let's consider what happens to a network of four banks, as illustrated in Figure 1. The...

    

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let's consider what happens to a network of four banks, as illustrated in Figure 1. The arrows represent exposures (holding other's securities). For instance, bank 2 is exposed to bank 1 (there is an arrow from bank 2 to bank 1), and that means bank 2's assets contain securities (debt or equity) issued by bank 1. Bank 1 Bank 4 Bank 2 Bank 3 Figure 1: Network of banks. Suppose every bank's balance sheet is of the following form: Assets Liability 20% in loans to other firms (1-1) fraction in debt Equity 80% in bank-issued securities fraction in equity Reminder: Assets = Liability + Equity That is, 80% of bank 2's assets are securities issued by bank 1, and the re- maining 20% are loans made to other firms (non-banks). This immediately implies that the health of bank 1 impacts bank 2. If bank 1 goes bankrupt, the securities (debt or equity) issued by bank 1 may go down in value, which will lead bank 2 to also suffer a loss in its assets, which may then trigger bank 2 to go bankrupt as well. Recall how investors are paid in bankruptcy: if a bank goes bankrupt, then its equity becomes worthless, and its debt holders get all remaining asset value with a possible "haircut". For instance, suppose a bank has leverage L = 10 (so equity is 1/L = 1/10 = 10% of total assets). Suppose the bank's asset value declines by 30%, so it goes bankrupt, its equity becomes worthless, and its debt is now worth 10% = as much as before. So the holders of the bank's equity suffer a loss of 100% (all lost!), and the holders of its debt suffer a proportional loss of 1 - = 22.2%. Suggestion: for all questions below, you don't need to think in dollar values, but only need to think about values in proportional terms e.g. loans are 20% of total asset value, in the balance sheet above. Now that we are done describing background information, let's go into the questions. In all questions below, your goal is to figure out what happens after (only) bank 1 suffers a negative shock: the value of bank 1's "loans to other firms" suddenly becomes zero. (The "bank-issued securities" on bank 1 balance sheet is not affected, and the "loans to other firms" held by other banks are also not affected.) Please answer the questions below. i. (1 point) How high can the leverage ratio L be so that bank 1 will not go bankrupt in response to this negative shock? ii. (2 points) Now suppose banks hold debt securities issued by other banks. Suppose all banks have a leverage ratio of L = 15. How many banks will go bankrupt? Please be specific in your answer - which banks are bankrupt and why. Support your answer with calculations. Hint: there could be a "chain reaction". When bank 1 gets the nega- tive shock, the value of its equity and its ability to pay back debt may be affected. That may impact the asset values of bank 2, because bank 2 holds securities issued by bank 1. And then that may impacts bank 3, and so on... iii. (2 points) Still assume that L = 15 for all banks. Now suppose banks hold equity securities issued by other banks. How many of the four banks will go bankrupt? iv. (1 point) What do you learn from the previous three questions? Please focus on how inter-bank relationships impact the likelihood of wide-spread bank failures. (There is no "absolutely correct" answer, even though there are "better" answers. You will receive full credit as long as you provide a thoughtful answer.) let's consider what happens to a network of four banks, as illustrated in Figure 1. The arrows represent exposures (holding other's securities). For instance, bank 2 is exposed to bank 1 (there is an arrow from bank 2 to bank 1), and that means bank 2's assets contain securities (debt or equity) issued by bank 1. Bank 1 Bank 4 Bank 2 Bank 3 Figure 1: Network of banks. Suppose every bank's balance sheet is of the following form: Assets Liability 20% in loans to other firms (1-1) fraction in debt Equity 80% in bank-issued securities fraction in equity Reminder: Assets = Liability + Equity That is, 80% of bank 2's assets are securities issued by bank 1, and the re- maining 20% are loans made to other firms (non-banks). This immediately implies that the health of bank 1 impacts bank 2. If bank 1 goes bankrupt, the securities (debt or equity) issued by bank 1 may go down in value, which will lead bank 2 to also suffer a loss in its assets, which may then trigger bank 2 to go bankrupt as well. Recall how investors are paid in bankruptcy: if a bank goes bankrupt, then its equity becomes worthless, and its debt holders get all remaining asset value with a possible "haircut". For instance, suppose a bank has leverage L = 10 (so equity is 1/L = 1/10 = 10% of total assets). Suppose the bank's asset value declines by 30%, so it goes bankrupt, its equity becomes worthless, and its debt is now worth 10% = as much as before. So the holders of the bank's equity suffer a loss of 100% (all lost!), and the holders of its debt suffer a proportional loss of 1 - = 22.2%. Suggestion: for all questions below, you don't need to think in dollar values, but only need to think about values in proportional terms e.g. loans are 20% of total asset value, in the balance sheet above. Now that we are done describing background information, let's go into the questions. In all questions below, your goal is to figure out what happens after (only) bank 1 suffers a negative shock: the value of bank 1's "loans to other firms" suddenly becomes zero. (The "bank-issued securities" on bank 1 balance sheet is not affected, and the "loans to other firms" held by other banks are also not affected.) Please answer the questions below. i. (1 point) How high can the leverage ratio L be so that bank 1 will not go bankrupt in response to this negative shock? ii. (2 points) Now suppose banks hold debt securities issued by other banks. Suppose all banks have a leverage ratio of L = 15. How many banks will go bankrupt? Please be specific in your answer - which banks are bankrupt and why. Support your answer with calculations. Hint: there could be a "chain reaction". When bank 1 gets the nega- tive shock, the value of its equity and its ability to pay back debt may be affected. That may impact the asset values of bank 2, because bank 2 holds securities issued by bank 1. And then that may impacts bank 3, and so on... iii. (2 points) Still assume that L = 15 for all banks. Now suppose banks hold equity securities issued by other banks. How many of the four banks will go bankrupt? iv. (1 point) What do you learn from the previous three questions? Please focus on how inter-bank relationships impact the likelihood of wide-spread bank failures. (There is no "absolutely correct" answer, even though there are "better" answers. You will receive full credit as long as you provide a thoughtful answer.)

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To address the questions in your screenshots we will need to follow the information provided in the description of the banks balance sheet and the relationships between the banks Lets take each questi... View the full answer