Mid 2016, questions and answers PDF

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FINS2624

MOCKTERM

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FAMILY NAME OTHER NAMES STUDENT ID SIGNATURE

THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF BANKING AND FINANCE

M oc kt er m

FINS2624 PORTFOLIO MANAGEMENT MID-TERM EXAMINATION - SEMESTER 1, 2016

TIME ALLOWED: 2 HOURS AND 15 MINUTES (or whatever)

To make sure that we can identify your exam if your student ID number is hard to read, please tick the boxes below to fill in your seven digit student ID number. Detailed instructions are on the next page. 1 2 3 4 5 6 7 8 9 0

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INSTRUCTIONS 1) Write your name, student ID number and signature in the assigned space on the front page. 2) To make sure that we can identify your exam if your student ID number is hard to read, please tick the boxes corresponding to your student ID number on the front page. Do this by marking the box corresponding to each of the digits in your seven digit student ID number, going from left to right. For example, my ID number is z3352704, so I would fill in the boxes as below.

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3) Fill in the details requested by the generalized answer sheet. 4) This paper has two sections: Section A: 30 multiple choice questions (worth a total of 30 marks) Section B: 5 free-format problem (worth a total of 42 marks) 5) Mark your answers to the multiple choice questions of section A in the generalized answer sheet using a 2B pencil. Write down the solution of the free format problem in the answers sheets in the back. All answers and solutions must be written in ink. Pencils may not be used. 6) Notation and terminology in this exam are as defined in the lectures. 7) Assumptions that have been made throughout the lectures may be assumed throughout the exam unless otherwise stated. For instance, unless explicitly relaxed, you may assume that there are no transaction costs, that bonds have no default risk, that investors are rational, that there are no restrictions on short positions etc. 8) Total number of marks for this paper is 72. 9) This is a closed book exam. Except calculators according to the UNSW guidelines, no other means are allowed. 10) This question sheet and the generalized answer sheet must be returned in full. Do not tear the pages. 11) You must prove your identity using your student ID card when turning in the exam.

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FOMRULA SHEET

The price of a bond, P , is given by:   FV 1 c 1− + P = T (1 + y)T (1 + y) y where c is the dollar coupon, y is the yield-to-maturity, T is the time to maturity and F V is the face value. If X and Y are two stochastic variables and α and β are two constants then: E (X + Y ) = E (X) + E (Y ) E(αX ) = αE (X) V ar(X) = Cov(X, X) Cov(X, Y ) = Cov(Y, X) Cov(X, Y ) = ρXY σX σY Cov(αX, βY ) = αβCov (X, Y ) The solution to the quadratic equation ax2 + bx + c = 0 is x1/2 =

−b ±

√

b2 − 4ac 2a

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DISCLAIMER

The formula sheet and instructions will be the same in the actual exam. However, the actual exam will consist of about 47 multiple choice questions and no short answer questions. Questions appearing in this mock exam are typically questions I have removed from the circulation of actual exam questions for one reason or another. That is, they’re not a random sample so the questions you’ll get in the actual exam may be somewhat different in character. This mock exam should nevertheless give you some idea about what to expect. I recommend that you try to solve all questions on your own before looking at the solutions.

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SECTION A OF THE MOCKTERM EXAM 30 MARKS IN TOTAL THIRTY MULTIPLE CHOICE QUESTIONS

• Mark the answers in the generalized answer sheet using a 2B pencil. Or don’t, since this is a mockterm. • Each question is worth one mark and there is no negative marking.

