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 50.5 Checking and savings 82.8 Auto loans 104.6 Certificates of deposit 101.7 Mortgages 148.7 ?Long-term financing 100.1 Total Assets 303.8 Total liabilities 284.6 ?Owner's equity 19.2 Total liabilities and equity 303.8 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 7.1 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 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 $ 148.7 million to $ 99.1 ?million, and increasing cash reserves to $ 100.1 million.
What is the duration of? Acorn's equity? now? what is the duration of assets in years? what is the duration of equity in years?
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?