acst201-14s2 - MACQUARI E)l UNIVERSITY This question paper...

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Unformatted text preview: MACQUARI E )l UNIVERSITY This question paper may be retained by candidates SESSION 2 FORMAL EXAMINATIONS — NOVEMBERIDECEMBER 2014 EXAMINATION DETAILS: ACST201 FINANCIAL MODELLING Duration of exam incL readin fime if a “cable : 3 HOURS (PLUS 10 MINUTES READING TIME) Total no. of questions: 7 QUESTIONS Total no. of pages incl. this cover sheet : 10 INSTRUCTIONS: ANSWER ALL QUESTIONS. TOTAL MARKS AVAILABLE—100 ANSWER EACH QUESTION IN A SEPARATE BOOK THE EXAMINER WILL ONLY MARK THE FIRST QUESTION ANSWERED. IN ANY EXAM. ANSWER BOOK. ALL OTHER MATERIAL WILL BE IGNORED. MATERIALS PERMITTEDINOT PERMITTED: YOU MAY REFER TO THE SINGLE A4—SIZE SHEET OF PAPER (WITH ANYTHING YOU LIKE WRITTEN/TYPED ON BOTH SIDES) THAT YOU BROUGHT WITH YOU TO THE EXAM. YOU MAY TAKE THESE NOTES WITH YOU AT THE END OF THE EXAM. PAPER-BASED TRANSLATION DICTIONARIES PERMITTED NON-PROGRAMMABLE CALCULATORS (NO TEXT RETRIEVAL CAPACITY) PERMITTED - Candidates are required to obey all instructions provided by the Final Examination Supervisor and must refrain trom communicating in any way with another student once they have entered the final examination venue. - Candidates may not write or mark the exam materials in any way durin reading time. - Candidates may only access authorised materials during this examination. A list of authorised material is available on this cover sheet. if it is alleged you have breached these nIles at any time during the examination. the matter may be reported to the University Discipline Committee for deten'ninaticn. QUESTION 1 [15 marks] a. Agnes purchased an 180—day $1 000 000 bank bill 76 days ago for $985 900.28. She sold it to Bertil today and receiVed $992 085.06. (i) [3 marks] Calculate the purchase yield (simple interest rate) and sale yield (simple interest rate) of this bill (as a percentage, rounded to 2 decimal places). (ii) [2 marks] Without any further calculations, explain how the sell— ing price will change if Bertil accepts a lower yield. (iii) [2 marks] Calculate the capital gain or capital loss component of Agnes’ investment (to two decimal places). (iv) [4 marks] Assuming Agnes borrowed to purchase the bill, what is the break—even rate of interest of borrowing (simple interest, as a percentage, rounded to 2 decimal places)? If the borrowing cost rate is 12 basis points higher than the break—even rate, explain whether Agnes will end up with aicash surplus or cash deficit. b. A 6% pa. Treasury bond pays semi-annual interest on 15 May and 15 November and is to be redeemed at par on 15 November 2018. (i) [3 marks] Find the price to yield 4% pa. (jg) on 1 October 2014. (ii) [I mark] Without doing any calculations, what will the approx— imate price be to yield 6% pa? Provide a brief explanation of how you arrived at your answer. Cease writing in your first booklet - Open your second examination booklet QUESTION 2 [14 marks] a. [4 marks] You have been asked to help ‘price a 21/2-year 12% pa. Trea- sury bond at a yield of 8% pa. (jg) in Excel by a colleague. - In cells A1 to A5 there are zeros. Cell A6 contains 100. o In cell B1 there is a zero; in cells B2 to B6 6 appears. 0 In cell Cl is a zero. In cell (22 your colleague has typed =1/1.04. In cell CS, =1/1.04“2. In cell 04, =1/1.04“3, and so on—cell CS contains =1/1.04“5. Please turn over Your colleague has asked you to type in a formula to value the bond in cell D1. What will you type? b. [4 marks] The following data appears in cells A3 : C40 in an Excel spread- sheet. Coupon Yield Price (5'2) (32) 2% 100.000 2% 91.017 2% 82.940 2% 75.667 2% 69.113 2% 63.200 2% 57.859 2% 53.029 2% 48.659 2% 44.699 Explain how you would graph prices (against yields) in Excel. Price should be on the vertical axis of your graph. You should label the curve you have plotted as “2% coupon”. c. [6 marks] A part of question 2 of your take—home quiz 1 read as follows. Belinda, who has just turned 25, will invest $1 500 every year on her birthday for the next 40 years. How large will this retirement fund be on her 65th birthday— immediately after making her annual payment—if her invest ment earns o 10% p.a. in years 1—51 0 8% p.a. in years 6—15, I 9% pa. in years 16—30, and o 3% pa. in years 31—40? A student’s answer to this part of the question is given below. 