FN2190 Asset Pricing and Financial Market 2020 Exam paper PDF

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FN2190 Asset Pricing and Financial Market 2020 Exam paper
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FN2190 Summer 2020 online assessment guidance FN2190 Asset Pricing and Financial Markets The assessment will be an open-book take-home online assessment within a 24hour window. The requirements for this assessment remain the same as the originally planned closed-book exam, with an expected time/effort of 3 hours. Candidates should answer THREE of the following FOUR questions. All questions carry equal marks. You should complete your examination using pen and paper. Please use BLACK ink only. Handwritten work then needs to be scanned, converted to PDF and then uploaded to the VLE as ONE individual file including the coversheet. Each scanned sheet should have your candidate number written clearly at the top. Please do not write your name anywhere on any sheet. The paper will be available at 12.00 midday (BST) on Thursday 2 July 2020. You have until 12.00 midday (BST) on Friday 3 July 2020 to upload your file into the VLE submission portal. However, you are advised not to leave your submission to the last minute. We will deduct 5 marks if your submission is up to one hour late, 10 marks if your submission is more than one hour late but less than two hours late (etc.). If you think there is any information missing or any error in any question, then you should indicate this but proceed to answer the question stating any assumptions you have made. The assessment has been designed with a duration of 24 hours to provide a more flexible window in which to complete the assessment and to appropriately test the course learning outcomes. As an open-book assessment, the expected amount of effort required to complete all questions and upload your answers during this window is no more than 3 hours. Organise your time well and avoid working all night. You may use any calculator for any appropriate calculations, but you may not use any computer software to obtain solutions. Credit will only be given if all workings are shown. You are assured that there will be no benefit in you going beyond the expected 3 hours of effort. Your assessment has been carefully designed to help you show what you have learned in the hours allocated.

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This is an open-book assessment and as such you may have access to additional materials including but not limited to subject guides and any recommended reading. But the work you submit is expected to be 100% your own. Therefore, unless instructed otherwise, you must not collaborate or confer with anyone during the assessment. The University of London will carry out checks to ensure the academic integrity of your work. Many students that break the University of London’s assessment regulations did not intend to cheat but did not properly understand the University of London’s regulations on referencing and plagiarism. The University of London considers all forms of plagiarism, whether deliberate or otherwise, a very serious matter and can apply severe penalties that might impact on your award. The University of London 2019-20 Procedure for the Consideration of Allegations of Assessment offences is available online at: https://london.ac.uk/sites/default/files/governance/assessment-offence-procedureyear-2019-2020.pdf The University of London’s Rules for Taking Online Timed Assessments have been included in an update to the University of London General Regulations and are available at: https://london.ac.uk/sites/default/files/regulations/progregs-general-2019-2020.pdf

© University of London 2020

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Question 1

You observe that the current three-year discount factor for default-risk free cash flows is 0.68. Remember, the t-year discount factor is the present value of $1 paid at time t, i.e. ฀฀฀ ฀ = (1 + ฀฀฀฀ )−฀฀ , where ฀฀฀฀ is the t-year spot interest rate (annual compounding). Assume all bonds have a face value of $100 and that all securities are default-risk free. All cash flows occur at the end of the year to which they relate.

a) What is the price of a zero-coupon bond maturing in exactly 3 years?

(5 marks)

b) Your friend makes the following observation about the above bond: “Since there is no risk of default and there are no coupons to re-invest, buying the 3-year zero coupon bond today is a risk-free investment; that is, you are guaranteed to earn an annual return of 13.72% (i.e. 3-year spot rate)”. Explain why your friend is not entirely correct and how you would modify the statement to make it correct. (5 marks) c) In addition to the bond in (a), you observe the following: a 2-year coupon bond paying 10% annual coupons with a market price of $97, and two annuities that are trading at the same market price as each other. The first annuity matures in 3 years and pays annual cash flows of $20, while the second annuity pays annual cash flows of $28 and matures in 2 years. Using this information: i.

