Need help with the 70 multiple choice questions for final exam - if you can, please provide explanation for harder questions.

A s ae o . s h r d n. . Surname: ______________________ Q1 Given names: ___________________ Q2 Student ID number: ______________ Q3 Signature: ______________________ Q4 THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF BANKING AND FINANCE FINS2624 PORTFOLIO MANAGEMENT FINAL EXAMINATION - SESSION 2, 2010 1. Time allowed - 3 hours 2. Reading time - 10 minutes 3. This examination paper has 22 printed pages 4. There are two parts. Part A has 70 multiple-choice questions, 1 mark each. Part B has 4 short-answer questions and a total of 30 marks. The entire paper has 100 marks. 5. Answer all questions. 6. For Part A, mark the answers on the generalised answer sheet provided. For Part B, write the answers in the space provided in this examination question booklet 7. This paper must not be retained by candidate 8. Candidates may bring to the examination approved calculators 9. Candidates must not bring to the examination any notes or books 10. Print your name and student number, and sign the paper on the top left hand corner of this page. The following equations are provided: U = E(r) - 0.005A2 Ct = StN(d1) - Xe-r(T - t)N(d2) 2 S ln t r T t X 2 where d1 ; d 2 d1 T t T t St is the current stock price at time t X is the exercise price r is the continuously compounded risk free rate per annum is the standard deviation of returns on the underlying stock T-t denotes the time remaining to maturity Page 1 of 22 A s ae o . s h r d n. . SECTION A - 70 Multiple-Choice Questions (1 mark each) Mark the answer to each question on the generalised answer sheet provided. Refer to the following table for Questions 1 to 4. The table is extracted from the Reserve Bank of Australia website, http://www.rba.gov.au/Statistics/indicative.html, on Monday, 20 July 2009. DAILY STATISTICAL RELEASE - Release date: Friday 17 July 2009 Indicative Mid Rates of Selected Commonwealth Government Securities (CGS) Treasury Fixed Coupon Bonds Coupon Maturity Yield (% p.a.) 7.50% Sep 2009 3.015 5.25% Aug 2010 3.315 5.75% Jun 2011 3.910 5.75% Apr 2012 4.410 1) For the 5.25% Aug 2010 CGS, the market is demanding A. a higher rate of return now than the time when the bond was issued. B. the same rate of return now as the time when the bond was issued. C. a lower rate of return now than the time when the bond was issued. D. an unfair return from the government. E. insufficient information to tell. 2) On Friday, 17 July 2009 the current yield of the 5.25% Aug 2010 CGS is A. smaller than 3.315% B. 3.315% C. larger than 3.315% but smaller than 5.25% D. 5.25% E. larger than 5.25% 3) Assuming T+2, on Friday, 17 July 2009 the capital (or adjusted) price of the 5.25% Aug 2010 CGS is _______ than the settlement price by $ _______. A. less; 0.540 B. less; 0.639 C. less; 1.509 D. less; 2.262 E. None of the above 4) Other things being equal, on the basis of T+2, for the 5.25% Aug 2010 CGS, on which of the following calendar day will the bond experience a fall in settlement price by an amount that is close to the amount of coupon interest per six-month period? A. Tuesday, 4 Aug 2009 B. Wednesday, 5 Aug 2009 C. Thursday, 6 Aug 2009 D. Friday, 7 Aug 2009 E. none of the above Page 2 of 22 A s ae o . s h r d n. . The following information applies to Questions 5 and 6. On Tuesday, 17 November 2009, the yield to maturity of the 5.25% Aug 2010 CGS was 4.150%. 5) On the basis of T+2, the settlement price was A. 99.206 B. 100.289 C. 100.786 D. 102.155 E. none of the above 6) Had you purchased the 5.25% Aug 2010 CGS on Tuesday, 17 November 2009 and sold it on Friday, 6 August 2010 on the basis of T+2, you would have sold the bond ___ and ___ the coupon interest on 15 August 2010. A. cum interest ; not received B. cum interest; received C. ex interest; not received D. ex interest; received E. none of the above 7) Which of the following attribute of a CGS is set by the government? A. Maturity date B. Coupon rate C. Yield to maturity D. A and B E. A, B, and C 8) Assume annual interest payment. The yields to maturity of a 10% 1-year bond and a 12.5% 2-year bond are 5.10% and 6.25% respectively. This term structure implies that the spot rate of a two-year bond is A. 6.259% B. 6.312% C. 6.319% D. 6.418% E. insufficient information to solve the problem Page 3 of 22 A s ae o . s h r d n. . The following term structure of interest rates applies to Questions 9 and 