Assign Case 2 draft 3

Assign Case #2
Problem 7-37 (Bhavika Investments)
Bhavika Investments, a group of financial advisors and retirement planners, has been requested to provide advice4 on how to invest $200,000 for one of its clients. The client has stipulated that the money must be put into either a stock fund of a money market fund, and the annual return should be at least $14,000. Other conditions related to risk have also been specified, and the following linear program was developed to help with this investment decision:
Minimize risk
=
12S + 5M

Subject to

S + M
=
200,000
Total investment is $200,000 0.10S + 0.05M
≥
14,000
Return must be at least $14,000 M
≥
40,000
At least $40,000 must be in money market fund S, M
≥
0

where S
=
dollars invested in stock fund M
=
dollars invested in money market fund
The QM for Windows output is shown below.

(a) How much money should be invested in the money market fund and the stock fund? What is the total risk?
Answer Money market fund = $120,000
Stock fund = $80,000
Total risk = $1,560,000

(b) What is the total return? What rate of return is this?
Answer
Total return
=
0.10(80,000) + 0.05(120,000)

=
14,000

Rate of return
=

=
7%

(c) Would the solution change if risk measure for each dollar in the stock fund were 14 instead of 12?
Answer
Total risk จะเปลี่ยนไป โดยที่สัดส่วนการลงทุนไม่มีการเปลี่ยนแปลง
New risk
=
14(80,000) + 5(120,000)

=
1,720,000

increase
=
1,720,000 – 1,560,000

=
160,000

(d) For each additional dollar that is available, how much does the risk change?
Answer เนื่องจากสมการ total investment เป็น binding constraint ดังนั้น เมื่อพิจารณาจาก dual price จะพบว่า ถ้าการเพิ่มขึ้นของเงินลงทุนไม่เกิน $280,000 à ความเสี่ยงจะเพิ่มขึ้น 2 หน่วย ทุกๆ การเพิ่มขึ้นของการลงทุน $1

(e) Would the solution change if the amount that must be invested in the money market fund were changed from $40,000 to $50,000? Answer เนื่องจาก อสมการ investment in the money market fund เป็น