A bank has $850,000 in assets to allocate among investments in bonds, home mortgages, car loans,...

A bank has $850,000 in assets to allocate among investments in bonds, home mortgages, car loans, and personal loans. Bonds are expected to produce a return of 10%, mortgages 8.5%, car loans 9.5%, and personal loans 12.5% To make sure the portfolio is not too risky, the bank wants to restrict personal loans to no more than 30% of the total portfolio. The bank also wants to ensure that more money is invested in mortgages than in personal loans. It also wants to invest more in bonds than in personal loans.

A. Write out the Linear Program

B. Having written out the LP model for this problem with the objective of maximizing the expected return on the portfolio, find the solution with Solver.

Solutions

Expert Solution

A. What we are trying to maximzie is the overall returns, with given constraints. So, the linear program is.

Maximize 1.1b+1.085m+1.095c+1.125p,

where b=amount on bonds

m=amount on mortgages

c=amount on car loans

p=amount on personal loans.

Subject to constraints:

b+m+c+p<=$850000 (total amount invested cant exceed 850000)

p<=.3(b+m+c+p) (personal loan cant exceed 30% of total investment)

m>p (more money is invested in mortgages than in personal loans.)

b>p (invest more in bonds than in personal loans)

B. Now lets solve the problem in solver.

Lets first setup the problem in excel. This is shown below (formula view for better understanding).

The total invested amount is sum of all 4 individual amounts invested.

The retrn is simply the %return of each, summed. This is what we want to maximize.

Now lets go to solver. (Its available in Data tab. If its not there, go to File->Options->Add ins and enable it). Clicking on solver, we setup the problem the following way

We are maximizing B6 (total return) with constraints as defined. Clicking on Solve, we get the following results-

The maximum return is $937550, with 240000 in bonds, 255000 in mortgages and 255000 in personal loans.

Rahul Sunny answered 1 year ago

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