讲解 ACFIM30008 Financial Crises辅导 留学生Matlab语言程序

ACFIM30008

Financial Crises

December 2025

DEADLINE: Tuesday, 9 December 2025 before 13:00 GMT

SUBMIT TO BLACKBOARD UNIT SUBMISSION POINT

Overview

•    Your summative coursework represents 100% of the final mark for the unit.

•    The coursework is in the form of a REPORT, analysing and interpreting the cases presented in the requirements.

•    The suggested length of your report is 8-12 pages, including tables and graphs, in a generously- spaced layout. (See detailed guidance below.) If your document exceeds the suggested length, markers may deduct marks on account of a lack of academic focus.

•    Penalties will apply if the coursework is submitted late.

•    The coursework is an individual piece of work – you should work on this yourself and not as a group.

•    The use of AI tools for this assignment has been categorised as “Category 2: Minimal” .  That is, you are allowed to make use of basic language tools such as spell-checkers, but only to identify individual mistakes, not to re-write entire segments of text. You are encouraged not to use grammar-checkers: markers will look out for authentic writing and will not penalise your report for minor language issues.

•    More general generative AI tools such as Copilot or ChatGPT will not help you in producing a satisfactory report. The use of such AI tools is strictly prohibited.

•    You will be required to make a plagiarism statement and your submission will be tested for originality.

Coursework requirement

The Brief

There are two parts to the assignments, each with several sub-questions. You are required to write a report that answers all sub-questions from both parts. The two parts have equal weight in the overall mark.

PART I [50 marks]

The Case (Part I)

Company Solar Pitch plc produces essential components for solar energy plants. You are the manager of an arbitrage-oriented investment fund. Early in January 2026 (today, date 0), your industry experts expect Solar Pitch’s earnings to grow at 4% per year, indefinitely. End-of-year earnings (December 2026) are safely expected to be 200 million pounds. The firm’s dividend payout ratio is fixed at 0.75. Dividends are discounted by the bank rate, which is 9% (same rate for loans and for deposits). There are 10 million shares outstanding. Many commentators have praised the firm’s performance and business model, and the over-excited demand from retail investors has pushed up the firm’s share price, beyond what you think is warranted by the firm’s fundamentals. The share price today (date 0) is p0  = 340 pounds per share.

For every given date t (t = 0, 1, 2, 3, …), we write pt for market price and vt for fundamental value, where fundamental value is determined by the firm’s earnings and dividends. Today at t = 0, we have p0 > v0  and in your view the stock is over-priced. Furthermore, you believe that if the stock is overpriced at any given date t > 0 (pt > vt), then there is an 80% chance that the price will remain over-priced at the next date. i.e. pt+1  > vt+1 with probability yup  = 0.8. The prices in such a continued bubble are called upswing prices (denoted by pt+1u). Alternatively, with a 20% chance the share price at date t+1 will go back to fundamentals, i.e. pt+1  = vt+1  with probability ydown  = (1 - yup) = 0.2.

You are risk-neutral, and your trading criterion is that a trade is good if its expected profits are positive. You have free access to bank loans and bank deposit at the given interest rate. You can borrow Solar Pitch shares from pension fund ABC. When lending the stock, fund ABC charges zero borrowing fees.

QI.1 Suppose that at date 0 you know for certain that the bubble will continue over the first three periods and that it will bursts at the end of the fourth period, so that p1  > v1 , p2  > v2 , p3  > v3 , followed by p4  = v4. Given p0 = 340 and p4  = v4 , describe a trading strategy that will lead to a positive expected profit for this scenario, regardless of how high market prices pt are at dates 1, 2, 3. Explain each aspect of your trading strategy and give full details of your corresponding cash flows for each date.

QI.2 Under the assumption of an 80% chance of the bubble not bursting at any one date in an upswing, and given p0  = 340, what sequence of potential upswing prices ptu will result in zero expected profits from your arbitrage strategy in Q1.1, or any similar strategy of any duration? Calculate these upswing prices for t = 1, 2, 3, 4.  Hence define and discuss the notion of a “rational stochastic bubble”.

