SUMMER TERM 2022 SAMPLE FINAL EXAM ECON0048: ECONOMICS OF FINANCE Time allowance You have 3 hours to complete this examination, plus an Upload Window of 20 minutes. The Upload Window is for uploading, completing the Cover Sheet and correcting any minor mistakes and should not be used for additional writing time. If you have been granted SoRA extra time and/ or rest breaks, your individual examination duration will be extended pro-rata and you will also have the 20-minute Upload Window added to your indi- vidual duration. All work must be submitted anonymously in a PDF le and you should follow the instructions for submitting an online examination in the AssessmentUCL Guidance for Students. If you miss the submission deadline, you will not be able to submit your work via AssessmentUCL and you will not be permitted to submit the work via email or any other channel. If you are unable to submit your work due to technical di￠ culties which are substantial and beyond your control, you should apply for a Deferral via the AssessmentUCL Query Form. Page limit: 20 pages. Your answers, excluding the Cover Sheet, should not exceed this page limit. Please note that a page is one side of an A4 sheet with a minimum margin of 2 cm from the top, bottom, left and right borders of the page. The submission can be handwritten or typed, but the font size should be no smaller than the equivalent to an 11pt font size. This page limit is generous to accommodate students with large handwriting. We expect most of the submissions to be signi cantly shorter than the set page limit. If you exceed the maximum number of pages, the mark will be reduced by 10 percentage points, but the penalized mark will not be reduced below the pass mark and marks already at or below the pass mark will not be reduced. Answer all questions from Part A and 3 questions from Part B. Questions in Part A carry 3.5 per cent of the total mark each, questions in Part B carry 24 per cent of the total mark each. In cases where a student answers more questions than requested by the examination rubric, the policy of the Economics Department is that the student s rst set of answers up to the required number will be the ones that count (not the best answers). All remaining answers will be ignored. If you have a query about the examination paper, instructions or rubric, you should complete an As- sessmentUCL Query Form. Please note that you will not receive a response during your examination. ECON0048 1 TURN OVER By submitting this assessment, you are con rming that you have not violated UCL s Assessment Regulations relating to Academic Misconduct contained in Section 9 of Chapter 6 of the Academic Manual. ECON0048 2 CONTINUED PART A Answer all questions from this section, 3.5 points per question (over a total of 100) True, false, or uncertain Distinguish di¤erent parts of each question (ie. in some cases part a) may be true but part b) false). Explain your answers. Use results derived in lectures without deriving them from scratch, simply mention what result you are using and what the result says. A1 Evidence for reduced stock-market risk at long horizons is evidence against weak-form market e￠ ciency. A2 The stock of Zoom Video Communications has multiplied by ve in the year 2020. a) Having taken ECON0048 you realise stocks are sometimes overvalued and you are certain this is the case with Zoom. There is a short selling strategy to take advantage of this knowledge and it is certain to make pro ts. Explain the short-selling strategy and say if it does or does not o¤er pro ts with certainty. b) Furthermore, being a software development enthusiast you know of a new publicly traded well funded company called LTFOT (Let s Take the Fun Out of Teaching) that is about to hit the market with a much better software for remote teaching. You conjecture that as a consequence Zoom shares will go down even further while prices of LoTFOT will go up. There is a short- selling strategy that is more likely to o¤er pro ts than in part a). Explain the short-selling strategy and why it does or does not o¤er certain pro ts. A3 Consider two mean-variance investors who are not leverage constrained, they can invest in a safe asset and two stocks. If their risky portfolio holds di¤erent shares of each stock it must be that they have di¤erent risk aversion. A4 An investor with $100,000 of nancial wealth to invest and safe labour income with a present value of $100,000 should invest twice as much in risky assets as an otherwise identical investor with the same nancial wealth but with no labour income. A5 According to the Capital Asset Pricing Model (CAPM) a) under rational expectations the market portfolio has the highest Sharpe ratio of any portfolio. b) however, there are several reasons why in practice the market portfolio may not have the highest Sharpe ratio. A6 If two risky assets have the same standard deviation, the optimal portfolio of the two risky assets is a) equally weighted b) it has a standard deviation that increases with the correlation between the two assets. ECON0048 3 TURN OVER A7 The yield on a sovereign bond in the euro area a) should exceed the yield of a safe bond by the expected rate of default loss on the sovereign. b) therefore it should exceed the yield of a US bond of the same maturity by the expected rate of default loss. If false in general, are there some special cases where this is true A8 The Gordon growth model a) describes a stock s price as the present discounted value of its expected dividends in the future. Mention some simplifying assumptions in this model. b) The Gordon growth model makes a simplifying assumption that, for any given holding period, the stock s return over that period consists only of dividend gains and no capital gains. ECON0048 4 CONTINUED PART B Answer 3 questions from this section. 