portfolio Optimization with transaction Costs Hauck Financial Services has a number of passive, buy-and-hold clients. For these clients, Hauck offers an investment account whereby clients agree to put their money into a portfolio of mutual funds that is rebalanced once a year. When the rebalancing occurs, Hauck determines the mix of mutual funds in each investor’s portfolio by solving an extension of the Markowitz portfolio model that incorporates transaction costs. Investors are charged a small transaction cost for the annual rebalancing of their portfolio. For simplicity, assume the following:
● At the beginning of the time period (in this case one year), the portfolio is rebalanced by buying and selling Hauck mutual funds.
● The transaction costs associated with buying and selling mutual funds are paid at the beginning of the period when the portfolio is rebalanced, which, in effect, reduces the amount of money available to reinvest.
● No further transactions are made until the end of the time period, at which point the new value of the portfolio is observed.
● The transaction cost is a linear function of the dollar amount of mutual funds bought or soldJean Delgado is one of Hauck’s buy-and-hold clients. We briefly describe the model as it is used by Hauck for rebalancing her portfolio. The mix of mutual funds that are being considered for her portfolio are a foreign stock fund (FS), an intermediate-term bond fund (IB), a large-cap growth fund (LG), a large-cap value fund (LV), a small-cap growth fund (SG), and a small-cap value fund (SV). In the traditional Markowitz model, the variables are usually interpreted as the proportion of the portfolio invested in the asset represented by the variable. For example, FS is the proportion of the portfolio invested in the foreign stock fund. However, it is equally correct to interpret FS as the dollar amount invested in the foreign stock fund. Then FS 5 25,000 implies $25,000 is invested in the foreign stock fund. Based on these assumptions, the initial portfolio value must equal the amount of money spent on transaction costs plus the amount invested in all the assets after rebalancing; that is, Initial portfolio value 5 amount invested in all assets after rebalancing + transaction costs
The extension of the Markowitz model that Hauck uses for rebalancing portfolios requires a balance constraint for each mutual fund. This balance constraint is
Amount invested in fund i = initial holding of fund i + amount of fund i purchased - amount of fund i sold
Using this balance constraint requires three additional variables for each fund: one for the amount invested prior to rebalancing, one for the amount sold, and one for the amount purchased. For instance, the balance constraint for the foreign stock fund is:
Jean Delgado has $100,000 in her account prior to the annual rebalancing, and she has specified a minimum acceptable return of 10 percent. Hauck plans to use the following model to rebalance Ms. Delgado’s portfolio. The complete model with transaction costs is
Assume you are a newly employed financial analytics specialist hired by Hauck Financial Services. One of your first tasks is to review the portfolio rebalancing model in order to resolve a dispute with Jean Delgado. Ms. Delgado has had one of the Hauck passively managed portfolios for the last five years and has complained that she is not getting the rate of return of 10 percent that she specified. After a review of her annual statements for the last five years, she feels that she is actually getting less than 10 percent on average.
1. According to the following Model Solution, IB_BUY = $41,268.51. How much in transaction costs did Ms. Delgado pay for purchasing additional shares of the intermediate-term bond fund?
2. Based on the Model Solution, what is the total transaction cost associated with rebalancing Ms. Delgado’s portfolio?
3. After paying transactions costs, how much did Ms. Delgado have invested in mutual funds after her portfolio was rebalanced?
4. According to the Model Solution, IB = $51,268.51. How much can Ms. Delgado expect to have in the intermediate-term bond fund at the end of the year?
5. According to the Model Solution, the expected return of the portfolio is $10,000. What is the expected dollar amount in Ms. Delgado’s portfolio at the end of the year? Can she expect to earn 10 percent on the $100,000 she had at the beginning of the year?
6. It is now time to prepare a report to management to explain why Ms. Delgado did not earn 10 percent each year on her investment. Make a recommendation in terms of a revised portfolio model that can be used so that Jean Delgado can have an expected portfolio balance of $110,000 at the end of next year. Prepare a report that includes a modified optimization model that will give an expected return of 10 percent on the amount of money available at the beginning of the year before paying the transaction costs. Explain why the current model does not do this.
7. Solve the formulation in part 6 for Jean Delgado. How does the portfolio composition differ from that of the Model Solution?
Maria sells 200 clay pots per month a tan average price of $80. Her explicit costs are $11,000 per month, and her implicit costs are $4,000 per month. What is her economi...May 28 2018
Compare and contrast aa and pahoehoe lava in appearance and how they form.ReferencesLutgens, F. K., & Tarbuck, E. J. (2014). Foundations of Earth science (7th ed.). Upper...Apr 16 2020
A related set of hypotheses that collectively explain some aspect of the natural world makes up a scientific ________.a. predictionb. testc. theoryd. authoritye. observationJun 22 2021
Effect of MDMA on Neural DevelopmentAnimal studies are often used to assess effects of prenatal exposure to illicit drugs. For example, Jack Lipton used rats to study the...Jul 06 2021
Given f(x)= f'(x)= f"(x)= The graph concaves up for ____________________________and concaves down for ____________________________. Can someone help me with the blanks? ThanksAug 02 2021
A methods and measurements analyst for Digital Devices needs to develop a time standard for the task of assembling a computer mouse. In a preliminary study, she observed ...Aug 22 2020
Forrester Company is considering buying new equipment that wouldincrease monthly fixed costs from $276,000 to $544,500 and woulddecrease the current variable costs of $60...May 29 2021
Darlene Page’s grandparents want to give her some money when she graduates from high school.They have offered Darlene three choices:a. Receive $16,000 immediately. Assume...May 03 2020
On January 1, 2017, Corgan Company acquired 70 percent of the outstanding voting stock of Smashing, Inc., for a total of $1,225,000 in cash and other consideration. At th...Aug 12 2021
Explain why business strategy is so difficult and challenging.Why is business strategy so important to the long-term success of a business?Think of a business with which ...Apr 06 2021