10. Assume that coupon interests are paid annually. Coupon rate % pa Time to Maturity YTM % pa 10.0 1 year 5.10 12.5 2 years 5.25 8.0 3 years 5.40 9) According to the expectations hypothesis, investors with an investment horizon of one year would A. prefer the 3-year bond to the other two bonds as it offers the largest yield B. prefer the 1-year bond to the other two bonds as its cash flows are certain C. prefer the 1-year bond to the other two bonds as its maturity matches the investment horizon D. prefer the 2-year bond to the other two bonds as it offers the largest coupon rate E. none of the above 10) The term structure implies that f(1,1), the forward rate of a 1-year bond one year from now is: A. 5.42% B. 6.42 C. 6.52 D. 6.74 E. none of the above 11) Assume semi-annual interest payment. You purchased and held a five-year bond for one and a half years. At the time of purchase and sale, the yield is the same as the coupon rate of 10%. If you were able to reinvest all the coupon interests received at 12% per annum compounded semi-annually, what is the holding period return? A. 10.094% B. 10.188% C. 11.889% D. 13.745% E. insufficient information 12) The expectations hypothesis asserts that market expectations of future interest rates are unbiased. This assertion implies that market expectations of future interest rates A. are always accurate B. can be above or below actual interest rates C. are always smaller than actual interest rates by the liquidity premium D. are always larger than actual interest rates by the liquidity premium E. none of the above Page 4 of 22 A s ae o . s h r d n. . 13) Which of the following is correct about the liquidity premium hypothesis? A. Issuers of long-term bond offer investors a higher than expected return to minimise uncertainty in the costs of refinancing. B. Household lenders demand a liquidity premium as they prefer to lend for a term that is longer than the maturity of the bond C. We add liquidity premium to forward rates to arrive at market expectation of future interest rates D. A and C E. A, B and C 14) According to the liquidity premium hypothesis, which of following has the largest liquidity premium? f(n,t) denotes the forward rate of a n-period bond in t periods' time. A. f(10,5) B. f(10,2) C. f(5,2) D. f(2,5) E. insufficient information to tell 15) The duration of a coupon bond is positively related to the bond's A. time to maturity. B. yield to maturity. C. coupon rate. D. B and C E. A, B, and C 16) Suppose you forecast that there will be a downward and parallel shift in the yield curve in the near future. You are holding an equally weighted portfolio in the following bond series now: 6.50% May 2013, 6.25% Apr 2015, 6.00% Feb 2017 Should the forecast come true, you would increase the portfolio value the most in the short-run by liquidating investment in the _____ series and investing the money in the ______ series now. A. 6.50% May 2013, 6.00% Feb 2017 B. 6.25% Apr 2015, 6.00% Feb 2017 C. 6.00% Feb 2017, 6.50% May 2013 D. 6.00% Feb 2017, 6.25% Apr 2015 E. Insufficient information 17) Which of the following is free from price and income risks? A. Buy and hold a CGS with six months or less to maturity B. Buy a 6.25% Apr 2015 CGS and the beginning of this session and sell the bond at the end of this session C. Buy a 5-year zero coupon bond and hold the bond for 2 years D. A and C E. None of the above Page 5 of 22 A s ae o . s h r d n. . 18) Other things being equal, the duration of a zero coupon bond A. does not change over time B. is inversely related to the bond's yield to maturity C. increases as the bond approaches the expiration date D. is independent of the bond's yield to maturity E. none of the above 19) Duration is defined as the weighted average time to recover the cost of a bond investment. The weight allocated to each future cash flow is A. computed by dividing the cash flow received by the cost of investment. B. computed by dividing the present value of the cash flow received by the present value of all future cash flows. C. the time when the cash flow is received. D. computed by dividing the time when the cash flow is received by the maturity of the bond. E. none of the above 20) You are currently holding a portfolio that consists of (a) $2000 cash and (b) one 10-year zero coupon bond with a face value of $1000 and 12% yield to maturity. The Macaulay duration of the portfolio is A. 1.3866 B. 2.4356 C. 2.7826 D. 3.9171 E. none of the above 21) Which of