QI.3 At date 0, you have taken a short position in Solar Pitch stock. Prices in the first three periods evolve as a continued upswing, as calculated in Q1.2. You find yourself at t = 3, with p3  = p3u  (the bubble has not yet burst). At this date, you have two options: (a) you liquidate your short position at price p3u, or (b) you maintain your short position for one more period, hoping that the bubble will burst at date 4. Compare these two options.

QI.4 You expect the upswing prices ptu to evolve as in QI.2, but at each date t, if the bubble bursts at that date (with a 20% chance), you expect an over-reaction in price, resulting in a new market price pt that will be at half the fundamental value for that date. Describe a short-selling strategy that exploits this situation.

QI.5 Discuss the dangers of maintaining your strategy from QI.4 if the bubble continues over many periods.

Reading (Part I)

The article by Blanchard/Watson, plus lecture notes.

PART II  [50 marks]

The Case (Part II)

Mayfair Securities produces securitised fixed-income products. One of these is RiskControl, a Collaterised Debt Obligation (CDO) that offers re-packaged payoff streams based on the US mortgage market.

RiskControl combines holdings in 10 large mezzanine tranches from various Mortgage Backed Securities (MBSs). Each of these tranches has a no-default value of 80 million dollars, so overall RiskControl holds assets with a no-default value of 800 million dollars. These holdings serve as the source of cash flows and as collaterals for RiskControl’s own “bond” offering. We label RiskControl’s ten collaterals C1, C2, C3, ... , C10.  Mayfair  Security’s  quant team assume that all ten collaterals  have the same  individual  default probability, each at 14%. They also assume that default events for the ten collaterals are uncorrelated. The resulting probability distribution is binomial, with the likelihood of k defaults among the 10 collaterals as follows:

RiskControl combines and re-packages the cashflows from C1, C2, C3, ..., C10 into ten large fixed-income offerings RC1, RC2, RC3, ..., RC10, each belonging to one of three tranches: Junior, Mezzanine and Senior. Mayfair Security’s marketing people call these ten payoff streams “macro bonds”. If there are no defaults, each of the ten macro bonds is a claim on one tenth of RiskControl’s asset base. If there are defaults, these are assigned first to Junior bonds, then to Mezzanine, then to Senior, hence the three tranches have different exposures to default risk and thus different value variations. RiskControl’s clients require the value of a Senior-class macro bond to have a standard deviation that is less than 1% of the Senior bond’s expected value. For the Mezzanine class, they allow for a much larger standard deviation, but they still require it to be less than 10% of the Mezzanine bond’s expected value.

QII.1 Discuss the principal rationale for a securitisation instrument such as RiskControl. If Mayfair Security wants to meet its clients’ risk requirements for Senior and Mezzanine bonds, how should the bank layer the three tranches: how many of RiskControl’s ten macro bonds should be in its Junior, Mezzanine and Senior tranches? Explain in detail how defaults are allocated to the various tranches, and present full details on the resulting default and payoff distributions (tables or diagrams are welcome).

QII.2 How does such a layered offering compare to a non-layered (single tranche) CDO under the same circumstances? Would it be possible for Mayfair Security’s clients to achieve the same risk reduction via simple diversification (purchasing more and more of the underlying assets)?

QII.3 Suppose that the quant team were wrong and the collateral defaults are mutually correlated. The probability of the first default is y1 = 0.14, as in the uncorrelated case, and if there have already been j defaults, then the probability for the next default is yj+1  = yj + (1-yj)×0.04, where 0.04 is the correlation coefficient. The resulting probability distribution is Moody’s correlated binomial default distribution, with the likelihood of k defaults among the 10 collaterals as follows:

Compare the distributional characteristics of the uncorrelated and the correlated case.

QII.4 How does the probability distribution from QII.3 impact on the Mezzanine and Senior tranches of RiskControl’s macro bonds? Under the tranche allocation from QII.1, do the ten macro bonds still meet client requirements?  Could  a  different  allocation  of  the  ten  bonds  to  the  three  tranches  ensure  that  client requirements continue to be met?

QII.5 With reference to the present stylised case, and also with reference to actual practice in the run-up to the Great Financial Crisis of 2007/8, what are typical sources of mispricing of a CDO tranche?

Reading (Part II)

Lecture notes, plus the FCIR Inquiry Report.