1. Which of the following statements about bonds is true? a) A bond with a higher coupon rate must be a better investment than a bond with a lower coupon rate. b) A bond that trades at a discount must be a better investment than a bond that trades at a premium. c) A bond with a higher yield-to-maturity is a better investment than a bond with a lower yield to maturity. d) Several of the above statements are true. e) None of the above statements are true. E is correct. C is false since the yield-to-maturity, y is the constant hypothetical interest rate that solves   FV 1 c 1− + P = (1 + y)T y (1 + y)T It says nothing about whether the bond is correctly priced (which we assume it is unless we have some specific reason to believe otherwise) or about how good an investment it is. Similar arguments go for A and B, e.g. the statements have no relevant pricing implications. 2. Which of the following statements about the efficient frontier is true? a) In practice, only the market portfolio is on the efficient frontier. b) The portfolios on the efficient frontier are only dominated by other portfolios on the efficient frontier. c) The efficient frontier tends to be concave. d) Several of the above statements are true. e) None of the above statements are true. The efficient frontier is a set of portfolios that minimize the standard deviation for their respective expected returns., so A is false. The portfolios on the efficient frontier are not dominated by any portfolios, so B is false. C is correct. Page 5 of 26 Please see over

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3. Which of the following statements about the yield-to-maturity is true? a) Discounting all cash flows of a bond with the bond’s yield-to-maturity only gives us the correct price if we have a flat term structure of interest rates. b) The yield-to-maturity is upwards sloping. c) The yield-to-maturity is always a spot rate. d) Several of the above statements are true. e) None of the above statements are true. E is correct. The yield-to-maturity, y is the constant hypothetical interest rate that solves   FV 1 c 1− + P = T (1 + y)T (1 + y) y The concept does not rely on the actual existence of such an interest rate, so A and C are false. By definition, it is a constant so B is false.

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4. Which of the following statements about bonds is true? a) A zero-coupon bond always trades at a discount as long as its yield-to-maturity is positive. b) A zero-coupon bond tends to have a lower yield-to-maturity than a coupon bond with the same time to maturity. c) In reality, zero-coupon bonds have higher default risk than coupon bonds. d) Several of the above statements are true. e) None of the above statements are true. A is correct. If the bond’s yield is positive the face value will be discounted and there are no coupons to balance that effect out. B is incorrect as the coupon rate does not have any direct effect on the yield. If anything, the zero-coupon bond would tend to have a higher yield as it has a higher duration and the term-structure of interest rates is typically (but not necessarily) upwards sloping. C is false as the coupon rate says nothing about default risk. 5. Which of the following statements about investors are true? a) A mean-variance investor will always choose the asset with the highest return. b) A mean-variance investor will always choose the asset with the lowest risk. c) A mean-variance investor will trade off expected returns and risk. d) Several of the above statements are true. e) None of the above statements are true. C is correct. The investor will balance expected returns and risk against each other. 6. Which of the following statements about duration are true? a) The duration of a liability is always negative. b) The duration of a bond is always positive. c) The duration of a portfolio is a weighted average of the duration of the bonds that are included in that portfolio. d) Several of the above statements are true. e) None of the above statements are true. D is correct. A is false and B is true, since the duration of a liability or a bond is always positive. This is obvious if you think about duration as an adjusted time-to-maturity measure. C is true. See lecture notes 2 for a sketch of the proof. 7. Which of the following statements about yield-to-maturity are true? a) A bond with a yield-to-maturity of 7% is never more sensitive to changes in the yield than a bond with a yield to maturity of 5%. b) A bond with a yield-to-maturity of 7% is always more sensitive to changes in the yield than a bond with a yield to maturity of 5%. c) A bond with a yield-to-maturity of 5% is never more sensitive to changes in the yield than a bond with a yield to maturity of 7%.

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d) A bond with a yield-to-maturity of 5% is always more sensitive to changes in the yield than a bond with a yield to maturity of 7%. e) None of the above statements are true. E is correct. The statements are not true, since the sensitivity depends on duration.