the following bond is the most price sensitive to interest rate movements? A. A bond with short term to maturity and high coupon rate B. A bond with short term to maturity and low coupon rate C. A bond with long term to maturity and low coupon rate D. A bond with long term to maturity and high coupon rate E. None of the above 22) Income risk is related to A. the uncertain amount of interest earned from reinvesting the coupon interests received from a bond investment B. the uncertain capital gain/loss arising from a bond investment C. the uncertain proceeds of sale when a bond is sold before the maturity date D. B and C E. A, B, and C Page 6 of 22 A s ae o . s h r d n. . 23) The Macaulay duration equation can be obtained by differentiating the present value of the cash flows of a coupon bond with respect to A. The coupon rate B. The discount rate C. The number of periods to maturity D. Income and price risks E. The weights of the cash flows 24) According to the mean-variance criterion, which of the following combination dominates all others? A. E(R) = 0.15; Variance = 0.20 B. E(R) = 0.10; Variance = 0.20 C. E(R) = 0.10; Variance = 0.25 D. E(R) = 0.15; Variance = 0.25 E. None of the above 25) The standard deviation of returns of a portfolio of risky assets is determined by A. the allocation of funds to the constituent assets of the portfolio. B. the correlation coefficients among the constituent assets of the portfolio. C. the standard deviations of returns of the constituent assets of the portfolio. D. B and C E. A, B, and C 26) In the absence of a risk free asset, which of the following ranking rule is needed to locate the optimal portfolio of risky assets? A. The portfolio with the largest utility is preferred. B. The portfolio with the largest reward to variability ratio is preferred. C. For a given level of expected return, the portfolio with the lowest level of risk is preferred. D. For a given level of risk, the portfolio with the largest expected return is preferred.. E. None of the above 27) The standard deviation of return on ABC and XYZ are 0.1 and 0.4 respectively. The correlation coefficient between the two assets is 0.6. The standard deviation of return of an equally weighted portfolio of the two assets is A. 23.35% B. 28.28% C. 28.72% D. 29.15% E. none of the above Page 7 of 22 A s ae o . s h r d n. . 28) Risk averse investors A. never take risk B. rank investments according to expected return only C. always demand a premium above the risk free asset for risky investments D. always have a negative degree of risk aversion E. None of the above 29) Given the portfolios lying on the capital allocation line, an investor should choose the portfolio that A. maximises his/her expected return B. minimises his/her risk C. maximises the reward to variability ratio D. maximises his/her expected utility E. none of the above 30) In the presence of a risk free asset, which of the following ranking rule is needed to locate the optimal portfolio of risky assets? A. For a given level of expected return, the portfolio with the lowest level of risk is preferred. B. The portfolio with the largest reward to variability ratio is preferred. C. The portfolio with the largest utility is preferred. D. B and C. E. A, B, and C. 31) If the borrowing rate is higher than the lending rate, which of the following is correct? A. Portfolios lying on the capital allocation line may have different reward to variability ratios. B. Investors with different degrees of risk aversion will always choose the same portfolio of risky assets. C. The capital allocation line is a straight line. D. Two of the above E. None of the above Information for Questions 32 and 33: Imagine that there are only two efficient portfolios of risky assets, EP1 and EP2. EP1 offers 10% expected return and 4% risk. EP2 offers 16% expected return and 6% risk. An investor has $100 to invest and can borrow or lend risk-free at 4%. 32) Calculate the minimum level of return required by the investor if he can tolerate 20% risk. A. 44% B. 46% C. 48% D. 54% E. None of the above Page 8 of 22 A s ae o . s h r d n. . 