Question
19. You have been hired as a risk manager for Acorn Savings and Loan. Currently, Acorn's balance sheet is as follows (in millions of dollars):
19. You have been hired as a risk manager for Acorn Savings and Loan. Currently, Acorn's balance sheet is as follows (in millions of dollars):
Assets | Liabilities | |||
Cash reserves | 48.2 | Checking and savings | 77.6 | |
Auto loans | 108.2 | Certificates of deposit | 102.7 | |
Mortgages | 148.3 | Long-term financing | 105.0 | |
Total Assets | 304.7 | Total liabilities | 285.3 | |
Owner's equity | 19.4 | |||
Total liabilities and equity | 304.7 |
When you analyze the duration of loans, you find that the duration of the auto loans is 2.2 years, while the mortgages have a duration of 6.8 years. Both the cash reserves and the checking and savings accounts have a zero duration. The CDs have a duration of 1.9 years, and the long-term financing has a 9.2-year duration.
a. What is the duration of Acorn's equity?
b. Suppose Acorn experiences a rash of mortgage prepayments, reducing the size of the mortgage portfolio from $148.3 million to $98.9 million, and increasing cash reserves to $97.6
million.
What is the duration ofAcorn's equity now?
If interest rates are currently 4% and were to fall to 3%, estimate the approximate change in the value of Acorn's equity. (Assume interest rates are APRs based on monthly compounding.)
c. Suppose that after the prepayments in part (b), but before a change in interest rates, Acorn considers managing its risk by selling mortgages and/or buying 10-year Treasury STRIPS (zero coupon bonds).
How many should the firm buy or sell to eliminate its current interest rate risk?
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