rs . Lupane State University ot mma te FACULTY OF COMMERCE DEPARTMENT OF ACCOUNTING AND FINANCE BACHELOR OF COMMERCE HONOURS DEGREE IN ACCOUNTING AND FINANCE PART IV FIRST SEMESTER EXAMINATION ADVANCED ASSET PRICING THEORY [COAF 4102] DECEMBER 2022 DURATION: 3 HOURS INSTRUCTIONS 1. Answer all questions in Section A, and any three questions from Section B. 2. Begin each question on a new page. 3. Show all your workings. 4. Please indicate your study format (Conventional/Block/Parallel) on the cover of your 1. Questions may be answered in any order 2. You may use a scientific calculator.SECTION A (Answer all parts of this question , each question carries 2 marks) QUESTION ONE 1.1, Which of the following would most likely indicate that an investor is subject to an emotional bias? ‘A. Regularly basing decisions on only a subset of available information. B. Reacting spontaneously to a negative earnings announcement by quickly selling a stock. Remaining invested in a profitable technology stock even though new information indicates its PE ratio is too high 1.2. Thubelihle has just received new information regarding her investment in Orange, Inc. The new information appears to conflict with her earlier forecast of what the stock price should ‘be at this point. Nonetheless, she is unwilling to incorporate the new information into her forecast and to revise it accordingly. What behavioral trait is Thubelihle displaying? A. Conservatism bias, B. Confirmation bias. C. Anchoring and adjustment 1.3, Asmall-cap, high P/E factor-based investment strategy is best classified as: A. risk oriented. B. return oriented. G. diversification oriented 1.4. Which of the following is incorrect about limit and market orders. A, Limit orders have price uncertinity while market orders have execution uncertainity. B. Limit orders have execution uncertainity while market orders have price uncertainity. C. Market orders are executed at the best price available wile limit orders specify the execution price. 1.5. Which of the following is a necessary characteristic for an equity index to have in order to use it as a benchmark for a passively managed equity portfolio? A. Investable, 8. Flexible. C. Selective. 1.6. Leesa an equity analyst at Zimbabwe Power Company groups companies based on economic activity. Leesa classifies Hwange Colliery, a coal manufacturing company, under Page 2 of 13the mining sector instead of the energy sector. Which economic classification approach is Leesa Following? A. Production oriented B. Market-oriented C. Style approach Consider the diagram below and use it to answer question 1.7. Individual Portfolios £ oe Se — — crteien Frontier 5 » a5 g 6 oe é fee 2 fa 2 wn tener ace a === == ~~ a \ ° Individual Assets é — . Volatility 1.7. From the above investment opportunity set, which of the following statements is incorrect? A. Portfolio A, C and E are the minimum variance portfolios B. Portfolio 8 is not attainable ©. Portfolio C dominates portfolio D 18. A credit analyst is evaluating the potential for fixed-income securities to provide an inflation hedge. Which of the following types of securities protects both the bond coupon ‘and notional principal amounts from inflation? ‘A. Fixed-coupon bonds. B. Inflation-linked bonds. C. Floating-coupon bonds 1.9. A portfolio has two