Question

Problem 1: 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

Using excel solver

model: min(total investment)

constraints:

total investment<= 60,000

potential return>= 4000

portfolio guaranteed return = 2000

	Invested	Interest
CD	19047.62	1142.857143
VC	28571.43	857.1428571	2857.143
Total invested	47619.05
		Total Potential	4000
		Total Guaranted	2000

a) Req investments in CD and VC are provided in above table

b) For personal use he can keep = 60000-47619.05 = 12380.9

Problem 1-1: Forming new model in solver as per new conditions:

Guatanted portfolio value = Guatanted portfolio return + 60000

Final output is:

	Invested	Interest
		LL	UL
CD	0	0
VC	38834.91	1165.0474	3883.4913
Oil	21165.09	-21165.08655	21165.087
Total invested	60000
		Total Potential	25048.578
		Total Guaranted	-20000.04
		Guatanted portfolio value	39999.961

So, to max profit:

Invest as below:

CD	0
VC	38834.91
Oil	21165.09