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 49.8 Checking and savings 79.5 Auto loans 98.1 Certificates of deposit 101.3 Mortgages 147.2 ​Long-term financing 94.8 Total Assets 295.1 Total liabilities 275.6 ​Owner's equity 19.5 Total liabilities and equity 295.1 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 7.1 years. Both the cash reserves and the checking and savings accounts have a zero duration. The CDs have a duration of 2.2 ​years, and the​ long-term financing has a 9.5​-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 $ 147.2 million to $ 98.1 ​million, and increasing cash reserves to $ 98.9 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?

Answer 1

Solution:

a. Asset duration = 49.8/295.1 (0) + 98.1/295.1 (2.1) + 147.2/295.1 (7.1)

Asset duration = 4.24 years

Liability Duration = 79.5/275.6 (0) + 101.3/275.6 (2.2) + 94.8/275.6 (9.5)

Liability Duration = 4.08 years

Equity duration = 295.1/19.5 (4.24) - 275.6/19.5 (4.08)

Equity duration = 6.50 years

b. Asset duration = 148.7/344.9 (0) + 98.1/344.9 (2.1) + 98.1/344.9 (7.1)

Asset duration = 2.62 years

Equity duration = 344.9/19.5 (2.62) - 275.6/19.5 (4.08)

Equity duration = -11.32 years

Therefore, if interest rates drop by 1%, we would expect the value of Acorn’s equity to drop by about 11%

c. Acorn would like to increase the duration of its assets, so it should use cash to buy long-term bonds.

Amount = (11 years x 19.5)/10

Amount = 21.45

We should buy $21.45 million worth of 10-year STRIPS.