Assets A and B. The standard deviation for Asset A and B are 30% and 20% respectively. If the covariance of the two assets is 0.1, what is the weight of A for the minimum variance portfolio? A. 0.86 8 058c. 0.42 1.10. In the Fama-french model,stocks with a high P/E ratio are classified as ; A. Growth stocks B. Value stocks C. Low market capitalization stocks 1.11, An investment manager is considering an incremental position in a callable, putable, or option-free bond with otherwise comparable characteristics. If she expects a downward parallel shift in the yield curve, it would be most profitable to be A. longa callable bond. B. short a putable bond. . ong an option-free bond. 1.12, Luzibo, a Quantitative equity analyst at PrinceQuants investments executes her trades by buying stocks when they are below their mean-revesion level and selling when they are above. Her belief is that , over time , the stocks will always revert to their average value. What type of market anomaly is Luzibo trying to capture? A. Technical anomaly B. Fundamental anomaly c Calendar anomaly 1.13. The current price of the stock is $30 and the exercise price is also $30. The risk- free rate is 7%, and the up-move factor and down-move factor are 1.333 and 0.75, respectively. Consider a one period put option that expires at the end of year. The Hedge ratio for the option is A. -0.57 Bo C. -0.43 1.14. Portfolio convexity is a second-order effect that causes the value of a portfolio to respond to a change in yields-to-maturity in a non-linear manner. Which of the following best describes the effect of positive portfolio convexity for a given change in yield-to-maturity? A. Convexity causes a greater increase in price for a decline in yields-tomaturity and a greater decrease in price when yields-to-maturity rise. B. Convexity causes a smaller increase in price for a decline in yields-tomaturity and a greater decrease in price when yields-to-maturity rise. C. Convexity causes a greater increase in price for a decline in yields-tomaturity and a smaller decrease in price when yields-to-maturity rise. Page 4 of 13 )- p/P!1.15. In real options analysis, an option to can be construed as a call option while an option to__can be construed as a put option. A. Abandon, Defer B. Expand, Defer © Defer, Abandon 1.16. The investor's strategic asset allocation specifies weights of 60% for Stocks and 40% for Bonds. Consider an investor who invested in both actively managed funds, with 68% of the total portfolio in Stock Fund and 32% in Bond Fund. Using the information given below ‘to decompose the Active return, what is the value of your asset allocation and security selection (respectively), [ Fund Return(%) | Benchmark Return(%) | Value Added{(%) 35.3 32.3 3.0 Bonds [29 -2.0) Ot Portfolio Return | 23.4 18.6 AL 4.8% 2.1% 5: Ge HOKN B. 2.7% 32.1% De heut C. 2.1% 52.7% 3 Me cor PB 1.17. Which of the following is true about the relationship of @ put option value with volatility and exercise price? A put option value is, A. Positively related to volatil ry and negatively related to exercise price. B. Positively related to volatility and positively related to exercise price. C. Negatively related to volatility and positively related to exercise price, 4.18. The difference between the Cox-Ingersoll-Ross model and the Vasicek