1. A portfolio manager has $20 million to invest in a fund consisting of the following bonds: Bond Category Quality Maturity Yield Rating (Years) (Percent) Treasury Bills Treasury Bonds Corporate Bonds Municipal Bonds Junk Bonds 5.0 5.0 3.5 3.0 1.0 0.4 4.0 3.2 2.0 2.5 4.0 6.0 4.4 5.6 8.0 The manager has listed the bonds in descending order of quality rating. The second column lists the average maturity in years (i.e. how long it takes). The final column gives the yield (in percent per year after tax) for each bond (Reminder: yield determines the return, bigger yield means larger return). The manager intends to create a bond fund by investing proportions of $20 million in the different securities and has announced an investment goal of a high-quality,medium-maturity portfolio. In particular, the fund's average quality rating, but be at least 3.5, and its average maturity should be no shorter than 1.5 years, but no longer than 2.5 years. The portfolio manager is seeking the highest expected return subject to the quality and maturity requirements given above. What proportion of the $20 million should be invested in each type of bond? 2. Suppose there is a municipality that contracts a private bus company for the transportation of students in primary grades to and from school. The private bus company is paid based on the total number of projected "kid-miles" the company transports them (e.g. 20 kids for 2 miles is 40 kid-miles and so is 8 kids for 5 miles). There are 4 communities near the 3 municipal primary schools. In the northern community, there are 240 students registered with the schools. In the east there are 120, the south has 400, and the west has 200 Each school has a limited capacity with school 1 being able to handle 360 students, school 2 being able to handle 400 students, and school 3 being able to handle 260 students. The distance between the community and the schools is shown in the table below: School-Community Distances School School 1 School 2 School 3 Community North East South West 2.0 3.0 1.4 3.2 3.2 2.4 2.0 2.0 3.6 1.4 3.0 2.2 a) If you are working for the school board (i.e. an employee of the municipality), what would you recommend be the allocation of students? b) Suppose the school board is concerned that a new housing project in the South will result in a number of new students. How many students could be added before there should be a concern regarding over crowding? c) Suppose instead you work for the bus company, what would your proposed allocation of students be? Why did it change? 1. A portfolio manager has $20 million to invest in a fund consisting of the following bonds: Bond Category Quality Maturity Yield Rating (Years) (Percent) Treasury Bills Treasury Bonds Corporate Bonds Municipal Bonds Junk Bonds 5.0 5.0 3.5 3.0 1.0 0.4 4.0 3.2 2.0 2.5 4.0 6.0 4.4 5.6 8.0 The manager has listed the bonds in descending order of quality rating. The second column lists the average maturity in years (i.e. how long it takes). The final column gives the yield (in percent per year after tax) for each bond (Reminder: yield determines the return, bigger yield means larger return). The manager intends to create a bond fund by investing proportions of $20 million in the different securities and has announced an investment goal of a high-quality,medium-maturity portfolio. In particular, the fund's average quality rating, but be at least 3.5, and its average maturity should be no shorter than 1.5 years, but no longer than 2.5 years. The portfolio manager is seeking the highest expected return subject to the quality and maturity requirements given above. What proportion of the $20 million should be invested in each type of bond? 2. Suppose there is a municipality that contracts a private bus company for the transportation of students in primary grades to and from school. The private bus company is paid based on the total number of projected "kid-miles" the company transports them (e.g. 20 kids for 2 miles is 40 kid-miles and so is 8 kids for 5 miles). There are 4 communities near the 3 municipal primary schools. In the northern community, there are 240 students registered with the schools. In the east there are 120, the south has 400, and the west has 200 Each school has a limited capacity with school 1 being able to handle 360 students, school 2 being able to handle 400 students, and school 3 being able to handle 260 students. The distance between the community and the schools is shown in the table below: School-Community Distances School School 1 School 2 School 3 Community North East South West 2.0 3.0 1.4 3.2 3.2 2.4 2.0 2.0 3.6 1.4 3.0 2.2 a) If you are working for the school board (i.e. an employee of the municipality), what would you recommend be the allocation of students? b) Suppose the school board is concerned that a new housing project in the South will result in a number of new students. How many students could be added before there should be a concern regarding over crowding? c) Suppose instead you work for the bus company, what would your proposed allocation of students be? Why did it change
