$7.$ Leverage and insolvency$----$

Consider the following balance sheets of two banks. These two banks have equal amounts of assets but are leveraged differently. Assume that there is no regulatory capital requirement.

Balance Sheet of Arch Bank

Assets

Liabilities

Outstanding Loans: $$100,000$ Deposits $($Liabilities$)$: $$80,000$

Capital $($Net worth$)$: $$20,000$

Total: $$100,000$ Total: $$100,000$

Balance Sheet of Medes Bank

Assets

Liabilities

Outstanding Loans: $$100,000$ Deposits $($Liabilities$)$: $$95,000$

Capital $($Net worth$)$: $$5,000$

Total: $$100,000$ Total: $$100,000$

Which bank has a higher leverage ratio?

Medes Bank

Arch Bank

Suppose both banks' assets increase by $20\%$ to $$120,000.$ Assume that the liabilities of both banks remain the same. Arch Bank's capital increases by$20\%,$ and Medes Bank's capital increases by $.$ Therefore, if the value of assets is rising and liabilities do not change, a higher leverage ratio results in a percentage increase in capital.

Now suppose all the items in the balance sheets of both banks return to their initial values. Suddenly, banks realize that loans they made are riskier than they thought, and the total value of their assets declines by $5\%$ to $$95,000.$ Again, assume that the liabilities of both banks remain the same. Arch Bank's capital decreases by $,$ and Medes Bank's capital decreases by $.$ Therefore, if the value of assets is falling, a higher leverage ratio means a percentage decrease in capital.

Under this second scenario, which bank is closer to insolvency?

Medes Bank

Arch Bank