Complete the term structure of interest rates, i.e. determine the one- and two-year discount factors, d1 and d2, respectively. (6 marks)

ii.

Determine the price of the annuities.

(2 marks)

d) Assuming annual compounding, determine the implied one-period forward rates ฀฀2 (i.e. between year 1 and 2) and ฀฀3 (i.e. between year 2 and 3) in this economy. What inference can you make about the market’s estimate of the one-year spot interest rate at ฀ ฀ = 1 if the liquidity preference theory is correct? (5 marks) e) Suppose you decide to purchase a 1-year zero-coupon bond today and also contract today to re-invest the proceeds from the bond for the following two years at 16.5% per year. Show that this arrangement presents an arbitrage opportunity. Demonstrate how you would take advantage of this opportunity. (6 marks) f) Consider discount factors such that d1 < d2 < d3. Explain why it would be odd to observe such a situation in a competitive market. (4 marks)

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Question 2

Assume the CAPM holds. Consider three feasible portfolios of stocks X, Y and Z with the following return characteristics: Portfolio X Y Z

Expected return 7.5% 5% 10%

Standard deviation 5% 10% 15%

a) Explain why beta is the appropriate measure of risk in this world.

(5 marks)

b) Portfolio Y is known to be uncorrelated with the market. Explain why this property implies that the risk-free rate in the economy is 5%. (5 marks) c) It is known that one of the portfolios X, Y, Z lies on the efficient frontier (which includes the risk-free asset). Which portfolio is efficient? Explain/justify your answer. (5 marks) d) An investment manager approaches you and offers you an investment product with a claimed expected return of 12% and standard deviation of 20%. Should you accept this investment? Why/why not? If not, show how the manager can optimally create a portfolio with an identical return volatility to his proposed portfolio but with a superior expected return. Illustrate your answer graphically, making sure to label all relevant elements of your picture. (6 marks) e) Consider an investor who invests $50,000 in a portfolio consisting of X and Z. $10,000 of that investment was funded with risk-free borrowing. The expected return of the investor’s portfolio is 9.375%. i.

Calculate the dollar amounts invested in each of X and Z.

ii.

If the correlation between X and Z is 2/3, what is the standard deviation of the investor’s portfolio? (2 marks)

(4 marks)

f) Show that any portfolio on the Capital Market Line (CML) with a positive weight in the market portfolio is perfectly correlated with the market portfolio. Interpret this result. (6 marks)

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Question 3

Assume all options are European, and that the underlying asset is a non-dividend paying stock, unless otherwise specified. (a) A ‘protective put’ strategy involves buying both a put option on a stock and the underlying stock itself. i.

Draw a payoff diagram (not a profit-and-loss diagram) for a protective put strategy. Make sure to label all relevant parts of the diagram. Why do you think this strategy has its name? (5 marks)

ii.

Using put-call parity, explain why the payoff of a protective put resembles the shape of the payoff of a call option. (5 marks)

(b) You observe two call options, A and B, with the same exercise price, written on the same underlying asset. Option A matures in one year, while B matures in 18 months. Which option has the higher value? Explain. (5 marks) (c) The value of a European put option must satisfy the following restriction: ฀฀0 ≥ ฀฀฀฀ −฀฀฀฀ − ฀฀0 where ฀฀0 is the current put price, ฀฀0 is the current price of the underlying stock, ฀฀ is the exercise price, ฀ ฀ > 0 is the annualised continuously compounded risk-free rate, and ฀฀ is the time till expiration. Prove by contradiction that the above arbitrage restriction must hold, i.e. show that if the condition does not hold, there is an arbitrage opportunity. (4 marks) (d) It is also known that the value of a European put cannot be greater than the present value of its exercise price, i.e. ฀฀0 ≤ ฀฀฀฀ −฀฀฀฀ . This restriction, along with the one in (c), suggests that the price of a European put can fall below its exercise value prior to maturity. When is this situation likely to arise? Give an intuitive explanation as to why its value is below its exercise value in such circumstances. (4 marks) (e) Stock K currently sells for $120. After one year, its price will either increase by 10% or fall by 10%. The annual risk-free interest rate is 5%. i.