Model is that in the Vasicek Model; A. volatility does not increase as the level of interest rates increase B. Interest rates are assumed to be mean reverting, €. There is no randomness in interest rates. Use the following information to answer questions 1.19 -1.20. ‘Alice a junior equity analyst at R &D uses the Black Scholes model to value a put option on stocks. During her meeting with the Cl Investment Officer, she makes the following statements concerning the Black-Scholes model. Page 5 of 13 5 koeI In the Black-Scholes valuation, we assume that the underlying follows a statistical Process called geometric Brownian motion, which implies that the continuously compounded return is normally distributed, AA, The Black Scholes assumes the options are a European style, Wf The N(d1) factor in the BSM model represents the delta of a call while the N(d2) factor represents the delta of a put option. Further in her computation of the value of a put, the N(d1) factor was found to be 0.6 while the N(d2) factor was 0.29, 1.19. Which of the statements made by Alice are correct? A Statement Il and III 8. Allof them c Statement | and II 1.20, The probability that the call option will expire in the money ,according to Alice’s computations is; A. 0.6 B. 04 c. 0.29 Page 6 of 13SECTION B (Choose any three questions from this section) QUESTION TWO. a) Suppose we have three well- diversified portfolios that are each sensitive to the same single factor (2a). The information for the three portfolios is given in the table below. Portfolio Expected Return Factor Sensitivity A 0.075 0s B 0.150 20 é 0.070 04 i, Using the arbitrage pricing model and the above information above , determine the factor premium (A1) [3 marks} li, Suppose we have a portfolio D with expected return of 8% and Factor Sensitivity of 0.45. ‘Show that an arbitrage profit can be made by replicating portfolio D using any of the ‘two portfolios in the table above (Use a notional principal of $ 1000). [6 marks] b) An equity analyst at a pension furci uses the Carhart multifactor model to evaluate Zim portfolios. The active return for the portfolio he manages is 2.0741%. eq You are also given the following information on factor return and sensitivities; Factor Sensitivity Factor Portfolio [Benchmark [Factor Return MRF .95 lb 15.52% MB. 1.05 1 3.35% ML 0.40 .00 [5.10% ML (0.05 p.03 (9.63% Decompose the active return into asset allocation and security selection [6 Marks}. ©) Explain the Fama-French Five Factor model [5 Marks}. iedied cicle Free vee \ . wees tot Ae Codeel = RF AS anne 4 resned poe £°% cog \ A™ pone 4 oF oY ugQUESTION THREE, a) Calculate the forward price two years from now for a $1 par, zero-coupon, three-year bond Biven the following spot rates. The two-year spot rate is 4%. The five-year spot rate is 6% [4 Marks} b) You are given the following (annual-pay) par curve, Maturity Par rate uke kat 1 1.00% 7 2 1.25% se 3 1.50% , canantne the Conaspmngiee rate curve using the bootstrapping process, [6 Marks} c) Pe ‘astor wants to value a three-year, 3% annual-pay Treasury bond and he wants to use a Path-wise valuation approach. The interest rate tree is shown below; One period Forward rates ww 0 1 2 ae 3% 5.7883% | 10.7303% 3.880% 7.1981% 4.825% Compute the value of the $100 par option-free bond [8 Marks} ii, Determine