Suppose a $$400$ million bank has an average asset duration of $3$ years and an average liability duration of $1$ year. The bank also has a total debt ratio of $80\%.R$ is $10\%$ and the bank is expecting a $50$ basis point increase in interest rates. The Fl can enter into a swap where the duration of the fixed rate payments is $5$ years and the duration of the variable rate payments is $2$ years. What is the optimal notional principle of the swap that immunizes the equity value? Does the FI make or receive the fixed rate payments?

Multiple Choice

$$293\mathrm{.}33$ million

$$145\mathrm{.}67$ million

$$200$ million

$$300$ million