33) In order to achieve a 64% return, the best way is to: A. borrow $400 at the risk-free rate and invest $500 in EP2. B. borrow $500 at the risk-free rate and invest $600 in EP1. C. borrow $1000 at the risk-free rate and invest $1100 in EP1. D. borrow $900 at the risk-free rate and invest $1000 in EP1. E. None of the above 34) The beta of CBA is 0.8. The expected return on the market is 15% and the risk free rate is 5%. CBA is currently priced at $25. If the market predicts that CBA will pay a dividend of $0.50 at the end of this year when its price will end up at $30, CBA is lying A. above the capital market line B. below the capital market line C. above the security market line D. below the security market line E. none of the above 35) As diversification increases, the total variance of a portfolio approaches A. 0. B. 1. C. systematic risk. D. unsystematic risk. E. none of the above 36) The single index model may be applied to A. conduct an event study. B. evaluate funds performance. C. estimate beta. D. A and C E. A, B and C 37) The difference between the actual excess return of a stock and that predicted by the Single Index Model (SIM) is known as A. alpha, the intercept. B. beta, the slope. C. e, the residual return. D. the risk premium. E. none of the above Page 9 of 22 A s ae o . s h r d n. . 38) In the context of the single index model, random and independent firm specific news are responsible for the observation of A. a non-zero alpha coefficient. B. a non-zero beta coefficient. C. non-zero residual returns. D. A and C E. A, B, and C 39) The single index model ______. A. is the empirical version of the capital asset pricing model B. studies the relationship between expected return and systematic risk C. studies the relationship between excess stock returns and excess market index returns D. A and C E. B and C 40) Based on the outputs of the single index model regression, a stock is said to have an abnormal return if A. the intercept is significantly different from 0. B. the slope coefficient is significantly different from 0. C. the average residual return is significantly different from 0. D. A and C E. A, B and C 41) Which of the following is correct about R2, one of the outputs from the Single Index Model regression? A. It shows the proportion of unsystematic risk of the stock relative to its total risk. B. The square root of R2 is the correlation coefficient between the excess returns of the stock and the market. C. R2 is the square of excess return. D. A and B E. A, B, and C 42) Which of the following is indicative of an inefficient market? A. Deviation of market prices from the fundamentals over an extended period B. Predictable returns that are based on dividend yields C. Predictable returns that are based on past returns D. A and B E. A, B and C 43) Which of the following strategy is shown to produce positive abnormal returns? A. Invest in stocks at the top end of the return scale (where return is measured over the past year) for a period of 3 to 6 months B. Invest in spinoffs and their parents for a period of 3 years C. Invest in initial public or seasoned equity offerings for a period of 5 years D. A and B E. A, B and C Page 10 of 22 A s ae o . s h r d n. . 44) Which of the following is correct about an event study? A. it may be used to test whether the market is semi-strong form efficient B. it measures the relationship between an event that affects securities and the return of those securities C. it may be used to assess the speed and timing of stock price reaction to a firm specific event D. A and C E. A, B and C 45) Researchers have found that most of the small firm effect occurs A. randomly B. in January C. in December D. during the spring months E. during the summer months 46) Which form of market efficiency do the chartists not believe in? A. weak form B. semi-strong form C. strong form D. all of the above E. none of the above 47) Proponents of the efficient market hypothesis think technical analysts A. should focus on relative strengths. B. should focus on resistance levels. C. should focus on momentum strategies. D. A, B and C E. are wasting their time. 48) In a semi-strong efficient market, A. security prices react quickly to new information B. investors are unable to use fundamental analysis to consistently earn abnormal returns C. investors can never earn an abnormal return D. A and B E. A, B, and C 49) Which of the following would provide evidence against the semi-strong form of the efficient market hypothesis? A. Observing a post-announcement drift in cumulated average residuals B. Past losers, stocks with the worst 3- to 5-year past return, turn out to be future winners C. Low price earnings ratio stocks tend to have positive abnormal returns D. A and C E. A, B and C Page 11 of 22 A s ae o . s h r d n. . 