the number of unique paths for this Bond 2 [2 Marks] UESTION FOUR. a) Suppose that the current stock price is $52 and the risk-free rate is 59, You have found a quote for a 3-month put option with an exercise price of $50. The put price is $1.50, but due to light trading in the call -options, there was not a listed quote for the 3-month, $50 call. Estimate the price of the 3-month call option using the Put-Call parity relationship, [3 Marks] Page 8 of 13,b) The current price of the stock is $30, the risk-free rate is 7%, and the up and down- factors are 1.333 and 0.75 respectively. Consider a two-period at the money call option that expires at the end of two years, Using the hedge ratio approach compute the value of this option [8 Marks) ¢} Calculate the no-arbitrage forward price for a 100-day forward contract on a stock that is currently priced at $30.00 and is expected to pay a dividend of $0.40 in 15 days, $0.40 in 85 days, and $0.50 in 175 days, The annual risk-free rate is 59, and the yield curve is flat. [4 Marks] 4) Assume that the Stock price movement follows geometric Brownian motion with an expected retum of 10% per annum and a volatility rate of 16% p.a. The initial stock price is $50. Compute the expected stock price after six months given a standard normal random variable "2" of 1.2. [5 Marks} ‘QUESTION FIVE 3) Malaba-investco Is considering a four year capital project that requires an intial outlay of 200,000. Annual after-tax operating cash flows have a 50 percent probability of being £40,000 for the four years and a 50 percent probability of being €80,000. Salvage value at Project termination is zero. The required rate of return is 10 percent. In one year, after realizing the first-year cash flow, the company has the option to abandon the project and receive the salvage value of €150,000. Compute the project NPV assuming no abandonment. [2 Marks} ii, Whatis the optimal abandonment strategy? Compute the project NPV using that strategy, [6 Marks] b) Madalisto holds a portfolio with a current value of $3.6 million.Madalisto has always self- managed the portfolio and has confidence in her investment abilities. Madalisto would like to be able to make independent decisions when opportunities arise, On several occasions, Madalisto has found herself holding positions with sizable losses and she has been celuctant. to sell when a security declines. Because of these losses and the general size of her portfolio, she is seeking professional help. She is willing to consider higher risk investments if her research identifies an attractive opportunity, Madalisto further reviews a recent memo from the technical analysis department that recommended overweighting clients’ portfolios in the technology and consumer goods sectors. The memo’s conclusion stated, “These sectors are depressed below their ten-year Page 9 of 13average levels. Every time that this has occurred in the Past, these sectors have recovered to their mean in a short period of time.” adalisto believes that technical analysis has the Potential to uncover opportunities where there are over- or under-reactions to relevant information, ‘Explain the behavioural bias exhibited by Madalisto in managing her portfolio [I The technical analysis department memo is most likely evidence of which of the