A Division of Windham Capital Management, LLC

Penalizing the Utility Function for Transaction Costs

How does the Windham Software adjust the utility function to incorporate transaction costs?

Transaction costs are calculated as a penalty to the optimization objective function.

For example, the standard Mean-Variance objective function is:

Maximize   U(w) = Expected Returns * w’ - w * Covariance * w’

We add a penalty to reflect the transactions incurred transitioning from the current portfolio to the optimal portfolio:

Maximize   U(w) = Expected Returns * w’ - w * Covariance * w’ - CostPenalty(w)

Where the CostPenalty is a quadratic approximation:

CostPenalty(w) = 2 * (w - CurrentPortfolioWeights) ^ 2 * sqrt(Transaction Cost)

and “Transaction Cost” is the vector specified in the Portfolio Construction screen. Transaction cost specified in the Windham Software as 0.01 would equate to 1%.

Related Articles

  1. Transaction Costs and Turnover Control

Category:Understanding the Software -> Optimization