Calculate the current value of an at-the-money European call option on stock K maturing in one year. (5 marks)

ii.

Now assume that the volatility of Stock K increases so that if the stock price increases, it will still increase by 10% but if it falls, it will fall by more than 10%. Everything else including the expiration date, current stock price, exercise price, and interest rate stays the same. Show

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mathematically that the current value of the call option is higher than the value you calculated in part (i). (5 marks) Question 4 (a) The table below lists some partial information about a firm. Assume that the number of shares outstanding stays constant forever. Year 0 100

Book equity per share Earnings per share (EPS) Return on equity (ROE) Payout ratio Dividends per share Dividend growth rate

1

0.20 0.25 5 -

2 132.25 0.20 0.25

3

4

0.15 0.50

21.325 0.15 0.50 0.075

i.

Fill in the missing values in the table from years 1 to 4.

ii.

Assume that after year 4, the company maintains its ROE and payout ratio at year 4 levels. The cost of capital is 12.5%. What is the fair price of the company’s stock today (i.e. at t = 0)? (3 marks)

iii.

Suppose the company announces today that it expects any new investments made in or subsequent to year 4 to only earn the cost of capital. The values you calculated in part (i) will be unaffected by this announcement. By how much will the share price change today after the announcement? (4 marks)

(6 marks)

(b) Consider the following statement: “For markets to be informationally efficient, all investors must be rational”. Is this statement true? Why/why not? (you will be marked on the justification(s) provided). (4 marks) (c) Companies sometimes try to match the duration of their assets and liabilities. Explain how you think this approach may be useful in protecting net worth from interest rate risk (net worth = A – L, the difference between the market value of assets and liabilities). When is this approach likely to prove less effective? Why? (5 marks) (d) Assume that the CAPM holds. Consider two firms X and Y, and the risk-free asset, with the following return characteristics: X

฀฀฀฀ ฀฀ 225

Y rf

1600 0

฀฀฀฀฀฀(฀฀฀฀ , ฀฀฀฀฀฀฀฀ ) 200

฀฀(฀฀฀฀ ) 7.5

600 5

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What is the expected return of stock Y?

(5 marks)

(e) Exactly one year ago, you entered into a forward agreement to purchase one unit of a commodity for $F in exactly T years from now. The current price of the commodity in the spot market is $S. The risk-free continuously compounded interest rate in the market is currently r per year. There are no convenience yields or storage costs associated with holding the commodity. Using a replicating portfolio approach, show that the current value of your forward agreement, f, is: ฀ ฀ = ฀฀ − ฀฀฀฀ −฀฀฀฀ (6 marks)

END OF PAPER

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Examiners’ commentaries 2020

Examiners’ commentaries 2020 FN2190 Asset pricing and financial markets Important note This commentary reflects the examination and assessment arrangements for this course in the academic year 2019–20. The format and structure of the examination may change in future years, and any such changes will be publicised on the virtual learning environment (VLE).

Information about the subject guide and the Essential reading references Unless otherwise stated, all cross-references will be to the latest version of the subject guide (2018). You should always attempt to use the most recent edition of any Essential reading textbook, even if the commentary and/or online reading list and/or subject guide refer to an earlier edition. If different editions of Essential reading are listed, please check the VLE for reading supplements – if none are available, please use the contents list and index of the new edition to find the relevant section.

General remarks Learning outcomes At the end of the course and having completed the essential reading and activities you should be able to: describe the important differences between stock, bond and derivative securities explain how to price assets using both present value and absence of arbitrage methods apply present value techniques to price stocks and bonds employ mathematical tools to compute risk and return for portfolios of securities evaluate portfolio choice problems present, explain and apply the Capital Asset Pricing Model for computing expected stock returns critically evaluate the evidence for informational efficiency of stock markets price derivative securities using absence of arbitrage.

