Bank A has a leverage ratio of 10, while Bank B has a leverage ratio of 20. Similar losses on bank loans at the two banks cause the value of their assets to fall by 7 percent. Which bank shows a larger change in bank capital? Does either bank remain solvent? Explain.

Answer 1

Bank A has a leverage ratio of 10, which means that its assets are 10 times its capital. If the value of the assets falls by 7%, it implies the value of bank A's assets declines by 0.07 * 10 * bank A's capital = 0.7 * bank A's capital.

Bank B has a leverage ratio of 20, which means that its assets are 20 times its capital. If the value of the assets falls by 7%, it implies the value of bank B's assets declines by 0.07 * 20 * bank B's capital = 1.4 * bank B's capital.

Since 1.4 (Bank B) > 0.7 (Bank A), Bank B shows a larger change in bank capital.

To determine if either bank remains solvent, we need to see if their capital is still positive after the decline in the value of their assets.

For Bank A:

New Capital = Old Capital - Change in Capital
New Capital = Old Capital - 0.7 * Old Capital
New Capital = 0.3 * Old Capital

Since the new capital (0.3 * Old Capital) is still positive, Bank A remains solvent.

For Bank B:

New Capital = Old Capital - Change in Capital
New Capital = Old Capital - 1.4 * Old Capital
New Capital = - 0.4 * Old Capital

Since the new capital (-0.4 * Old Capital) is negative, Bank B becomes insolvent.

In conclusion, Bank B shows a larger change in bank capital, and it becomes insolvent, whereas Bank A remains solvent.