Final Exam: Econ/FM 9587
Instructor: Jim MacGee and Matt Davison and Nazmul Ahsan Monday, December 10, 2018 9:30-11:30
Name: Student I.D.
Instructions
1. This is an closed book exam: you are not permitted to refer to any textbooks, notes or papers/manuscripts or to communicate with any living entity while writing the exam – doing so during the writing of this exam will be regarded as academic dishonesty.
2. There are a total of 100 points on this exam, plus 2-bonus points. The value of each question is given below. The exam is worth 25 percent of your final grade in this class.
3. There are 7 pages in this exam (including the instructions page).
4. Please write your answers legibly. Be sure to write your name and
student I.D. number on the file you submit.
5. You have two hours (122 minutes).
6. Good Luck!
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1. Bonus Question (2 pts) In your opinion, what is one (ideally the most important) change that could be implemented to improve this course.
2. (5 pts) What is “risk” from the point of view of risk management? How does the responsibility of risk managers to ”manage” risk differ from that of managers?
3. (5 pts) Briefly explain the difference between market risk, credit risk and operational risk. Provide an example of each type of risk for an bank such as Canada Western Bank.
4. (5 pts) Describe the risk culture of a firm? Why is it important? How can you tell if a firm has good risk culture?
5. (10 pts) You are working as a risk manager at an international prop- erty investment firm. One morning the CIO asks you to evaluate a proposed purchase of a commercial tower in the ”other London” (i.e., London, England). The proposed deal sees the purchase financed by borrowing in Canadian dollars at a fixed rate (the prime rate of a Big 5 Canadian bank minus 25 basis points) for a fifteen year term. Rents in the tower are denominated in (British) pounds, and are indexed to the U.K. consumer price. The tenants in the tower also have a clause in their lease agreement that they can terminate their lease with 60 days notice without any penalty at any time over the next fifteen years.
(a) Briefly outline (and explain) the main ”risk factors” that would need to be evaluated as part of your assessment of the risks asso- ciated with this project.
(b) Outline how you would quantitatively go about the risk assess- ment. You should specify the data you would use in your analysis, as well as the quantitative techniques and any scenarios. [Note: This question does not require you to do any calculations – in- stead, outline the calculations you would undertake]. Be sure to briefly explain how your approach would help quantify the main risk factors associated with this deal.
6. (10 pts) What is a risk management failure? Briefly provide two types of risk management failures, and outline a possible way to deal with each type of failure.
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7. (13 pts) Consider two different investments, each worth $ 100 million. Suppose each of two investments has two possible outcomes: (1) 99.1% chance of a gain of $ 50 million and (2) 0.9% chance of a loss of $ 90 million. Further, the investments are independent of each other.
(a) What is the VaR for one of the investments when the confidence level is 99%?
(b) What is the expected shortfall for one of the investments when the confidence level is 99%?
(c) What is the VaR for a portfolio consisting of the two investments when the confidence level is 99%?
(d) What is the expected shortfall for a portfolio consisting of the two investments when the confidence level is 99%?
(e) Show that in this example VaR does not satisfy the subadditivity condition, whereas expected shortfall does.
8. (12 pts) Consider two stocks. The first has price today of $10, volatility of 20% (in annual units), and an expected return of 0%. The second has price today of $100, volatility of 10% (in annual units), and also has an expected return of 0%. The correlation between the two stock returns is 0.5.
(a) Suppose $1 Million is invested, half in the first stock, the other half in the second stock. Assuming normal returns for both stocks, what is the 95% 5 day VaR of this portfolio?
(b) After reading Taleb, your boss meets you to express his concern that the distribution of stock returns may differ from a normal distribution due to being ”fat tailed”. What impact would this have on the estimates you made in (a)?
(c) Suggest a model that deals with fat tail distribution of returns. Is it possible to model returns (which has a fat tail distribution) with conditional normality? Why or why not?
9. (20 pts) A credit union funds itself using $1 MM capital provided by its members and $9MM in short term deposits. It uses these deposits to lend $10MM in 5 year mortgages. It pays only 100 bps on the deposits
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but lends the mortgages at 3.5%. The credit union must pay two tellers earning $40,000 and a manager/book-keeper earning $60,000, as well as incur other expenses of $20,000 The mortgages are all low loan-to-value, with at least 25% downpayment required.
(a) How much money does the credit union bring in every year? Is it enough to cover its fixed expenses?
(b) Describe the risks inherent in running this credit union.
(c) If the bank could borrow money by issuing 2.25% GICs rather than by using demand deposits, how much should they fund in this way? Be quantitative about the risks and rewards of this strategy.
10. (10 pts) You have recently joined a retail credit risk management team. After looking at some historical data, your coworkers have concluded that loan applicants (for the 1 year loan your group offers) can be grouped into three types:
• No-risk borrowers: who are certain to repay their loans (i.e., their default probability is zero)
• Moderate Risk Borrowers: these borrowers will default on average 6 percent of the time
• High Risk Borrowers: who are certain to default on their loans
Your data indicates that a 40 % of loan applicants are no risk types, 40 % are moderate risk types and 20 % are high risk types. If a borrower defaults, the recovery rate is 0 (i.e., LGD is 100%).
You have been told that the internal charge for one dollar of funds in 5%. However, since your group is small compared to the rest of the bank, you can treat this supply of funds as perfectly elastic (i.e., you can access as much funds to lend out as you wish – so long as you can make a case that lending is profitable.
