5187 01572> Week 8 Moodle Quiz: Week 8 Question 1 Not yet answered Marked out of
ID: 2815664 • Letter: 5
Question
5187 01572> Week 8 Moodle Quiz: Week 8 Question 1 Not yet answered Marked out of 10.00 Consider a mortgage team with $100,000,000 to finance various investments. There are five categories of loans, each with an associated return and risk. The goal for the mortgage team is to allocate the money to the categories so as to maximize the return per dollar. Find the maximum return per dollar subject to the following conditions 1. Have a weighted average risk of investments no more than 1 2. Invest at least 20% in government securities 3. The amount in second mortgages and personal loans combined should be no higher than the amount in first mortgages Flag question Item No Loan/ Investment First Mortgages Second Mortgages Personal Loans Government Securities8 Commercial Loans Return (%) 15 12 15 Risk 0.8 0.9 16 AnswerExplanation / Answer
1
$ 20 mn will be invested in Government securities so balance $ 80 mn has to be invested in such a way that weighted average risk is no greater than 1
By hit and trial we can work out the proportion of investments in different options as below
Government security $ 20 mn @ 8% gives return $ 1.6/dollar
Second Mortgage $ 30 mn @ 12% gives return $ 3.6/dollar
Personal Loan - we make no investment
First Mortgage $ 30 mn @ 15% gives return $ 4.5/ dollar
Commercial Loan $ 20 mn @ 16% gives return $ 3.2/ dollar
Total return of portfolio = 1.6 + 3.6 + 4.5 + 3.2 = $ 12.9 for every dollar of investment
Total risk of portfolio = (20% * 0.9) + (30% * 1) + (30% * 0.8) + (0% * 1.1) + (20% * 1.4)
= 0.18 + 0.30 + 0.24 + 0.00 + 0.28 = 1
2
Commercial Loans will provide the maximum return per dollar if entire amount of $ 100 mn is invested @ 16% if all risk prefernces are ignored - the return will be $16 for every $1 dollar invested.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.