Question

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: $200,000 deposits (liabilities): $160,000 capital (net worth): $40,000 total: $200,000 total: $200,000 balance sheet of medes bank assets liabilities outstanding loans: $200,000 deposits (liabilities): $180,000 capital (net worth): $20,000 total: $200,000 total: $200,000 which bank has a lower leverage ratio? medes bank arch bank suppose both banks' assets increase by 10% to $220,000. assume that the liabilities of both banks remain the same. arch bank's capital increases by , 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 10% to $180,000. 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

Answer 1

Arch Bank has a lower leverage ratio compared to Medes Bank. In the second scenario, where the value of assets declines, Medes Bank is closer to insolvency due to its higher leverage ratio.

Step-by-step explanation:

The leverage ratio is a measure of a bank's capital adequacy and is calculated by dividing a bank's total assets by its capital. In the given scenario, Arch Bank's leverage ratio is $200,000/$40,000 = 5, and Medes Bank's leverage ratio is $200,000/$20,000 = 10. Therefore, Medes Bank has a higher leverage ratio compared to Arch Bank, indicating that Medes Bank is more leveraged.

When the assets of both banks increase by 10% to $220,000, the capital of Arch Bank increases by 10% of $40,000, which is $4,000, and the capital of Medes Bank increases by 10% of $20,000, which is $2,000.

Under the second scenario, where the assets decline by 10% to $180,000, the capital of Arch Bank decreases by 10% of $40,000, which is $4,000, and the capital of Medes Bank decreases by 10% of $20,000, which is $2,000. Therefore, in this scenario, both banks see a percentage decrease in capital, but Medes Bank, with its higher leverage ratio, is closer to insolvency.