The interest rate on the one-year loan your group offers is fixed as r = 10%. This is a simple loan, where a face value of $X is borrowed today, in exchange for repaying $X(1+r) in one year.
All applicants report a single credit score. The high risk applicants report credit scores uniformly distributed on the interval [a,b], the mid- dle risk applicants are uniformly distributed on [c,d] and the no risk
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borrowers credit scores are uniformly distributed on the interval [e,f]. a < b, c < d, e < f . Your analytical team reports that reaosnable value of these parameters are a = 100,b = 300,c = 200,d = 400,e = 300, f = 600. (a) Sketch the distribution of credit scores across all applicants. (b) What cutoff score will maximize profit? (If more than one score will maximize profits, give the range). If you use this cut-off, what fraction of loans will repay (be ”good”)? What is your profit per dollar lent on a ”book” of such loans? (c) You are contacted by the retail lending group head, who tells you that if you decline a customer this year, they will never apply again. However, any customers who you accept (and who do not default) will borrow again the following year with probability 0.5. She asks you to work out what the profit maximizing cut-off would be if you took a two year perspective, where you assume that after one year you can drop customers who default from your pool (i.e., if a borrower defaults in year 1, you will not lend to them again). 11. (10 pts) Read the following article from The Economist of Dec 7th 2017. Briefly summarize what the article claims are the key changes to the Basel regulations that are part of ”Basel IV”. Briefly argue whether these regulations create incentives for banks to substitute from very low risk assets towards moderately riskier assets (inside a fixed asset class such as mortgages or business loans? EIGHT years ago, bank supervisors began overhauling the global cap- ital standards that proved too flimsy to withstand the financial storm of 2007-08. Their work is at last done. On December 7th Mario Draghi (pictured), the president of the European Central Bank, who heads the committee of supervisors that approves the standards, declared that agreement had been reached on a thorny set of revisions to Basel 3, as the post-crisis rules are known. Banks, already obliged by Basel 3 and national supervisors to add lots of equity to their balance-sheets, have moaned about further fiddling. They, analysts and many commentators often call these revisions Basel 4. Basel 3 uses several gauges of banks ability to survive catastrophes that 5 sweep away equity and drain liquidity. Perhaps most closely watched is the CET1 ratio, of common equity to risk-weighted assets (RWAs). Most banks calculate RWAs using a standardised method, itself revised as part of Basel 4. But big ones often use their own internal models. The snag is that internal models vary: if one bank uses lower risk- weights than another with an identical balance-sheet, its RWAs will be lower, allowing it to hold less shock-absorbing equity to achieve a given CET1 ratio. So Basels standard-setters have been trying to narrow the variation by limiting the use of internal models and setting a floor for the minimum ratio of RWAs calculated from internal models to that from the standardised approach. Because European banks tend to hold a lot of safe-ish assets with low risk-weights, such as mortgages and corporate loans, they argued for a low floor, or even none. Low weights, they said, reflected their sober business models; their supervisors and politicians backed them up. American banks have fewer such loans. They often sell on housing loans to Fannie Mae and Freddie Mac, two government-owned giants, and their corporate clients often sell bonds rather than borrow from banks. American banks and officials wanted a higher floorarguing that without it the use of internal models gave the Europeans an unfair, even unsafe, advantage. A first draft of the revised standards proposed a floor for RWAs of between 60% and 90% of the answer from the standardised model. For the past year officials have been haggling over numbers in the middle of that range. The French have been the hardest to persuade. Mr Draghi said that 72.5% is the magic number. The new rules also forbid the use of fancier internal models for loans to large companies and other banks. Risk weights for residential mortgages will depend on loan-to- value ratios. At first blush, this could mean a hefty additional increase in capital requirements for European banks. In a note on December 1st analysts at Citigroup estimated that a 72.5% floor could deplete their average CET1 ratio from a bonny 13.5% to a peakier 11.5%. (That includes the effect not only of the floor, but also of other bits of the package, including tweaks to market-risk and operational-risk standards, as well as a new accounting rule that takes effect on January 1st.) Banks could face a combined capital shortfall of e162bn ($191bn). 6 In fact, the Citi team also noted, it wont be anything like that bad. The Basel standard-setters said long ago that the revisions would not ”significantly increase overall capital requirements”. On December 7th the European Banking Authority said it reckoned the average CET1 ratio would drop by just 0.6%. Minimum requirements would rise by about an eighth, but most banks should clear that hurdle comfortably. Those requirements are partly set by national supervisors, who are likely to use their discretion to offset Basel 4; some, notably in Britain and the Nordic countries, have already indicated as much. So it may be that only a few banks have a shortfall. And as with Basel 3s previous strictures, the revisions will not take effect at once. They do not kick in until 2022, when the floor will be only 50%; it will be raised over five years. That said, markets are less patient than supervisors: they have tended to view banks as if all Basel 3s requirements were already in place, regardless of the regulatory timetable. But even if some banks have to consider raising more capital, they may breathe a sigh of relief. After almost a decade of uncertainty, they at last know what the Basel rule-book will look like for years to come. The question is whether it will make the financial system robust enough to withstand another disaster. Banks and supervisors say so. A few former watchdogs and some outspoken academics aren’t so sure. Everyone else? In the next crisis, theyll find out 7