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8. Which of the following statements about diversification are true? a) The diversification benefits in a portfolio of two assets are smaller when the correlation between the returns of the assets is larger. b) The diversification benefits in a portfolio of two assets are larger when the correlation between the returns of the assets is larger. c) The diversification benefits of combining three perfectly correlated assets is typically larger than the diversification benefits of combining two perfectly correlated assets. d) Several of the above statements are true. e) None of the above statements are true. A is correct. A is true and B is false as the less correlated two assets are, the more of their risk will ”cancel out”. C is false as there are no diversification benefits of combining perfectly correlated assets. 9. Which statement is true regarding the market portfolio? a) It includes all publicly traded financial assets. b) It lies on the efficient frontier. c) All securities in the market portfolio are held in proportion to their market values. d) It is in principle unobservable. e) All of the above statements are true. E is correct. 10. Which of the following statements is false about the capital allocation line (CAL)? a) It includes all publicly traded financial assets. b) Investors prefer assets further to the right on the CAL to assets further to the left on the CAL. c) The risk-free asset plots on the CAL. d) More than one of the above statements are false. e) None of the above statements is false. D is correct. A is false as assets generally carry some unsystematic (and hence unpriced) risk. They will therefore plot below the CAL. B is false (as a general statement) because the investors’ choice of assets on the CAL depend on their risk aversion. 11. Which of the following statements is false about the CAPM? a) The CAPM describes the required return of any risky asset. b) The CAPM assumes that investors agree on the statistical properties of all assets. c) The CAPM assumes that all investors have the same preferences. d) More than one of the above statements are false. e) None of the above statements is false. C is correct. Investors typically have different risk preferences, and the CAPM allows for this. Page 9 of 26 Please see over

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12. The risk free rate is 4% and the expected return of the market portfolio is 12%. If a stock has a CAPM β of 1.5, a standard deviation of returns of 20% and a current price of $100, what is the expected price one year from now? a) $100 b) $116 c) $120 d) There’s not enough information to say. e) None of the above. First find the expected return through the CAPM equation: E(r) = 0.04 + 1.5(0.12 − 0.04) = 0.16 Since the price today is $100, the expected price in one year is 100(1 + 0.16) = 116. B is correct. 13. If the standard deviation of a stock’s return increases, what happens to its required return? a) It decreases. b) It increases. c) It stays the same. d) There’s not enough information to tell. e) None of the above. D is correct, because the standard deviation has a systematic and an unsystematic component. If the standard deviation increases as a result of an increase in unsystematic risk alone, the required return is not affected. 14. Suppose a stock that was traded on the market magically disappears. What happens to the CAL? a) Its slope decreases. b) Its slope increases. c) Its slope stays the same. d) There’s not enough information to tell. e) None of the above. Since the stock was traded, it was held in the optimal risky portfolio. By definition, the optimal risky portfolio maximizes the Sharpe ratio. If one stock disappears, the portfolio has to be adjusted, and it can only be adjusted to a worse position. A is correct. For the next 3 questions, assume that there is some risky portfolio Q, which has an expected return of 15%, and a standard deviation of 12%. The risk-free rate is 5%. There is also some asset P that is not part of Q, which has an expected return of 10%, and a standard deviation of 7%. 15. What is the Sharpe ratio of Q? a) 0.71 Page 10 of 26 Please see over

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b) 1 c) 1.34 d) 0.83 e) There’s not enough information to tell D is correct. From the definition of the Sharpe ratio: SQ =

0.15 − 0.05 ≈ 0.83 0.12

16. What is the Sharpe ratio of the market portfolio? a) Between 0.71 and 1.34 b) Larger than or equal to 0.83 c) Exactly 1 d) Lower than or equal to 0.83 e) There’s not enough information to tell We cannot calculate the Sharpe ratio of the market, but we know that it must be the best possible Sharpe ratio given the investment universe. Since SP =

0.1 − 0.05 ≈ 0.71 0.07

SQ =

0.15 − 0.05 ≈ 0.83 0.12

The market portfolio must have a Sharpe ratio that is larger or equal to 0.83. B is correct. 17. You want to invest in some combination of the Q and the risk-free asset to achieve an expected return of 40%. What is the standard deviation of your returns? a) 42% b) 32% c) 16% d) 40% e) There’s not enough information to tell Let wQ be your investment in Q. It must be chosen so that (1 − wQ )0.05 + wQ 0.15 = 0.4 0.05 + wQ (0.15 − 0.05) = 0.4 wQ =

