You have been hired as a risk manager for Acorn Savings and Loan. $$Currently$,$ Acorn$\text{'}$s balance sheet is as follows$($in millions of$$ dollars$)$: LOADING....

When you analyze the duration of$$ loans, you find that the duration of the auto loans is $1\mathrm{.}9$years$,$ while the mortgages have a duration of $6\mathrm{.}9$ years. Both the cash reserves and the checking and savings accounts have a zero duration. The CDs have a duration of $1\mathrm{.}9$years$,$ and the$$ long$-$term financing has a $9\mathrm{.}4-$year duration.

a$.$ What is the duration of Acorn$\text{'}$s $$equity$?$

b$.$ Suppose Acorn experiences a rash of mortgage$$ prepayments, reducing the size of the mortgage portfolio from $ $151\mathrm{.}1$ million to $ $100\mathrm{.}7$million$,$ and increasing cash reserves to $ $100\mathrm{.}0$ million. What is the duration of Acorn$\text{'}$s equity$$ now? If interest rates are currently $4\%$ and were to fall to $3\%,$ estimate the approximate change in the value of Acorn$\text{'}$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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