1.15 — 1 m 15 . 9 1.0810 — 1 . . . 1 —— 01 (1 08) (1 09) (1 03) + 500 0.08 1.0915 — 1 9 1.039 4 1 —— . ——— 1 +1500 009 103 +1500 (103 + 500 = 939623970 + 103.273.5471 + 574640042 + 15238.6592 + 1500 = 271 438.61 1500 (1.09)15(1.03)9 Please turn over The correct answer was $279 536.77. What errors has this student made? Write out the correct expression. Cease writing in your second booklet a Open your third examination booklet QUESTION 3 [16 marks] An investor bought a 3~year 6% Treasury bond on 15 June 2014 at a yield of jg = 4% pa. The investor will reinvest all coupons over the life of the bond at jg = 3.2% p.a. The bond will be redeemed at par on the maturity date (face value $100). 7 a. [2 marks] Calculate the total accumulated value of the cash flows gen- erated by this bond at maturity, assuming the investor holds it to maturity. b. [2 marks] Calculate the total realised compound yield (TROY) of this bond under the circumstances given in a. c. [2 marks] Decompose the total accumulated value generated by this bond (if it is held to maturity) into: original purchase price, coupons, interest on coupons, and capital gain/ loss. ‘ d. [2 marks] If the investor holds the bond for 1 1/2 years and sells it for a yield of jg = 3.8% p.a., calculate the holding period yield (HPY). e. [4 marks] At the original purchase date, what was the duration of this bond? f. [2 marks] As at 15 June 2014, use the concept of modified duration to estimate the price of the bond if the yield to maturity falls to jg = 3.9% p.a. immediately after the investor buys the bond. g. [2 marks] What are two major factors affecting duration of a Treasury bond? In which direction do they affect duration? Cease writing in your third booklet Please turn over a Open your fourth examination booklet QUESTION 4 [14 marks] In the distant land of Imbroglio, Syed is considering buying corporate bonds.1 He has formed the View that there is a constant probability of default of 0.05 in any half year. Syed knoWs that if the bond defaults he will receive no further payments at all from the bond. 3.. [3 marks] Draw a detailed contingent cash flow diagram, from Syed’s perspective, that models the possible financial outcomes of purchasing a 4—year 4% bond (jg rates). b. [3 marks] What price should Syed pay for a 4-year 4% bond to earn a yield of 5% pa? Carefully set out all your working. Prior to Syed’s purchase, the government of Imbroglio introduces a program of quantitative easing. Syed’s analysis of the program suggests that, for those firms that default in the next six months, each will have a probability of 0.6 of recovering and paying coupon (and 0.4 of remaining in default) in the next six month period. Thereafter, the program will have no effect, and all defaulting firms will remain in default. The probability of a solvent firm moving into default remains at 0.05. In summary, then, (with all times in years): 0 From t = 0 to t = 0.5, the probability a solvent firm will default is 0.05, and the probability a defaulted firm will return to solvency is 0.0. a From t = 0.5 to t = 1.0, the'probability a solvent firm will default is 0.05, and the probability that a defaulted firm will return to solvency is 0.6. a From t = 1.0 to t = 1.5, the probability a solvent firm will default is 0.05, and the probability that a defaulted firm will return to solvency is 0.0. a From 15 = 1.5 to t =‘ 2.0, the probability a solvent firm will default is 0.05, and the probability that a defaulted firm will return to solvency is 0.0. 0 From 75 = 2.0 to t = 2.5, the probability a solvent firm will default is 0.05, and the probability that a defaulted firm_will return to solvency is 0.0. 