuring and decomposing transaction costs
- 8.2 Optimal single-asset portfolio with quadratic costs
- 8.3 Optimal single-asset portfolio with linear costs
- 8.4 Multi-asset case and practice
- 8.5 Trading strategies
The full lesson, with worked examples and exercise solutions, is for members.
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