kindly answer all parts of this question. thanks Problem 6: (10 Points) tGroup w

Question

kindly answer all parts of this question. thanks

Problem 6: (10 Points) tGroup wants to invest $500,000 in the following optiona listed below with their associated risk and expected annua returns: OPTION RISK EXPECTEDANNUAL RETURN Stock- Insurance Stock- Industry Stock- Cement Bonds-Long Term Bonds-Short Term Certificate of Deposit CD 15t 128 94 115 8% High Moderate Low The G he Group has decided on the following requirements for investment with an objective to generate as much annual return as po5sb1e ollowing 1) Generate as much return as possible is written as the f objective: 0.06x Maximize o. 15x, + 0.12x0.o9x0.11x 0x write the mathematical expression to retlect the following Group' requirements: 2) Invest all the 5,00 3) Allocate at least $100,000 to be invested in the co 4) At least 25s of the funds invested in stocks are to be in the Low-Risk stock (Cement. 5) At least as much is to be invested in Bond as stocks 6) No more than $125,000 is to be placed in Options with Expected Annual Returns of less than 10%. Noto: Let x ropresents dollars inveated in option i

Explanation / Answer

Answer to question b2:

By choosing above option as stated in question b1, we will lose = $145.52 - $128.81 = $16.71

Let the investments in various instruments as follows :

Stock – Insurance = $ X1

Stock – Industry = $X2

Stock – Cement = X3

Bonds – Long term =$ X4

Bonds – Short term = $ X5

Certificate of deposit ( CD) = $X6

With,

X1,X2,X3,X4,X5.X6 > = 0

With expected returns mentioned.

Objective function will be to maximize profit :

                Thus , Z ( Objective function) = Maximize 0.15.X1 + 0.12.X2 + 0.9.X3 + 0.11.X4 + 0.8 X5 + 0.6X6

Constraints:

Since full amount of $500,000 has to be invested.

Therefore , Total investment :

X1 + X2 + X3 + X4 + X5 + X6 = $500,000

Allocate at least $100,000 to be invested in CD

OR, X6 >= 100,000

III) At least 25 percent of funds invested in stocks should be in low risk stock cement

Therefore ,

X3 > = 0.25 x ( X1 + X2 + X3 )

Or, 0.75.X3 – 0.25.X1 – 0.25.X2 > = 0

IV) At least as much is to be invested in bonds as stocks

Total investment in stocks = X1 + X2 + X3

Total investment in bonds = X4 + X5

Therefore ,

X1 + X2 + X3 > = X4 + X5

Or, X1 + X2 + X3 – X4 – X5 >= 0

v) Options with expected annual return of 10% or less = X3. X5. X6

Since no more than $125,000 is to be invested in these 3 instruments cumulatively

X3 + X5 + X6 < = $125,000

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