Question

G. Rifkin is considering investing some or all of a $60,000 inheritance. He looks at a one year cirtificate of deposit paying 6%, and/or a venture capital group project with a guaranteed 3% return but the potential of earning 10%. Mr. Rifkin woul like to invest the minimum amount of money neccessary to achieve the following
(i) An over all portfolio potential return of at least $4000. Note: The CD's guarantteed return is also its potential.
(ii) An over all portfolio guaranteed return of $2000.
a. Formulate a LP model and recommend an investment strategy (how much to invest in each investment).
b. How much can Rifkin keep for personal use?
Problem 1-1: Rifkin has decided to invest all his inheritance. Therefore, in addition to the two invetments mentioned above, he now looks also at an oil exploration investment. The return could be potentially 100% but he might also lose all his money. Therefore he set up risk protection conditions as follows:
(i) At most $30K will be nvested in oil.
(ii) At least $20K will be invested in CD.
(iii) The portfolio value must have a guarantteed value of at least $40K at the end of the year.
How can Rifkin maximize the potential return of his portfolio?

Answer 1

Answer:

The answer is developed below.

Explanation:

1)a) Let A be investment in CD and B be investment in VC

LP Conditions:

A * 6% + B* 3% >=2000

A * 6% + B* 10% >=4000

A+B<=60000

Minimize(A+B)

Result of solving LP:

A= 19047.62

B= 28571.43

Total investment= 47619.05

b) Total money left for personal use = 12380.95

2) Let A be investment in CD and B be investment in VC and C be investment in Oil Exploration

LP Conditions:

60000 - (A*6% + B*3% - C)>=40000

C<=30000

A>=20000

A+B+C=60000

Maximize(A*6%+B*10%+C*100%)

Solving we get:

A=20000

B=18252.43

C=21747.57