Assignment_2-RMFM-2023

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University of Toronto *

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432

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Jan 9, 2024

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Assignment 2 RSM432: Risk Management for Financial Managers November 29, 2023 The assignment questions are to be completed in groups of two. Do not share your work with students from other groups. Only original work done by your group members is to be submitted. Plagiarism will not be tolerated. The assignment will be marked based on (1) How you arrive at the solution, (2) Is the solution logical, consistent with the materials taught in class? (3) The presentation of your results. Remember, you must present your work in a clear and concise manner. How you communicate your work visually and verbally matters. You are required to submit a spreadsheet with your calculations for the numerical questions and a separate document with the answer for the conceptual questions and where you show the key steps involved to get the solution of the numerical questions. Assignment due : Saturday December 9th by 11:59 pm (EST). Question 1 (15 points) The value of a company’s equity is $5 million and the volatility of the equity is 50%. The debt that will have to be paid in three years is $12 million. The risk-free interest rate is 3% per annum. 1. What is the difference between risk-neutral versus real-world probabilities? When should you use each of them? 2. Use Merton’s model to estimate the probability of a default on the debt in the next three years. 3. What is the market value of debt? what is the debt’s expected loss from default? Question 2 (10 points) Consider following transactions with the same counterparty 1. 5 year foreign exchange forward (a) Principal 500 1
(b) Current Value -20 2. 3 year option on stock (a) Principal 800 (b) Current Value -55 3. 4 year interest rate swap. (a) Principal 800 (b) Current Value 90 Under Basel I, what is RWA WITH and WITHOUT netting if counterparty is a corporation? How much capital has to be set aside? Question 3 (15 points) Sigma company, a Ba-rated company, has a market credit spread of 240 basis points on a 5-year bond. The recovery rate is 50%. Calculate: 1. The average hazard rate per year over 5 years using the data from table 19.1. 2. The average hazard rate per year over 5 years using credit spreads. 3. What is the expected risk premium earned by bond traders 4. What factors can help to explain the magnitude of the expected risk premium calculated in part c. 5. Assume next that the bond provides a coupon of 5% per year paid semi annually, has a yield of 6% (with continuous compounding) and the risk free yield is flat at 3%(with continuous com- pounding). Assume that default occurs at the end of the year (right before coupon payments). Estimate the default probability assuming that it is the same each year. Question 4 (10 points) JP Rotman Bank’s balance sheet (in billions USD) is shown below. Under Basel III requirements, bank management must ensure that the Net Stability Funding Ratio (NSFR) exceeds the minimum threshold. 2
Cash 5 Retail Deposits (Stable) 10 Treasury Bonds ( > 1 yr) x Retail Deposits (Less Stable) 10 Corporate Bonds rated A y Wholesale Deposits 60 Mortgages z Preferred Stock ( > 1 year) 5 Small Business Loans ( < 1 yr) 40 Tier 2 Capital 5 Fixed Assets 20 Tier 1 Capital 10 1. What is the NSFR for JP Rotman when x = 5 , y = 10 , z = 20? 2. Suppose that treasuries have a return of 3%, Corporate Bonds (rated A) a return of 5%, and mortgages a return of 7%. Find the values of x, y, z that maximize returns subject to the NSFR requirement. Question 5 (25 points) Suppose that you are in charge of the investment strategy at Rotman Dominion. There are three types of assets, offering different returns. A 1 returns a 2% in any state of the economy. A 2 loans are risky, they return a 15% with probability 0.8 and -30% with probability 0.2 (i.e., if you invest a dollar in asset A 2 , it pays $1.15 w.p. 0.8 and $0.7 w.p. 0.2 ). A 3 loans are riskiest, they return a 40% with probability 0.6 and -47% with probability 0.4. On the liability side, the bank has $100 MM in debt and $10 MM in Equity. 1. In the absence of any regulation, find what would be the best investment strategy (i.e., what are the values of A 1 , A 2 , and A 3 ) from the point of view of shareholders? 2. What is the best investment strategy from the point of view of debt holders? 3. (Basel I) What would be the best investment strategy (for shareholders) assuming that the bank needs to comply with E/ ( A 2 + A 3) 0 . 08? Comment on the efficacy of such a regulation. 4. (Basel II) What would be the best investment strategy (for shareholders) assuming that the bank needs to comply with E/ ( A 2 + 1 . 5 × A 3) 0 . 08? Comment on the efficacy of such a regulation . 5. Ignoring the potential externalities from default, what is the efficient investment strategy? What risk weights ω 1 ω 2 ω 3 would you choose (if any) to implement it? 6. Suppose that the regulator is willing to accept a maximal probability of default of 8%. What is the constrained-efficient investment strategy? 3
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Question 6 (10 points) The assets of a bank consist of $300 million of loans to A-rated corporations with the principals being repayable at maturity. The Probability of Default for the corporation is estimated as 0.4% per year. The loan maturities are three years and the LGD is 45%. 1. What is the total risk-weighted assets for credit risk under the Basel II advanced IRB approach? 2. How much Tier 1 and Tier 2 capital is required? 3. How does this compare with the capital required under the Basel II standardized approach and under Basel I? 4. How much equity capital (including that for the capital conservation buffer) will be required under Basel III if the advanced IRB approach is used. Question 7 (15 points) 1. Explain the concept of wrong way risk and provide two examples of it. 2. What is the relationship between bond yield, risk free rate, and CDS spreads. Carefully explain why the identity should hold? 3. Name 4 reasons that contributed to trigger the Global Financial Crisis (GFC). 4. Provide 4 examples of how to prevent a run from a financial institution identifying the difficul- ties or costs associated with each of them. 5. Explain the benefits and costs of disclosing information to mitigate run risk. 4