CT8-QA.pdf - CT8 QUESTION BANK FINANCIAL ECONOMICS CT8 Ques\ufffdon Bank CT8 Q&A Bank Part 1 \u2013 Questions Page 1 Part 1 \u2013 Questions Introduction The

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Unformatted text preview: CT8 - QUESTION BANK FINANCIAL ECONOMICS CT8 Ques�on Bank CT8: Q&A Bank Part 1 – Questions Page 1 Part 1 – Questions Introduction The Question and Answer Bank is divided into 5 parts. The first 4 parts include a combination of: ● bookwork questions ● developmental questions and ● exam-style questions. We have indicated the type of question throughout. All bookwork questions could be asked in the exam so you should start immediately learning this bookwork well. Developmental questions are not as likely to be asked in the exam, especially in terms of the style of the question. That is not to say that they are not useful! These questions are to help you understand the course better in order that you are in a much stronger position to attempt exam-style questions. Ultimately, the more questions you attempt, the greater your understanding of the course and the greater the chances of being able to answer whatever is asked in the exam. For all questions, you should attempt the questions by yourself, before looking at the solutions provided. This distinction represents the difference between active studying and passive studying. Given that the examiners will be aiming to set questions to make you think (and in doing so they will be devising questions you have not seen before), it is much better if you practice the skills that they will be testing. It may also be useful to you if you group a number of the exam-style questions together to attempt under exam time conditions. Ideally three hours should be set aside, but anything from one hour (ie 35 marks) upwards will help your time management. Once you have exhausted Parts 1 to 4 of the Question and Answer Bank, you can move on to Part 5, which contains a set of exam-style questions covering the whole course. The Actuarial Education Company © IFE: 2017 Examinations Page 2 CT8: Q&A Bank Part 1 – Questions Question 1.1 (Bookwork) (i) Describe what is meant by an “efficient market”. [2] (ii) Describe the three different forms of the Efficient Markets Hypothesis. [3] (iii) Discuss the implications of the Efficient Markets Hypothesis. Question 1.2 [5] [Total 10] (Bookwork) (i) In the context of semi-strong market efficiency, explain what is meant by informational efficiency. Describe briefly the main difficulties in testing for informational efficiency. [3] (ii) Discuss in detail the empirical evidence concerning informational efficiency. [11] [Total 14] Question 1.3 (Exam-style) At the quarterly meeting of the Auger Close Investment Club, four members are making proposals for new equity investment for the club. Albert wants to buy shares in Armadillo Adventures, claiming that they have performed poorly in recent weeks and are due an upturn. Brian wants to invest in Biscuits-R-Us. They have recruited a new head of marketing, who has had success at other companies. Brian feels that this new appointment will have a positive effect on the firm. Colin selects shares at random. This quarter he is recommending the club buy into Cash 4 Kidneys PLC. Dennis wants the club to buy shares in Diamond Dentists (“DD”). His brother works for a major health insurer and has insider information that DD’s shares will rise sharply in the near future, when it is announced that his company has appointed DD as its “dentist of choice”. For each club member, describe how their share selection strategy would work in strongly efficient, semi-strongly efficient, weakly efficient and inefficient markets. [7] © IFE: 2017 Examinations The Actuarial Education Company CT8: Q&A Bank Part 1 – Questions Question 1.4 Page 3 (Exam-style) (i) Explain what is meant by an “excessively volatile” market. [2] (ii) Describe how you would test if a market is “excessively volatile”. [7] (iii) Explain the practical and conceptual difficulties in using a test of an excessively volatile market to establish whether or not a market is efficient. [4] [Total 13] Question 1.5 (Developmental) Colin’s preferences can be modelled by the utility function such that: U ¢( w) = 3 - 2w, ( w > 0). (i) Determine the range of values over which this utility function can be satisfactorily applied. [1] (ii) Explain how Colin’s holdings of risky assets will change as his wealth decreases. [3] (iii) Which of the following investments will he choose to maximise his expected utility? Investment A Investment B Investment C outcome probability outcome probability outcome probability 0.1 0.3 0 0.3 0.2 0.45 0.3 0.4 0.2 0.2 0.3 0.1 0.5 0.3 0.9 0.5 0.4 0.45 [3] [Total 7] The Actuarial Education Company © IFE: 2017 Examinations Page 4 CT8: Q&A Bank Part 1 – Questions Question 1.6 (Developmental) By considering the relationship R ( w) = w. A( w) , explain which of the following statements is true. 1. If an investor’s preferences display decreasing relative risk aversion then they must also display decreasing absolute risk aversion. 