Question - 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 49.9 Checking and savings 81.5
Auto loans 103.6 Certificates of deposit 101.4
Mortgages 150.8 Long-term financing 100.2
Total Assets 304.3 Total liabilities 283.1
Owner's equity 21.2
Total liabilities and equity 304.3
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 6.9 years. Both the cash reserves and the checking and savings accounts have a zero duration. The CDs have a duration of 1.8 years, and the long-term financing has a 10.3-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 $ 150.8 million to $ 100.5 million, and increasing cash reserves to $ 100.2 million. What is the duration of Acorn'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?