An FI is planning the purchase of a $4 million loan to raise the average duratio
ID: 2718660 • Letter: A
Question
An FI is planning the purchase of a $4 million loan to raise the average duration of its assets from 3.5 to 5.0 years. The FI currently has total assets worth $20 million, with $4 million in cash (duration of zero) and $16 million in loans.
A) Assuming the bank uses the cash to purchase the loan, should the bank purchase the loan if its duration is 8 years?
B) What duration loan should the FI purchase to obtain an asset duration of 5?
An FI is planning the purchase of a $4 million loan to raise the average duration of its assets from 3.5 to 5.0 years. The FI currently has total assets worth $20 million, with $4 million in cash (duration of zero) and $16 million in loans.
A) Assuming the bank uses the cash to purchase the loan, should the bank purchase the loan if its duration is 8 years?
B) What duration loan should the FI purchase to obtain an asset duration of 5?
Explanation / Answer
Amount of Loans = $ 16 Million
Amount of Cash = $ Million
Total Value of assets = $ 16 Million + $ 4 Million = $ 20 Million
Given the duration of the total portfolio = 3.5 years
Duration of Cash = 0
Duration of Loan assets = X (say)
Weight of cash in total portfolio = $ 4 Million / $ 20 Million = 0.20
Weight of loans in total portfolio = $ 16 Million / $ 20 Million = 0.80
Duration of portfolio = weight of cash * duration of cash + weight of loans * duration of debt
3.5 = 0.2 * 0 + 0.8 * X
3.5 = 0.8 *X ==> X = 3.5/0.8 = 4.375 years
Answer (A)
If Bank uses $ Million cash available to purchase a loan with duration 8 years.
Portfolio duration = 0.20 * 8 + 0.8 * 4.375
Portfolio duration = 1.6 years + 3.5 years
= 5.1 years
As the target duration is 5 years and the portfolio duration by purchasing a loan with duration the total duration will be 5.1 years, the loan should not be purchased.
Answer (B)
Target duration = 5 years
Let duration of loan purchased is X
Target Portfolio duration = 0.2 * duration of loan to be purchased + 0.8 * duration of existing loans
5 = 0.2 * X + 0.8 * 4.375
5 = 0.2 * X + 3.5
0.2 * X = 5 – 3.5
0.2 * X = 1.5
X = 1.5/0.2 = 7.5 years
The Bank should purchase a loan with duration of 7.5 years with the cash available to achieve the target duration of 5 years
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