50) Which of the following is used to explain the underperformance of actively managed funds relative to the index funds? A. Brokerage cost B. Bid-ask spread C. Market impact cost D. A and B E. A, B and C Consider the following portfolios for Questions 51 and 52. All values are annualised and the risk-free rate is 10%. Portfolio Average Standard deviation Residual standard Beta return of returns deviation A 20% 30% 4.00% 0.8 B 18% 10% 1.25% 1.0 C 23% 20% 1.20% 1.2 All Ords 20% 16% 1 51) The Treynor index of portfolio B is A. -0.02 B. 0.08 C. 0.80 D. 6.4 E. none of the above 52) The appraisal ratio of portfolio C is A. 0.8333 B. 2.1667 C. 10.83 D. 19.17 E. none of the above Page 12 of 22 A s ae o . s h r d n. . Consider the following portfolios for Questions 53 and 54. All values are annualised and investors can borrow and lend at a risk-free rate of 5%. Portfolio A B C All Ordinaries index Average return 10% 12% 22% 7% Standard deviation Beta of returns 0.16 0.65 0.53 0.75 0.63 2.50 0.25 Residual deviation 0.01 0.50 0.10 standard 53) Which of the above portfolios has the highest abnormal return? A. Fund A B. Fund B C. Fund C D. All Ordinaries index E. The abnormal returns for all of the funds is zero 54) An investor plans to invest all the spare money in a managed fund. The investor does not have any other investment. Which fund should the investor choose? A. Fund A B. Fund B C. Fund C D. Indifferent between A and C E. Indifferent between B and C 55) If a stock's price is S0 at time zero and S1 one period later, then the continuously compounded return on the stock, r, is given by A. 1 + r = ln(S1/S0) B. r = ln(S1/S0) S1 S 0 C. r = S0 D. 1 + r = e S1 / S 0 E. none of the above 56) Tracy won $10,000 from the Channel 7 game show \"Deal or No Deal\". She already has a $50,000 investment in an index fund. Tracy wishes to invest the windfall in an active portfolio managed by either Macquarie Bank or Platinum Asset Management, the most appropriate performance index to evaluate the two active portfolios is the A. Jensen alpha B. Sharpe index C. Treynor index D. appraisal ratio E. diversification index Page 13 of 22 A s ae o . s h r d n. . 57) When a superannuation fund is large and has many managers, the ___________ is typically used in practice to evaluate individual managers. A. diversification index B. Sharpe index C. Treynor index D. appraisal ratio E. none of the above 58) Suppose two portfolios have the same average return, the same beta, but portfolio A has a higher standard deviation of returns than portfolio B. According to the Treynor index, the performance of portfolio A __________. A. is better than the performance of portfolio B B. is the same as the performance of portfolio B C. is poorer than the performance of portfolio B D. cannot be measured as there is no data on the alpha of the portfolio E. none of the above 59) Traders may use options alone or together with the underlying stock to benefit from A. no or immaterial change in the value of the underlying stock B. persistent upward or downward movements in the value of the underlying stock C. volatility movements in the underlying stock D. B and C E. A, B and C 60) Which of the following scenario violates the assumptions of the Black Scholes model? A. Stock returns have fat tails B. Stock movements follow a jump-diffusion process C. Time-varying volatility D. A and C E. A, B and C 61) If you write a put option written on a stock, which of the following is true? A. You may close off the position by buying another put option written on a different stock B. The final payoff is unlimited. C. You gain the right to sell the underlying shares on or before the expiration date at the predetermined exercise price. D. B and C E. None of the above 62) A European put option with six months to maturity has a strike price of $35. The underlying stock, which does not pay dividends, now sells for $34. The put premium is $1.58. The time value of the put option is A. zero B. $0.58 C. $1.00 D. $1.58 E. $35.58 Page 14 of 22 A s ae o . s h r d n. . Information for Questions 63 to 65: Today the share price of CBA is $23. You write one CBA Sep $22.75 call at a premium of $0.60, buy two CBA Sep $23 calls at a premium of $0.45 for each option, and write one CBA Sep $23.25 call at a premium of $0.32. Assume the size of one contract is one share of the underlying asset. 