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	48.8		Checking and savings	77.7
Auto loans	96.0		Certificates of deposit	99.7
Mortgages	152.8		​Long-term financing	98.4
Total Assets	297.6		Total liabilities	275.8
			​Owner's equity	21.8
			Total liabilities and equity	297.6

When you analyze the duration of​ loans, you find that the duration of the auto loans is 1.8 ​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 2.1

​years, and the​ long-term financing has a 9.6-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 $ 152.8 million to $ 101.9

​million, and increasing cash reserves to $ 99.7 million. What is the duration of​ Acorn's equity​ now? If interest rates are currently4 % 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