Further Guidance

In each of the two parts, try to write your report as one overarching argument, using the items from the listed sub-questions as your guide. There are no fixed weightings attached to individual sub-questions; in each part, your report will be marked as one piece. Depending on how you arrange your arguments, your answer to one of the aspects of the questions may take up much more space than the other aspects; this is fine.

This assignment gives you a chance to demonstrate your in-depth understanding of specific models and instruments. You should consult the key readings used in the course, as published on Blackboard, as well as the lecture notes, but otherwise there is no need for further reading. These sources are taken for granted and need not be listed explicitly. Any other sources need to be referenced, but you will benefit from working primarily with these two sources.

Clean layout is important. To make all submissions comparable, please adhere to the following guidelines: Font should be Arial, font size should be 12pt.  Linespacing should be 17pt. Your left and right margins should be 42mm. Top margin also 42mm, bottom margin 62mm. Subheadings are welcome. Pages need to be paginated. There should be a title page (not included in the word count). Paragraphs should be “justified” (flush on both sides).

With this layout, your report should have between 8 and 12  pages (plus the title page as an additional page). This is treated as equivalent to a word count of 3,000 words. If you adopt the suggested layout format, there is no need to use the word count of your word processor. All you need to do is make sure to stick to the specified layout. Do not try to beat the word count by shrinking the margins or by using smaller fonts. Do not exceed the 12-page limit. If your report does exceed the page limit, markers may consider this lack of focus as a weakness in the academic argument of your report.

Tables and graphs are welcome, but only if you have produced them yourself. Do not use tables and graphs from external sources.  If you  include tables  and graphs, they count toward the  page  limit  and will  be considered as part of the allowed 8-12 pages. There is no need for a reference list but if you need to have one, the reference list should be on a separate page and it does not count toward the page limit.

AI tools such as Copilot or ChatGPT are not going to help you work through this task — they are certain to weaken your analysis and dilute your narrative. You are not allowed to use them.

Your report should discuss the given case concretely, using specific numerical values wherever possible, and on this basis it should present a coherent general narrative about the issue. When discussing a trading strategy, be specific about the cashflows associated with each part of your strategy, at each date.

The case and the question provide you with a lot of material to work with. The markers recognise that not all aspects of the material can be covered in your report, and they will appreciate a sense of focused selectivity that helps bring out the main points well. Good depth on selected points is better than superficial coverage of too many points. The questions listed in each part naturally suggest relevant issues for you to look at, but the markers have no fixed checklist of items that need to be ticked off. Coherence of your overall argument and clear focus are more important.

Markers  will  appreciate  a  coherent  overall  narrative  that  carries  through  the  whole   report.  Highlight interlinkages between the different parts of your argument, and make sure to illustrate abstract arguments with the specific numerical figures from the case.

The space limit will not permit you to show all of your numerical workings, but you may want to show full details in selected aspects of your workings.

You should make every effort to avoid close paraphrasing of your source materials. It is essential that you express each of your points entirely in your own words. Reports that repeatedly stay very close to the sources will not receive high marks. The markers recognise that for many of you, English is not your first language. As long as your statements are clear, minor grammatical or stylistic errors will not be penalised.

Spreadsheets

The unit makes extensive use of spreadsheets to present and analyse stylised cases. You are expected and encouraged to use these spreadsheet tools in your assignment work. You may use the files that can be found on Blackboard, or you may develop similar spreadsheets yourself. Graphs and tables produced with these tools may be included in your essay. Remember that all graphs and tables count toward the space limit of max 8-12 pages.

Mathematical typesetting

Variables such as p or v should be italicised, indices should be shown as subscripts (as in pt). Numbers, brackets or mathematical operators must never by italicised: (2a+3b)/m=c is wrong, whereas (2a+3b)/m=c is is right. Likewise in subscripts: vt+1 > vt+2 is wrong whereas vt+3 > vt+2  is right. All of this can be done with straight formatting, without an equation editor. It is ok to write expressions such as v0  = [1/(1+r)](d1+v1), without using a large fraction in a displayed equation.

Forum for Queries

The online discussion forum will be open for clarification and background queries. Obviously we will not discuss specific details of the actual cases, but you are welcome to post questions about the underlying finance issues, about related exercises from the tutorial classes, and about the coursework requirements.