63) What is the position value today? A. -$0.25 B. -$0.02 C. $0.02 D. $0.25 E. None of the above 64) If the share price of CBA rises to $24.00 on the expiration date, the position value on the expiration date is A. $0.00 B. $0.20 C. $0.25 D. $0.50 E. none of the above 65) If the share price of CBA rises to $24.00 on the expiration date, the profit/loss on the expiration date is A. -$0.02 B. $0.02 C. $0.25 D. $0.27 E. None of the above 66) The put-call parity equation for European options is derived by constructing two portfolios in such a way that their values at the common option expiration date are equal and the assumption that one can borrow and lend at the same risk free rate, r. One portfolio, P1, consists of a long stock and a long put (with a strike price of $X and time remaining to maturity T). The second portfolio, P2, consists of A. a long call with a strike price of Xe-rT and an investment of Xe-rT in the risk free asset. B. a long call with a strike price of X and an investment of X in the risk free asset. C. a long call with a strike price of X and an investment of Xe-rT in the risk free asset. D. a long call with a strike price of Xe-rT and an investment of X in the risk free asset. E. none of the above Page 15 of 22 A s ae o . s h r d n. . 67) A collar strategy contains A. a short out-of-the-money put, a long out-of-the-money call, and a long position in the underlying asset. B. a long out-of-the-money put, a short out-of-the-money call, and a long position in the underlying asset. C. a long out-of-the-money put, a long out-of-the-money call, and a short position in the underlying asset. D. a long out-of-the-money put, a short out-of-the-money call, and a short position in the underlying asset. E. none of the above 68) If ABC's standard deviation of monthly continuously compounded returns is 1.2%. Its annualised standard deviation of continuously compounded returns is A. 4.16% B. 13.15% C. 14.40% D. 37.95% E. None of the above The following payoff diagram refers to the Questions 69 and 70. Payoff 0 50 60 ST 69) You can achieve the payoff in the above diagram by using the following combination of options: A. buy a call with X = 50, sell a call with X = 60. B. sell a call with X = 50, sell a call with X = 60. C. sell a put with X = 50, sell a call with X = 60. D. sell a put with X = 50, buy a call with X = 60. E. buy a put with X = 50, buy a call with X = 60. 70) Which of the following is true? A. The diagram suggests that the maximum payoff on the option expiration date is $0. B. The diagram suggests that the loss on the option expiration date may be unlimited. C. The position that corresponds to the diagram must generate a positive cash flow when the position is established. D. A and B. E. A, B and C. Page 16 of 22 A s ae o . s h r d n. . SECTION B - 4 Short-Answer Questions (Total = 30 marks) Print your name and student number below. Write the answers in the space provided underneath the questions. Surname: ______________________ Given names: ___________________ Student ID number: ______________ QUESTION 1 - Term Structure of Interest Rates Total = 2 marks The following questions are written in the context of the liquidity premium hypothesis. i) Denote f(3,5) as the forward rate of a three-year bond in five years' time inferred from the term structure of interest rates today. LP(3,5) is the corresponding liquidity premium. How do you obtain today's market expectation of the yield of a 3-year bond in five years' time using f(3,5) and LP(3,5)? (1 mark) E[r(3,5)] = _____________________________________ ii) Investor should demand (a) more or (b) less liquidity premium than LP(3,5) for investing in a 6-year bond for 5 years. (1 mark) My choice is _________________ . Page 17 of 22 A s ae o . s h r d n. . QUESTION 2 - Portfolio Theory Total = 10 marks Assume that short-selling is banned, there are six risky assets to consider, and investors can lend and borrow risk free at 4.75% p.a. (rfL) and 6.00% p.a. (rfB), respectively. We have identified two optimal portfolios of risky assets, ORPL and ORPB, for those who may lend and borrow at the respective risk free rate of interest. Composition of the optimal portfolio of risky assets Risk return combination E(RP) P RA1 RA2 RA3 RA4 RA5 RA6 ORPL 0.0285 0.9715 0.0000 0.0000 0.0000 0.0000 58.62% 28.23% ORPB 0.0182 0.9818 0.0000 0.0000 0.0000 0.0000 58.87% 28.36% i) An investor knows that he will neither borrow money to invest nor put all his money in a portfolio of risky assets. State the underlying linear programming problem that the investor needs to solve in order to find out the best allocation of