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):

When you analyze the duration of loans, you find that the duration of the auto loans is 2.1 years, while the mortgages have a duration of 7.2 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 $151.3 million to $100.9 million, and increasing cash reserves to $101.7 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.

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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Assets Cash Reserves Auto Loans Mortgages Total Assets 51.3 98.1 151.3 300.7 Liabilities Checking and Savings Certificates of Deposit Long-Term Financing Total Liabilities Owner's Equity Total Liabilities and Equity 79.8 100.2 99.4 279.4 21.3 300.7