0.4 − 0.05 = 3.5 0.15 − 0.05

As we saw in lecture 5, it follows that the standard deviation is:

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σ = wQ σQ = 3.5 · 0.12 = 0.42 A is correct. For the next 4 questions, consider a market where the risk free rate is 3% and the expected return on the market portfolio is 10%. 18. What is the required rate of return of an investment with a beta of 0.5? a) 10% b) 5% c) 3% d) There’s not enough information to tell. e) None of the above. According to the CAPM, the required rate of return is E(r) = 0.03+0.5(0.1−0.03) = 0.065 E is correct. 19. What is the standard deviation of the market portfolio returns? a) 1 b) 20% c) 22.59% d) There’s not enough information to tell. e) None of the above. D is correct. 20. An investment has a beta of 0.8 and an expected return of 8%. Should you undertake the investment? a) Yes. b) No. c) It doesn’t matter. d) There’s not enough information to tell. e) None of the above. The required rate of return is E(r) = 0.03 + 0.8(0.1 − 0.03) = 0.086 > 0.08. Since the required return is larger than the expected return, B is correct. 21. If the market expects a return of 20.5% from a certain stock, what is its beta? a) 21 b) 2.5 c) 2.45 d) There’s not enough information to tell. e) None of the above. Page 12 of 26 Please see over

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The CAPM states that E (ri ) = rf + β(E [rM ] − rf ) β=

0.205 − 0.03 E(ri ) − rf = = 2.5 E(rM ) − rf 0.1 − 0.03

B is correct. 22. According to the CAPM a well-diversified portfolio’s rate of return is a function of a) market risk. b) unsystematic risk. c) unique risk. d) reinvestment risk. e) liquidity risk. A is correct.

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23. Which of the following statements is true about the security market line, SML? a) It is a different name for the CAL. b) It contains all efficient portfolios. c) It is convex for risk averse investors. d) More than one of the above statements are true. e) None of the above statements are true. B is correct. 24. The total value of the market portfolio is $100,000. Stock A is trading at $10. The company has issued 1,000 stocks. There are 5 other companies on the market. What is the weight of company A in the market portfolio? a) 20% b) 0.01% c) 10% d) 1% e) 25% The weight of an asset i in a market with N assets is wi =

Vi N P Vj

j=1

where Vj is the market value of asset j. In this case we have wA =

10 · 1000 = 0.1 100000

C is correct. 25. The shape of the term structure of interest rates is determined by a) Expectations on future spot rates b) The risk aversion of investors c) Mismatches between the investment horizon of investors in bonds and issuers of bonds d) A and C e) All of the above The expectations hypothesis predicts A and the liquidity preference theory predicts B and C. Since both effects are likely at work, E is correct. 26. The convexity of a bond... a) Leads to an undesirable asymmetry in the price response to yield changes b) Leads to a desirable asymmetry in the price response yield changes c) Is a measure of the bond’s time to maturity Page 14 of 26 Please see over

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d) A and C e) B and C B is correct. Please see lecture slides 3 for details. 27. If all spot rates decreased by 1%, the duration of a 10-year 5%-coupon bond would... a) Increase b) Decrease c) Be unaffected d) Change in a direction that depends on its convexity e) There’s not enough information to tell If all spot rates decreased, the yield of all bonds would decrease too. The present value of cash flows further away in time would increase relatively more, so the duration would increase. A is correct.

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28. Duration... a) Is a measure of the time to maturity of a bond’s cash flows b) Is a measure of the sensitivity of a bond’s price to changes in the yield c) Can be used to approximate the price of a bond at other yields d) A and B e) All of the above E is correct. 29. According to the expectations hypothesis a) The term structure of interest rates is upwards sloping b) Investors are risk-neutral c) Future spot rates are known today d) All of the above e) None of the above E is correct. The expectations hypothesis states that E(s rt ) =s ft , which does not imply any of the statements. 30. A synthetic instrument... a) Is typically a portfolio of other instruments b) Is typically used to set up an arbitrage ...