Problem 6: (10 Points) An Investment Group wants to invest 500,000 in the follow

ID: 409978 • Letter: P

Question

Problem 6: (10 Points) An Investment Group wants to invest 500,000 in the follow ing option listed below with their associated risk and expected annura returns: OPTION RISK EXPE RETURN Stock- Insurance Stock- Industry Stock- Cement Bonds-Long Term Bonds-Short Tem Certificate of DepositCD High Moderate Low 158 12% 98 11% 8% The croup has decided on the following requirements for investment with an objective to generate as much annual zeturn as po8s 1be 1) Generate as much return as possible is written as the objective: Maximize 0.15x, 0.12x2 +0.o9x, 0.11x. 0.08x,0.06x the mathematical expression to reflect the following Groups requirements: e. 2) Invest all the $500,000. 3) Allocate at least S10- to be invested in the CD 4) At least 25% 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 108. Note: Let x, ropresents dollars invested in Option i

Explanation / Answer

Let following amounts ( in $) are being invested in various types of instruments :

Stock - Insurance

Stock – Industry

Stock – Cement

Bonds – Long term

Bonds – Short term

Certificate of deposit, CD

Following will be corresponding mathematical expressions :

Invest all $500,000

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

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

X6 > = 100,000

At least 25% of the funds invested in stocks are to be in low risk stock cement

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

0.75.X3 – 0.25.X1 – 0.25.X2 > = 0

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

( X4 + X5 ) > = ( X1 + X2 + X3), OR,

X4 + X5 – X1 – X2 – X3 = 0

No more than $125,000 is to be placed in options with expected annual returns of less than 10% ( remarks : such options are Stock – Cement, Bond – short term, Certificate of deposit )

X3 + X5 + X6 < = 125,000