### 2008 Crisis Overview Question

Chapter 13 Recommended Exercise Solution
Problem No. 4: Systematic Risk - Consider the following balance sheets for two hypothetical financial institutions, bank B and bank C:

 Bank BAssets Liabilities Cash 1,000 Deposits 1,400 Loans to Bank C 500 Total Liabilities 1,400 Total Assets 1,500 Equity (Net Worth) 100

 Bank CAssets Liabilities Mortgage Back Securities 800 DepositsLoans from bank B 200500 Total Liabilities 700 Total Assets 800 Equity (Net Worth) 100

(a) Fill in the missing entries in the balance sheets

Solutions in italics & bold above.

Total assets is the sum of all assets, total liabilities is the sum of all liabilities. And equity (net worth) is just (Total Assets) – (Total Liabilities).

(b) What is the leverage ratio in each bank?

The leverage ratio (defined in the book) is the following:

 For bank B: For bank C:

Bank B has higher leverage.

.
(c) Suppose housing prices fall sharply and the mortgage-backed securities held by bank C
fall in value to only \$500. What happens to bank C's net worth?

Bank C's net worth decreases from 500 to 700, a decrease in total assets of 200.
Bank C’s New Worth is now; 500-700 = -200 (it’s insolvent)

Bank C’s new balance sheet, bold-italics reflect changes.
 Bank CAssets Liabilities Mortgage Back Securities 500 DepositsLoans from bank B 200500 Total Liabilities 700 Total Assets 500 Equity (Net Worth) -200 (insolvent)

(d) The short-fall in bank C's equity means that it cannot repay the loans it received from
bank B. Assume bank C pays back as much as it can, while still making good on its deposits.
What happens to the net worth of bank B?

Bank C is insolvent, they have assets worth 500 but owe in liabilities to others a total of 700.
We are asked to assume that the bank pays depositors. Paying off the 200 of the depositors leaves only 300 to repay Bank B.

Turning to Bank B, the value of their “Loan to Bank C” drops from 500 to 300 (since they can only expect to ever see 300 with C insolvent). This change decreases B’s Total Assets from 1,500 to 1,300. The change also reduces Bank B’s equity to -100 (insolvent).

 Bank BAssets Liabilities Cash 1,000 Deposits 1,400 Loans to Bank C 300 Total Liabilities 1,400 Total Assets 1,300 Equity (Net Worth) -100 (insolvent)

(e) Discuss briefly how this is related to systematic risk.

One might think of this problem as an example of systemic risk in the financial market. A housing crisis occurred, hitting one bank’s balance sheet & pushing it into insolvency. Because of their interbank loans, Bank B was also negatively affected by this crisis.

Bank B didn’t make any loans to the housing industry, and so in a sense appeared to be insulated from the crisis in that market. But because of the loan it made to Bank C – which was exposed to the crisis – Bank B was pulled into the crisis and into insolvency.

Imagine an economy with thousands of banks connected to each others’ balance sheets. similar to what we see in this problem. With some shock big enough to significantly harm asset values in some interconnected banks (like Bank C), that shock in asset values will cascade to other banks that have made loans to the initially shocked banks, decreasing their asset values and worsening their net worth. That may then cascade to many other banks far from the epicenter.

Thus, with a set-up like this, a shock to a few banks can spread throughout the economy through deteriorating bank balance sheets. If the shock is great enough and banks are significantly interconnected, it is possible for many banks to become essentially insolvent, even if they are only distantly connected to the original shock.