Portfolio with Transaction Costs

Problem: Adjusting a portfolio of assets in such a way that desired return after broker's fees and other transaction costs is met with minimum variance.

As the expected return and variances of each asset change, the optimal portfolio is almost certain to change. Adjusting your investments with every change may cheer up your broker, but the commissions or transaction costs will slowly erode the value of your portfolio. Typically, there's a cost associated with each sale or purchase. Using this model, you need to take these transaction costs into account in calculating how to adjust your portfolio.

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According to your estimates, your current holdings will yield a 12.2% return. You are interested in adjusting your portfolio to lower the variance, yet achieve a return of at least 9.5%.

Your portfolio currently consists of 50% of Asset 1, 30% of Asset 2, and 20% of Asset 3. You pay a transaction fee at the beginning of the period that is a percentage of the amount bought or sold. The transaction fee is 1.0% for Asset 1, 1.5% for Asset 2, and 2.0% for Asset 3. You have estimated the expected return and the covariance terms for each asset.

The objective is to determine the percent to invest in each asset while minimising the risk of the entire portfolio.

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