2. If an investor’s preferences display decreasing absolute risk aversion then they must also display decreasing relative risk aversion. [4] Question 1.7 (Exam-style) Explain the four axioms that are required to derive the expected utility theorem. Question 1.8 [6] (Exam-style) Jenny has a quadratic utility function of the form U ( w) = w - 10 -5 w2 . She has been offered a job with Company X, in which her salary would depend upon the success or otherwise of the company. If it is successful, which will be the case with probability ¾, then her salary will be $40,000, whereas if it is unsuccessful she will receive $30,000. (i) Assuming that Jenny has no other wealth, state the salary range over which U ( w) is an appropriate representation of her individual preferences. [2] (ii) Calculate the expected salary and the expected utility offered by the job. (iii) Suppose she was also to be offered a fixed salary by Company Z. Determine the minimum level of fixed salary that she would accept to work for Company Z in preference to Company X. [3] (iv) Suppose that the owners of Company X are both risk-neutral and very keen that Jenny should join them and not Company Z. Determine whether the firm should agree to pay her a fixed wage, and, if so, how much. Comment briefly on your answer. [1] [Total 8] © IFE: 2017 Examinations [2] The Actuarial Education Company CT8: Q&A Bank Part 1 – Questions Question 1.9 Page 5 (Exam-style) Suppose that Lance and Allan each have a log utility function and an initial wealth of 100 and 200 respectively. Both are offered a gamble such that they will receive a sum equal to 30% of their wealth should they win, whereas they will lose 10% of their wealth should they lose. The probability of winning is ¼. (i) State whether or not the gamble is fair. [1] (ii) Calculate Lance’s certainty equivalent for the gamble alone and comment briefly on your answer. [2] (iii) Repeat part (ii) in respect of Allan and compare your answer with that in part (ii). [2] (iv) Confirm that your comments in part (iii) apply irrespective of the individual’s wealth. [2] [Total 7] Question 1.10 (Exam-style) Consider the two risky assets, A and B, with cumulative probability distribution functions: FA ( w) = w FB ( w) = w½ In both cases, 0 w 1. (i) Show that A is preferred to B on the basis of first-order stochastic dominance. [3] (ii) Verify explicitly that A also dominates B on the basis of second-order stochastic dominance. [3] [Total 6] The Actuarial Education Company © IFE: 2017 Examinations Page 6 CT8: Q&A Bank Part 1 – Questions Question 1.11 (Exam-style) (i) Within the context of behavioural finance, explain fully what is meant by overconfidence. [4] The board of directors of an actively managed investment trust are concerned that the decisions of the trust’s investment manager may subject to overconfidence bias, which could adversely affect the performance of the trust. (ii) Discuss possible actions that the board could take in order to try and limit the impact of the investment manager’s overconfidence bias. [6] [Total 10] Question 1.12 (Exam-style) (i) Define framing and outline how it relates to some of the other behavioural finance themes. [5] (ii) The marketing team of a unit trust management company are updating the promotional literature for their actively managed UK Equity trust. The trust produced a return of 5% over the last calendar year, compared to 4% for the FTSE 100 index. Give examples of how the marketing team could present the past performance of the fund favourably to prospective investors. [4] (iii) A financial advisor is due to present a range of possible investment strategies to a high net worth individual. Explain the decisions she will need to make with regard to the presentation of the possible strategies. [4] [Total 13] Question 1.13 (Developmental) Adam, Brett and Charlie are all offered the choice of investing their entire portfolio in either a risk-free asset or a risky asset. The risk-free asset offers a return of 0% pa, whereas the returns on the risky asset are uniformly distributed over the range –5% to +10% pa. Assuming that each individual makes his investment choice in order to minimise his expected shortfall, and that they have benchmark returns of –2%, 0% and +2% pa respectively, who will choose which investment? Comment briefly on your answer. [9] © IFE: 2017 Examinations The Actuarial Education Company CT8: Q&A Bank Part 1 – Questions Page 7 Question 1.14 (Developmental) (i) Define “shortfall probability” for a continuous random variable. (ii) An investor holds an asset that produces a random rate of return, R , over the course of a year. Calculate the shortfall probability using a benchmark rate of return of 1%, assuming: (iii) (a) R follows a lognormal distribution with m = 5% and s 2 = (5%) 2 (b) R follows an exponential distribution with a mean return of 5%. [1] [3] Explain with the aid of simple numerical examples the two main limitations of the shortfall probability as a basis for making investment