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Penalizing the Utility Function for Transaction Costs

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

Answer
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

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