Adding Proportional and Minimum Trading Costs to Mean-CVaR Portfolios

Summary

The document presents a Markowitz-style mean-CVaR portfolio optimization setup. It defines scenario losses from portfolio returns, uses a confidence level to form CVaR, and balances expected return against tail risk with a risk preference parameter. The portfolio is constrained to have the same total value as the existing holdings.

It raises how to extend this setup when trades incur both a proportional cost and a minimum fee per asset. The document does not provide a formulation or worked solution for including either cost. It therefore introduces a practical modeling question rather than demonstrating a complete transaction-cost-aware strategy; readers would need to determine how to represent trade amounts and minimum fees in the optimization model.

Key ideas

• The model balances expected portfolio return against CVaR using a risk preference parameter.
• Scenario losses are calculated from portfolio holdings and asset returns in each scenario.
• The portfolio value is constrained to match the value of the existing portfolio.
• The document asks how to include proportional trading costs and per-trade minimum fees but does not answer the question.

Tags

# Mean-cVaR model: How can one include transaction cost


# Mean-cVaR model: How can one include transaction cost












$$ \min \delta CVaR - (1-\delta) \sum_i^{n} \mu_i x_i \\ \sum x_i = \sum x^{old}_i \\ Losses(s) = \sum x_i - \sum_i^{n} (R(s,i))x_i \\ VaRDev(s) = Losses(s) - VaR \\ CVaR = VaR + \frac{\sum_s^{} p_s VaRDev(s)}{1-\alpha} $$

The Markowitz style Mean-cVaR portfolio is stated above. It Appears in Practical financial optimization by Zenios. $x^{old}$ is exciting portfolio and now you want to optimize and create a new portfolio $x$. $s$ is the different scenarios.

But what if transaction costs existing so you should pay $c_{variable}$ % of how much you trade an asset and each trade have a minimum cost as well. How can we add transaction cost to this model?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.