Need all parts of question 2 answered. Only showing question 1 for context, but don't need question 1 answered. Leverage is defined as L=Assets/Equity (asset-to-equity ratio)

1. Question 1 (Fragility of the banking system). The goal is to understand the role of leverage and interconnectedness in creating fragility in widespread bank failures. This question will take significant time to solve. Please start early (a) First, consider a single bank. Suppose it has $10 million in sets and SE million in equity, so the remaining $(10 - E) is debt. Let's define leverage detined as L - 10/E (set-to-equity ratio). Asset values fluctuate. Suppose the value of the bank's asset next year has the following probability distribution Created with help and feedback frien Kached Nelse You may find beverage ratio defined in other ways, such as the bear/espuity ratio (rather than Requity ratio, as we do here). Ime those alternative definition For instance, there is a chance that the set value will be $7 millised period 1 57 Asset value million) Probability 5 89 20% $11 50% $13 20% 815 5% Recall from accounting if the bank's asset value goes up (down) by one dollar, its equity value will also go up (down) by one dollar. The bank will be bankrupt if its asset vahie is equal to or lower than debt value. Question: what is the probability that this bank will go bankrupt if it has a leverage of 10 to 1 (L. = 107? What if 5 to 1 (L=5)? Bank 1 Bank 2 Bank 4 Bank 3 Figure 1: Network of banks (1) Now let's consider what happens to an economy in which there are four bands, illustrated in Figure 1. The arrows representerposure. For instance, bank 2 is exposed to bank 1 (tlure is an arrow from bank 2 to bank 1), and that mentus bank 2's assets contain securities (debt or equity) isted by bank 1 Suppw each bank's balance sheet is of the following form: Assets Liability 20% in loans (1 - ) fraction in debt Equity 80% in bank-issued securitas fraction in equity For instance, sex of bank 2's sts are securities sued by tonk 1: sok of 2 bank 3'sts are securities isted by bank 2, and etc. (follow the arrows in Figure 1). The lontis held by different banks are all separate from each other. Throughout this question, you don't need to think in dollar values, but only need to think about valtoes in proportional terms (eg forts are 20% of total set value in the balance sheet above). Recall how investors are paid in bankruptcy: if a bank goes bankrupt, then its equity become worthless and its debt holders get all remaining et value with haircut". For instance, suppose L-10 (equity is 10% of total st), and uppe the value of a bank declines by 30%. Then, it goes bankrupt, and its city becomes worthless. Its debt is now worth = 3 is much as before. So the holders of its equity suffet a love of 100% (worthles now), and the holders of its debtsutler a proportional loss of 1-1 = 22.2% In all sub-questions below, we want to figure out what happens if bank 1 suffers a negative shock: the value of its louns suddenly becomes x (The bank-issted securities" on bunk 1 balance sheet is not affected, and the boats bekl by other banks are also not affected.) For simplicity, suppose all four banks have the same leverage ratio of L before the negative shocked happened. Please answer the questions below 1. How high can the leverage ratio L be for there to be no bankruptcy among will four banko in response to this entive shock il. Now suppose banks bold debe securities issued by other banks Sup pose 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 is a chain reaction" When bank I gets the negative shock the value of its equity and its ability to pay back debt may be affected. That will impact the act values of bank 2, because bank 2 holds securities bank 3's assets are securities issued by bank 2, and etc. (follow the arrons in Figure 1). The boats held by different banks are all separate from each other. Throughout this question, you don't need to think in dollar values, but only need to think about values in proportional terms (c.5. Boats are 20% of total asset value in the balance sheet above) 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 haircut". For instance, suppost L = 10 (so equity is 10% of total assets), and suppose the asset value of a butik declines by 30%. Then, it goes bankrupt, and its equity becomes worthless. Its debt is now worth 1 as much as before. So the holders of its equity suffer a loss of 100% (worthless Dow), and the holders of its debt suffer a proportional loss of 1-1 = 22.2%. In all sub-questions below, we want to figure out what happens if bank 1 suffers a negative shock: the value of its loans suddenly becomes to. (The "bank-issued securities on bank 1 balance sheet is not affected, and the loans held by other banks are also not affected.) For simplicity, suppose all four banks have the same leverage ratio of L before the negative shocked happened. Please answer the questions below 1. How high can the leverage ratio L be for there to be no bankruptcy among all four banks in response to this negative shock? II. Now suppose banks hold debe securities issued by other banks! Sup- pose 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 is a "chain reaction". When bank I gets the negative shock, the value of its equity and its ability to pay back debt may be affected. That will impact the asset values of bank 2, because bank 2 holds securities issued bw bank 1. And then that impacts bank 3, and so on. ii. Still assume that L - 15 for all banks. Now suppose banks hold equity securities issued lw other banks. How many banks will go bankrupt? iv. What do you loarn from the previous three questions? Please focus on how inter-bank relationships impact the likelihood of widespread 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.) That is, even bank I does not go bankrupt. Thes, 80% of batik 2's assets are debt isted by bank 1: 80% of bank 3's sets are diebt Esed by bank 2. etc. 3