his capital. (4 marks) The investor needs to find __________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ that ____________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ subject to the constraint(s) __________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________ Page 18 of 22 A s ae o . s h r d n. . ii) Another investor knows that she will neither lend nor borrow money at the above risk free rates. Compute the range of degree of risk aversion of the investor. Report the answer to 4 decimals. (4 marks) ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ iii) A third investor who has $1,000.00 finds it optimal to borrow an additional $4,000.00 to invest. Compute the expected return and risk of the consequent allocation. Report the answer in percentage value and to 2 decimals, e.g., 1.23%. (2 marks) ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ Page 19 of 22 A s ae o . s h r d n. . QUESTION 3 Total = 10 marks Information for parts (i) to (vii) - Suppose the current market price of a European call option, c0, is $3.00. The option has six months to maturity and the strike price, X, is $35. The current price of the underlying stock, S0, which does not pay dividends, is $34. The continuously compounded risk free rate, r, is 6% per annum and the stock volatility, , is 25% per annum. Based on the above information, d1 = 0.0941, d2 = -0.0827, N(d1) is 0.5375 and N(d2) is 0.4671. Assume that there are no transactions costs, investors can borrow and lend at the risk free rate, and the option contract size is one share per option. i) Is the call option in, at, or out of the money? (1 mark) The call option is _________________________. ii) Write down the equation for the intrinsic value of a call option. Apply the equation to compute the intrinsic value of the call option. (1 mark) ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ iii) According to the Black Scholes option pricing model, the theoretical value of the call option is $2.41. Hence the market has a) overpriced or b) underpriced the option. (1 mark) My choice is ___________________________. iv) The probability that the call option will finish in the money is __________. (1 mark) v) The hedge ratio of the call option is _____________ . (1 mark) vi) Given the hedge ratio of the call option and the current mispricing situation, tell us the transactions that you may execute today to earn a risk-free arbitrage profit. (3 marks) ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ Page 20 of 22 A s ae o . s h r d n. . ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ vii) Suppose you enter into a covered call position at the current market prices. If the stock price goes up to $40 on the expiry date of the option and the call is exercised, describe your obligation on the option maturity date, i.e., the consequent flow of fund and stock from your point of view. (2 marks) ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ Page 21 of 22 A s ae o . s h r d n. . QUESTION 4 - CAPM Total = 8 marks Symbols and equations are accepted for part (iii) only. i) Among the many applications of the CAPM, what is the most important piece of investment advice that has been adopted and embraced by the funds management industry? (1 mark) The most important piece of investment advice is ________________________________ ________________________________________________________________________ _______________________________________________________________________. ii) Investors may also apply the CAPM to measure and price risk. What are the two yardsticks to measure risk? (For example, we may use inch and centimeter to measure length.) (3 marks) We may use _________________________________________________________ and _______________________________________________ to measure risk. iii) How much return should investors expect for each unit of risk as specified by the answers in part (ii)? (2 marks) st Investors should expect for each unit of risk as specified by the 1 expression in (ii) ______________________________________________________________________. Investors should expect for each unit of risk as specified by the 2nd expression in (ii) ______________________________________________________________________. iv) Prof. William Sharpe is a Nobel Prize winner, True or False? The statement is ___________. (1 mark) v) Prof. Harry Markowitz is Prof. William Sharpe's student, True or False? The statement is ___________. (1 mark) The End Page 22 of 22