Covering the syllabus In order to maximise your chances of performing well in the examination, you should ensure that you have covered the entire syllabus. Focusing narrowly on a few topics in the hope that these topics will cover enough material to pass the examination is a strategy which often backfires badly. Furthermore, do not ignore the theoretical elements of the course – after all, this is a course on asset pricing theory. Candidates often fall into the trap of assuming that asset pricing is just about doing

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FN2190 Asset pricing and financial markets

numerical calculations using a handful of equations. Yes, numerical calculations are important, but your ability to interpret and evaluate is equally, if not more important, which is difficult to do well if you do not understand where the equations come from and what they are saying. For example, there is a lot more to the capital asset pricing model (CAPM) than just plugging numbers into the security market line (SML) equation. Finally, be aware that, as asset pricing theories and methods are often inter-related, examination questions can cover material from different chapters in the subject guide (another reason not to focus too narrowly during your preparation).

Expectations of the examination paper In general, the examiners are looking to gauge the breadth and depth of a candidate’s understanding of the asset pricing theories and methods covered in the syllabus. In practice, this means the examination questions cover a wide range of topics from the syllabus, with sub-questions being set at varying levels of difficulty so that stronger candidates are able to differentiate themselves. What does a ‘strong candidate’ look like? A key indicator that a student truly understands a concept or method is their ability to correctly apply it in a novel context. Because of this, some parts of the examination are likely to seem unfamiliar; by definition, these are questions which you will likely not have come across previously. In other words, you should expect to be surprised by some of the questions. Of course, you will only be examined on material in the syllabus, so all questions can still be answered using the concepts covered in the syllabus. There will also be enough routine, familiar content in the examination so that a candidate who has achieved basic competence in the course should pass, but for candidates aspiring to a high(er) mark, more is expected. Simply regurgitating previously seen material is not enough; you will have to demonstrate a mastery of the material by solving new and unfamiliar problems.

Answer the question A common bugbear among examiners, particularly relating to qualitative questions, is where candidates simply reproduce materials from the subject guide verbatim without paying attention to what the question actually asks. This approach results in answers that are often too general (or sometimes too narrow) and contain irrelevant content. It is important that you read the question carefully and address what it asks, and only what it asks, not what you would like it to. The examiners are looking for succinct, focused answers tailored to the requirements of the question. Although it can be enticing to write down everything you know about a topic so as not to miss something, excessively long answers containing irrelevant material waste valuable examination time and actually suggest a lack of understanding, not an abundance of it. A related issue in the domain of quantitative questions pertains to the choice of solution method. Often, there will be multiple routes that lead to the correct answer and you will have free rein to use whichever method takes your fancy. Sometimes, however, a question will specify the exact approach it would like you to take. Do not ignore this instruction. The examiner has specified an approach because they want to test your ability to apply a specific technique. It is the technique they are interested in, not the answer, so do not expect to be rewarded if you ignore the instructions, even if you get the correct answer. To avoid falling into these traps, it can be useful to take some time to think about what the question is asking and how to best answer it before you start writing. This advice applies to any question type and also to the examination as a whole. Regarding the latter, take some time to read through the examination paper before deciding which 3 of the 4 questions you will attempt; candidates who focus their energies on answering 3 questions well tend to do better than candidates who abandon a question midway to start another. Given the three-hour length of the examination, you can afford to spend a few minutes to consider your approach. It will be time well spent.

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Examiners’ commentaries 2020

Examination revision strategy Many candidates are disappointed to find that their examination performance is poorer than they expected. This may be due to a number of reasons, but one particular failing is ‘question spotting’, that is, confining your examination preparation to a few questions and/or topics which have come up in past papers for the course. This can have serious consequences. We recognise that candidates might not cover all topics in the syllabus in the same depth, but you need to be aware that examiners are free to set questions on any aspect of the syllabus. This means that you need to study enough of the syllabus to enable you to answer the required number of examination questions. T...