decisions. [4] [Total 8] Question 1.15 (Exam-style) Consider a zero-coupon corporate bond that promises to pay a return of 10% next period. Suppose that there is a 10% chance that the issuing company will default on the bond payment, in which case there is an equal chance of receiving a return of either 5% or 0%. (i) (ii) Calculate values for the following measures of investment risk: (a) downside semi-variance (b) shortfall probability based on the risk-free rate of return of 6% (c) the expected shortfall below the risk-free return conditional on a shortfall occurring. [5] Discuss the usefulness of downside semi-variance as a measure of investment risk for an investor. [3] [Total 8] The Actuarial Education Company © IFE: 2017 Examinations Page 8 CT8: Q&A Bank Part 1 – Questions Question 1.16 (Exam-style) An investor is contemplating an investment with a return of £ R , where: R = 250, 000 - 100, 000 N and N is a Normal [1, 1] random variable. Calculate each of the following measures of risk: (a) variance of return (b) downside semi-variance of return (c) shortfall probability, where the shortfall level is £50,000 (d) Value at Risk at the 95% confidence level (e) Tail Value at Risk at the 95% confidence level, conditional on the VaR being exceeded. [13] Hint: For part (e), you may wish to use the formula for the truncated first moment of a normal distribution given on page 18 of the Tables. Question 1.17 (Bookwork) Explain what is meant by the following terms, in the context of mean-variance portfolio theory: (i) efficient frontier [1] (ii) indifference curves [1] (iii) optimal portfolio. © IFE: 2017 Examinations [2] [Total 4] The Actuarial Education Company CT8: Q&A Bank Part 1 – Questions Page 9 Question 1.18 (Developmental) An investor can invest in only two risky assets A and B. Asset A has an expected rate of return of 10% and a standard deviation of return of 20%. Asset B has an expected rate of return of 15% and a standard deviation of return of 30%. The correlation coefficient between the returns of Asset A and the returns of Asset B is 0.6. (i) What is the expected rate of return if 20% of an investor’s wealth is invested in Asset A and the remainder is invested in Asset B? [1] (ii) What is the standard deviation of return on the portfolio if 20% of an investor’s wealth is invested in Asset A and the remainder is invested in Asset B? [1½] (iii) Explain why an investor who invests 20% of his wealth in Asset A and the remainder in Asset B is risk-averse. [1½] [Total 4] Question 1.19 (Bookwork) Consider a portfolio, P , which consists of N assets held in equal proportions. Let RP represent the return on the portfolio, and let Ri represent the return on asset i . The covariance of the return on asset i with that on asset j is Cij . (i) State the total number of data items needed to calculate E ( RP ) and var( RP ) . [2] (ii) Write down an expression for var( RP ) . (iii) Using your expression from part (ii), show that the specific risk of the portfolio (ie the risk associated with the individual assets) tends to zero in a well-diversified portfolio. [3] [Total 7] The Actuarial Education Company [2] © IFE: 2017 Examinations Page 10 CT8: Q&A Bank Part 1 – Questions Question 1.20 (Exam-style) (i) Describe in detail the assumptions underlying the use of mean-variance portfolio theory. [3] Consider a two-security world in which the returns yielded by Assets 1 and 2 are perfectly positively correlated, though they have different expected returns. (ii) Using the method of Lagrangian multipliers or otherwise, derive the equation of the efficient frontier in expected return-standard deviation space. [6] (iii) Use your answer in (i) to: (a) determine the gradient of the efficient frontier (b) show that the efficient frontier is a straight line in expected returnstandard deviation space that passes through the points representing Assets 1 and 2. [5] [Total 14] Question 1.21 (Exam-style) Consider a world in which there are only 2 securities, 1 and 2, such that: E1 = 5%, V1 = (10%) 2 E2 = 10%, V2 = (20%) 2 Let r denote the correlation coefficient between the returns yielded by the two securities. (i) Derive the equation of the opportunity set in E–V space. (ii) Derive expressions for the portfolio expected return E and the portfolio proportion x1 invested in Security 1 at the point of global minimum variance and hence comment briefly on how E and x1 vary with r . © IFE: 2017 Examinations [5] [5] [Total 10] The Actuarial Education Company CT8: Q&A Bank Part 1 – Questions Page 11 Question 1.22 (Exam-style) Show that in the single-index model of asset returns: Ei = a i + b i EM Vi = bi2 VM + Vei and Cij = bi b jVM where Vei is the variance of ei . [8] Question 1.23 (Developmental) Consider the data in the table below, which relates to Securities 1, 2 and 3. ai 1 0.0 Security 2 2.0 3 –2.2 bi 1.1 0.6 2.0 Vei 2.2 1.3 1.2 You are given that: ● the expected return and standard deviation of the market return are 10 and 5 respectively ● the returns of each security can be modelled using an