Reference no: EM133004278

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 48.9                    Checking and savings 82.1

Auto loans 101.3                   Certificates of deposit 102.7

Mortgages 152.5                        Long-term financing 96.5

Total Assets 302.7                       Total liabilities 281.3

Owner's equity 21.4              Total liabilities and equity 302.7

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 6.9 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 9.4-year duration.

Problem a. What is the duration of Acorn's equity The duration of the assets is how many years.

Problem b. Suppose Acorn experiences a rash of mortgage prepayments, reducing the size of the mortgage portfolio from $152.5 million to $101.7 million, and increasing cash reserves to $99.7 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. (Assume interest rates are APRs based on monthly compounding.)

Problem 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?