three behavioural finance biases anchoring, confirmation bias and, the gambler's fallacy? Explain your answer [3 Marks}. ¢} Ncube, a portfolio manager at PrinceQuants Investments, is reviewing with his firm’s chief Nader the execution ofa ticket to sell 1,000 shares of Gamma Company. The ticker gan split into three trades executed in a single day as follows: AA market order to sell 200 shares was executed at a price of C$10.15, ‘The quote that was in effect at that time was as follows: Ask Price Ask Size Bid Price Bid Size csi0.24 200 810.12 300 8 A market order to sell 300 shares was executed at a price of C$10.11. The ‘uote that was in effect at that time was as follows: Ask Price Ask Size Bid Price Bid Size s10.22 200 csto.aL 300 ©. A market order to sell 500 shares was executed at an average price of $10.01. The quote that was in effect at that time was as fellowes Ask Price Ask Size Bid Price Bid size csi0.19 200 cs10.05 300 Compute the share-volume- weighted effective spread {5 Marks) END OF EXAMINATION PAPER Page 10 of 13Formula Sheet The Black-Scholes Model formula ny 4¢ Sor (ke 7 ovT Stock Simulation sete Page 11 of 13,ree Cumutarive Z-TaBie : Stanpaxp Noraat Distaisutton P(Z <2) =N(z) ronz20 z | 000 0.01 0.02 | 0.03 | 0.04 | 0.05 | 006 | 007 | 008 | 009] 90 | 0.5000 | 0.5040 | 0.5080 [0.5120 | 0.5160 | 0.5199 | 0.5239 | 0.5279 | osaia 10.5550 2.1 |_0.5398_| 0.5498 | 0.5478 | 0.5517 | 0.5557 | 0.5596 | 0.5636 | 0.5675 | 05714 | 0.5753 02 | 05793 | 0.5832 | 0.5671 | 0.5910 | 0.5948 | 0.5987 | 0.6026 | 0.6064 | 0.6103 | 01a pos4 size | 06217 [0.6255 [0.6293 | .6331_| 0.6368 | 0.6406 | 0.6643 | 0.6480 | 0.6517 04 | 06554 | 0.6591 | 0.6628 | 0.6664 | 0.6700 | 0.6736 | 0.6772 | 0.6808 | o.4sss | 0.6879 p25} 0.6015 | 6950 | o.6oas [0.7019 | 07054 | 07088 | 0.7123 | 07157 | oreo osama os |_o7as7 | 0.7291 | 0.7324 | 0.7357 | 0.7309 | 0.7422 | 0.7454 | 0.7486 | 07517 [0.7549 02 | 07590 | 076 | 07642 | 0.7673 | 0.7704 | 07734 | 0.7764 | 0.7794 | 0.7823 [0.7052 os | o7gs1_/ 0.7910 | 0.7999 | 0.7967 | 0.7995 [0.8023 | 0.8051 | 0.8078 | o.si06 | 0133 09 |_o8is9 | oss | 08212 | o4258 | 0.8264 | 0.8209 | 0.9515 | 0.8340 | 0.9365 | 0.8989 0.8413 | 0.8438 | 0.8461 | 0.8485 | o.ss08 | 0.8531 | 0.8554 | 0.0577 | 0.8599 | Oneal oss {0.8665 | "o.8636 | 0.8708 | 0.8729 | 0.8749 | 0.8770 | 0.8790 | 0.8810 | 0.8850 0.8849 | 0.8869 | o.s888 0.8925 | 0.8944 | 0.8962 | 0.8980 | 0.8997 | 0.9015 0.9032 | 0.9049 | 0.5066 5099 | 05115 | 0.9181 | os147 | 09162 | 09177 0.9192 | 0.9207 | 0.9222 e251 | 09265 | 0.9279 | 0.9292 | 0.9306 | 0.9319 4:5 | 0.9332 1 0.9345 | 0.9857 [09370 | o99e2_| 0.9394 | 09400 | osate | 05am | vada 16 | 09452 | 9463 | os474 | onsn4 | 0.9495 | 0.9505 | 0.9515 | 0.9595 | 0.9535 | 09545 17 | 09554 | 0.9564 | 0.9573 | 0.9582 | 0.9591 | 0.9599 | 0.9608 | 0.9616 | 0.9625 | 0.0483 48 | 9641 _{ ose49 | os656 | 0966s | 09671 | 0.9678 | 0.9686 | 0.9693 | 0.9699 | 0.0706 19 | 09713 | os7i9 | 09726 | 09732 | 09738 | 0.9746 | 0.9750 | 0.9756 | 0.9761 | as76r os772 | os7s | 09783 | 0.9788 | 09793 | 09798 | 0.9903 | 09808 | 09812 | aosi7 ova2i_| 0.9826 | 0.9830 | 0.9934 | 0.9858 | o.e42 | 9846 | 0.9950 | 0.9854 0.9857 09861 | 09864 | 0.9068 | 0.9871 | 0.9875 | 0.9878 | 0.9881 | 0.9884 | 0.9887 | 0.9890 0.9893 | 09896 | 09898 | 0.9901 | 0.9904 | 0.9906 | 0.9909 | 0.9911 | 0.9913 | 0.9916 24 | 09918 | 0.9920 | 0.9922 | 0.9925 | 0.9927 | 09929 | 0.9931 | 09932 | 0.9934 | 9936 +251 09938 { oso40 [ova | 09949 | 0.9945 | 09946 | 09946 | ood | 09951 | 0.9950 } 26 | 03953 | 0.9955 | "0.9956 | 0.9957 | 0.9959 | 0.9960 | 0.9961 | 0.9962 | 0.9963 | 0.0964 27 | 0.9965 | 0.9966 | 09967 | 0.9968 | 0.9969 | 0.9970 | 0.9971 | 0.9972 | 0.9973 | 0.0974 28 | 05976 | 0.9975 |" 0.9976 | 0.9977 | 0.9977 | 0.9978 | 0.9979 | 0.9979 | 09980 | v.9961 2.9 | o.9sa1_| 0.9982 | 0.9982 | 0.9983 | 0.9984 | 0.9984 | 0.9985 | 0.9985 10,9986 | 0.9986 3.0 | 0987 | 0.9967 | "0.9987 | 0.9988 | 0.9988 | 0.9989 | 0.9989 | 0.9989 | 0.9990 | 05950 Page 12 of 13Cumutative Z-TABLE (conr.) Stanparp Normat Disrrisurron Peg PZ <2) =N(@) rorz <0 0.00 | 0.01 [0.02 [0.03 | 008 | 00 0.06 | 0.07 | 0.08 | 0.09 2.5000 | 04960 [ 0.4920 | o.4080 | o.4s40 [0.4801 | 04761 | 0.4701 | O4ear | Oot 04602 | 0.4562 | 0.452 [0.4403 | 0.4443 | 0.4406 | 0.4964 | 0.4325 | 0.4286 Loin od2o7 | o416s | 0.4129 | ova {0.4052 | o4013 | 0.3974 | 0.3936 | oane7 bo saye 0.3821 | 0.3783 | 0.3745 | 03707 | 0.3669 | 0.3632 [0.3594 | 0.3 0.3520 | 0.348: os4is |_o3409 | 0.5972 {0.3396 | 0.3300 | 0.5264 | 0.3228 | 0192103156 Losiat S085 | _0.3050 | 0.5015 { o.2961 | 2946 [0912 | 02577 | ones | 02810 | ome oe o270s 1 oners | 0263 | o261 | o.2s7e | 02sec | o2si4 | 0.2485 | 02451 | 0.2420 |_02389 | 0.2858 { 0.2327 | 02297 | 0.2266 [0.2236 | 0.2207 02177 Lo.2iat e2u9__0.2090 | 0.2061 { 0.2038 [0.2005 [0.1977 [0.1949 | 0.1927 | ~0-1894 [0.1867 oagél_| o.t6i4 | o.7ae [0.1762 | 0.1736 [0.1711 | 0.1685 | 0.1660 | 0.1635 [oii 0.1587 | 0.1562 | 0.1539 9.1492 | 0.1469 | 0.1446 [0.1423 | 0.1401 | 0.1379 | 0.1357 | 0.1335 | 0.1314 6.1271 | 0.1251 | 0.1230 | 0.1210 [0.1190 | 0.1170 212 { otis [0131 | 012. 0.1075 | 0.1057 [0.1038 | 0.1020 [0.1003 | 0.098: -1:3| 0.0968 [0.0951 | 0.0934 0.0301 _| 0.0885 | "0.0869 | 0.0853 | 0.0838 | 0.0823 -14{ 0.0808 | 0.0793 | 0.0778 0.0749 J 0.0735 | 0.0721 | 0.0708 _|_0.0694 | 0.0681 0.0668 | 0.0655 | 0.0643 | 0.0630 | 0.0618 | 0.0006 0.0582 | 0.0571 | 0.0559 0.0548 | 0.0537 | 0.0526 0.0495 0.0475 | 0.0465 | 0.0455 =12| 0.0446 | 0.0436 | 0.0427 | 0.0418 | 0.0409 | 0.0401 _| 0.0384 | 0.0375 | 0.0367 <1 1_0.0359_|_0.0351_T 0.0344 | 0.0336 [0.0329 | 0.0322 | 0.0314 | 0.0307 | 0.0301 | 0.0294 120.0287 | 0.0281 | 0.0274 | "0.0268 |" 0.0262 [0.0256 | 0.0250 | 0.0244 | 0.0239 | 0.0233 -2.0| 0.0228 {0.0222 | 0.0217 | 0.0212 0.0202 | 0.0197 | "0.0192 | 0.0188 | 0.0183 -21| 0.0179 | 0.0174 | 0.0170 | 0.0166 0.0158 {0.0154 | 0.0150 | 0.0146 | 0.0143 2.21 0.0139 | 0.0136 | 0.0132 | 0.0129 0.0122 | oous | 0.016 [0.0113 | 0.010 -2.3| 0.0107 {0.0104 [0.0102 | 0.0099 0.0094 | 0.0091 |" .0089 |" 0,0087 | 0.0084 -24| 0.0082 |" 0.0080 | 0.0078 | 0.0076 0.0071 | 0.0069 {0.0068 | 0.0066 } 0.0068 33 -o008 | 0.0060 | 0.0059 | 0.0057 {0.0055 [0.0054 | “o-0059 |_o00s1_| o.00a9 | onoae| =2.6 + 0.0047 | 0.0085 "0.0044 [0.0043 |" o.0041 [0.0040 | 0.0039 | 0.0038 | 0.0037 | vose =2:2} 0.0035 _| 0.0034 | 0.0083 {0.0032 | 0.0031 | 0.0030 | 0.0029 | 0.0028 1 0.0027 |-opone 810.0026 0.0025 | 0.0024 | 0.0023 [0.0023 [0.0022 | 0.0021 [0.0021 | 0.0020 .0019 28.0019 —_o.o1s_{ 0.0018 {0.0017 [0.0016 | 0.0016 | 0.0015 | 0.0015 | 0014 o-00it 8.0013 |_0.0013 | 0.0013 | 0.0012 | 9.0012 [0.0011 | 0.0011 | o.0011 10.0019 1 0.0010 Page 13 of 13,