appropriate single-index model. (i) Calculate: (ii) (a) the expected return and standard deviation of return for each security (b) the covariance of returns between each pair of securities. [4] Consider a portfolio which consists of Securities 1, 2 and 3 in equal proportions. Calculate: (a) the variance of the portfolio (b) the systematic risk of the portfolio (c) the specific risk of the portfolio. The Actuarial Education Company [3] [Total 7] © IFE: 2017 Examinations Page 12 CT8: Q&A Bank Part 1 – Questions Question 1.24 (Bookwork) Distinguish between the three main classes of multifactor model. © IFE: 2017 Examinations [6] The Actuarial Education Company CT8: Q&A Bank Part 1 – Solutions Page 1 Part 1 – Solutions Solution 1.1 (i) Definition of efficient market An efficient market is one in which every security’s price equals its investment value at all times. [1] In an efficient market information is fully reflected in the price. [½] This means that share prices adjust instantaneously and without bias to new information. [½] [Total 2] (ii) Three forms of Efficient Markets Hypothesis The strong form requires that prices reflect all information that is currently known – whether or not it is publicly available. [1] The semi-strong form requires that prices reflect all information that is publicly available. [1] The weak form requires that prices fully reflect all information contained in the past history of prices. [1] [Total 3] (iii) Implications of the Efficient Markets Hypothesis The past history of prices is a subset of publicly available information, so a market must be weak form efficient if it is semi-strong form efficient. Similarly, if it is strong form efficient it must also be semi-strong and weak form efficient. [1] The Efficient Markets Hypothesis does not imply that beating the market is impossible, since investors could out-perform the market by chance, or by accepting above average levels of market or systematic risk. [1] However, it does imply that it is not possible consistently to achieve superior (ie riskadjusted) investment performance net of costs without access to superior information. [½] The Actuarial Education Company © IFE: 2017 Examinations Page 2 CT8: Q&A Bank Part 1 – Solutions Weak form efficiency implies that it is impossible to achieve excess risk-adjusted investment returns purely by using trading rules based upon the past history of prices and trading volumes. It therefore suggests that technical analysis cannot be justified. [½] If only weak form efficiency applies, excess risk-adjusted returns are still possible by good fundamental analysis of public information. [½] The semi-strong form means that prices adjust instantaneously and without bias to newly published information. This implies that it is not possible to trade profitably on information gained from public sources. So neither fundamental analysis (without insider information) nor technical analysis will yield excess risk-adjusted returns. [½] Fundamental analysis may still, however, aid the investor in selecting the investments that are most suitable for meeting its investment needs and objectives. [½] If the strong form is correct then the market reflects all known knowledge about the company and consequently excess risk-adjusted returns are possible only by chance. This implies that insiders cannot profit from dealing on inside information, ie insider trading is not profitable. [½] [Total 5] Solution 1.2 (i) Informational efficiency The market for a particular security is said to exhibit informational efficiency if new information is incorporated quickly and accurately into the price of the security. [1] The main difficulties in testing for informational efficiency are: ● It is hard to establish exactly when information arrives. This may be because many events are widely rumoured prior to being announced officially. [1] ● The theory of market efficiency does not predict exactly how a particular piece of information should be incorporated into the price of a security, ie what effect it will have on the price. We therefore need to make an assumption about this. However, this means that if the price does not change in the way we expected, this may be due to an invalid assumption, rather than an inefficient market. [1] [Total 3] © IFE: 2017 Examinations The Actuarial Education Company CT8: Q&A Bank Part 1 – Solutions (ii) Page 3 Discuss the empirical evidence The empirical evidence suggests that markets do over-react to certain events and underreact to other events and that the over/under-reaction is corrected over a long time period. [1] If this is true then traders might be able to take advantage of the slow correction of the market to make excess risk-adjusted returns, and so efficiency would not hold. [1] Some of the effects found by studies can be classified as over-reaction to events. For example: 1. Past performance: past winners tend to be future losers and vice versa. The market appears to over-react to past performance. [1] 2...
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