24 points per question (over a total of 100). B 1 Stock A has an expected return of 8% and the standard deviation of the return is 15%. Stock B has an expected return of 6%, standard deviation of 15%. (a) If the returns on the two stocks have zero correlation, and the risk-free rate is 2%, is there an arbitrage opportunity here If so, how would you exploit it Is it rational to hold stock B even if it has the same variability but lower mean return than stock A (b) Suppose the same investor has mean-variance preferences and she can invest in the risk-free asset, in addition to stocks A and B. Recall that the risk-free rate is 2%. Assume the correlation of the two stock returns is 0.5 and RRA is 4. What percentage of her wealth does she invest in the risk-free asset (c) Assume now that the investor can only invest in the risky assets (i.e., no risk-free asset), what percentage of her wealth will she invest in each asset (We did not do this formula in class so you will have to derive it for a fully correct numerical answer). Show the optimal solution in a diagram. You will get a large percentage of the credit by showing a correct diagram. Compare in a diagram the solution to parts b) and c). (d) How do your answers to parts (b) and (c) change if the RRA increased Be speci c about which assets will have higher weights and which assets will have lower weights. Explain in each case. B 2 You are analyzing the behaviour of long-term interest rates. (a) You regress the change in the log yield on an m-period bond onto the log yield spread: ym1;t+1 ym;t = + (ym;t y1;t) + “m1;t+1 Suppose the time interval is one year, and maturities are measured in years. You use data for m = 5. When you run this regression using historical data you estimate = 0:1. Is this result unusual or is it likely to be a mistake in the estimation What value of would you expect if the expectations hypothesis of the term structure is correct (b) Given the above empirical result, what is the e¤ect of an increase of one percentage point in the log yield spread of a 5-year bond over a 1-year bond for example, an increase in the log yield spread from 1% to 2% on the expected excess log holding period return of the 5-year bond over the 1-year bond Is the e¤ect positive Is the e¤ect greater than one percentage point Explain. ECON0048 5 TURN OVER (c) Using the same historical data, you estimate the average 5-year log yield spread as 0.7% and the average excess log holding period return on 5-year bonds as 1.6%. Someone states “this discrepancy is odd, the di¤erence 1.6%-0.7%=0.9% should be proportional to the average change in interest rates, which should be zero over long enough periods of time given that interest rates do not trend up or down”. You respond that this is the case only under a certain hypothesis that has been already shown not to hold in practice. Discuss how to justify both sides of this conversation. (d) Using the same historical data, you estimate that the standard deviation of the excess return on 5-year bonds is 10%. What is the average simple excess return (arithmetic average excess HPR) on 5-year bonds over 1-year bonds What is the Sharpe ratio for 5-year bonds At the same time the standard deviation of y1;t is 1%. Given that HPR are the returns of one- year investments, is the higher standard deviation of HPR immediately a sign of ine￠ cient markets B 3 Consider a nancial market with one risk-free asset and many risky assets. The risk-free asset delivers a return of 2%. There is a stock A that delivers a return of 10% with a standard deviation of 30%. The market portfolio of all traded risky assets has a standard deviation of 8%. The correlation coe￠ cient between stock A and the market portfolio is 0:5. (a) Calculate the beta of stock A with respect to the given market portfolio. (b) For this subquestion assume that the CAPM assumptions hold in this nancial market. Then, what is the expected return on the market portfolio (c) What is the alpha for stock A (d) Suppose you are a mean-variance optimizing investor. Would you increase or decrease your holding of stock A relative to the market portfolio If so, explain verbally how you would change your portfolio. (e) Suppose you also own a private business. Does this violate any of the CAPM assumptions As it happens, stock A represents a company that is an industry whose return is negatively correlated with the return of your private business. Does your answer to part d) change Why or why not B 4 A producer of chemical products has been sued for damages over cancer cases in the community where one of its plants is located. Tomorrow the case will be decided. If the decision goes in the company s favour, its stock price, currently ￡ 2.00, will increase to ￡ 5.00. If the decision goes against the company, the rm will be liquidated and the stock price will drop to zero. The rm has also issued a certain amount of corporate bonds, each corporate bond has a face value of ￡ 1.00. If the company is liquidated, each corporate bond will be worth only ￡ 0.25, as this would be the value of assets per bond issued if the company is liquidated. ECON0048 6 CONTINUED For simplicity, you may assume that the overnight interest rate for money invested safely is zero. That is, ￡ 1.00 invested today at the safe interest rate will be worth ￡ 1.00 tomorrow for sure. Also, assume the company does not pay dividends. Both long and short positions are permitted throughout this question. (a) Using the stock and the risk-free asset (ie, not the corporate bond), construct a portfolio that pays ￡ 1.00 tomorrow if the company wins the case, and ￡ 0.00 if the company loses. What is the price of this portfolio today Assume no-arbitrage pricing. (b) Using the stock and the risk-free asset, construct a portfolio that pays $1.00 tomorrow if the company loses the case, and $0.00 if the company wins. What is the price of this portfolio (c) Label the two states of the world tomorrow as state 1 if the company wins the case, and state 2 if the company loses. What is the Arrow-Debreu state price vector in this example (d) Use your answers to parts a) through c) to determine the price of the company s corporate bonds today, under the assumption that there are no arbitrage opportunities. (e) Suppose the company s bonds are selling today for $0.60. Show that there is an arbitrage opportunity, and show how you would trade to exploit it. (AD securities are not available, only the stock, risk-free asset and corporate bond) (f) Explain why you don t need to know the probability that the company will win the case to answer any part of this question. (g) Discuss how one could change the above setup so that the stock and the risk-free asset would not be able to replicate the corporate bond as in part e). ECON0048 7 END OF PAPER
