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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 sold. Jean 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 = 25,000 implies that $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, The extension of the Markowitz model that Hauck uses for rebalancing portfolios requires a balance constraint for each mutual fund. This balance constraint is 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%. Hauck plans to use the following model to rebalance Ms. Delgado's portfolio. The complete model with transaction costs is to Notice that the transaction fee is set at 1% in the model (the last constraint) and that the transaction cost for buying and selling shares of the mutual funds is a linear function of the amount bought and sold. With this model, the transaction costs are deducted from the client's account at the time of rebalancing and thus reduce the amount of money invested. The solution for Ms. Delgado's rebalancing problem is shown as part of the Managerial Report.

Managerial Report :

Assume that you are a financial analytics specialist newly 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 past five years and has complained that she is not getting the rate of return of 10% that she specified. After reviewing her annual statements for the past five years, she feels that she is actually getting less than 10% on average.

1. According to the following Model Solution, . 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% on the $100,000 she had at the beginning of the year?

MODEL SOLUTION

Optimal Objective Value 27219457.356 Variable Value Variable Value 18953.280 IB START 10000.000 10000.000 IB BUY 41268.510 11569.210 IB SELL 0.000 5663.961 LG START 10000.000 9693.921 LG BUY 0.000 4119.631 LG SELL 5060.688 FS 15026.860 LV_START 40000.000 IB 51268.510 LV_BUY 0.000 LG 4939.312 LV_SELL 40000.000 LV 0.000 SG_START 10000.000 SG 0.000 SG BUY 0.000 SV 27675.000 SG SELL 10000.000 TRANS COST 1090.311 SV_START 20000.000 FS START 10000.000 SV_BUY 7675.004 FS BUY 5026.863 SV_SELL 0.000 FS_ SELL 0.000 TRANS_FEE 0.010