1Assume that the corporate bonds of Imbroglio have patterns and valuation rules iden- tical to Australian Treasury bonds. Please turn over 0 And so on. c. [.4 marks] Draw a detailed contingent cash flow diagram, from Syed’s perspective, that models these revised possible financial outcomes. (:1. [4 marks] What price should Syed pay for a 4-year 4% bond to earn a yield of 5% pa. under these new circumstances? Carefully set out all your working. Cease writing in your fourth booklet Please turn over a Open your fifth examination booklet QUESTION 5 [14 marks] Johno, a jeweller, has won the contract from the NRL to design and build a new trophy. He will need a kilogram of gold on 1 April 2015 to start work on his project. Johno’s daughter is doing the HSC at the moment, and he’s got marital problems. He’s got enough stress in his life, and is further worried that the price of gold will rise over the next few months. Gordo, a gold miner, will easily have this supply of gold available for sale on 1 April 2015. Silvio, Johno‘s brother-in—law, runs a security firm. He is able and willing to store gold for J ohno for no cost—and at no risk of loss or theft. Johno is aware that he could buy the gold forward—that is, negotiate a price now with Gordo for the delivery of the gold on 1 April 2015. Then he wouldn’t have to worry about any rises on the price of gold over the next few months. a. [3 marks] By using two carefully labelled cash flow diagrams in your answer, setting out the cash flows associated with the forward con- tract and the replicating portfolio, explain how you can determine the arbitrage-free forward price of gold for the forward contract between Johno and Gordo. In your solution, take the current date as 25 November 2014 and the current price of gold per kilogram as AUD$46 711.42. Also, take the current simple interest rate for all loans up to 180 days duration as 2.8% p.a. J ohno and his wife have just had a huge row, and have decided to get di- vorced. Silvio is not speaking to Johno any more, so Johno will have to re—price his forward contract. b. [5 marks] Using the details given above, but now factoring in a cost of secure storage of $40 for terms up to 180 days, and an insurance cost of $16, repeat a. above. Immediately after concluding his deal with Gordo (i.e., the same day, when the market price of gold is $46 711.42 per kilogram), Johno meets Wacka. Wacka is prepared to buy or sell a kilogram of gold from, or to, Johno in a forward contract with a forward price of gold of $47 500 per gram on 1 April 2015. c. [3 marks] Explain how Johno could make an arbitrage profit in these circumstances. Please turn over d. [3 marks] How much profit could Johno make on one such (one kilo- gram) forward contract? Illustrate your answer with a carefully labelled cash flow diagram. Cease writing in your fifth booklet 0 Open your sixth examination booklet QUESTION 6 [16 marks] Linze is thinking of buying a European call option on shares in Echidna Pty. Ltd. He is trying to price the option using a simple (binomial) model, assuming monthly price increases of 10% on the current price, or decreases of 5% on the current price. The current price of one Echidna share is $28. The European call option will expire at the end of one month. The strike price is $29. The share will not pay any dividends during the few months. Linze can borrow money today for one month at the rate of 312 = 6% p.a. a. [4 marks] Consider the replicating portfolio (i.e., the investment strat- egy which will give identical payoffs, at the end of one month, to the call option) that-involves buying h shares in Echidna Pty. Ltd. today, and borrowing $3 for one month. Find the values of h and B. b. [2 marks] What is the initial cost (i.e., net outlay) today of investing in the replicating portfolio? c. [1 mark] What is the fair price (premium) for the call option, using the arbitrage—free pricing method? 7 d. [3 marks] The contingent payments method will give the same option value as the arbitrage pricing method, as long as the appropriate value is used for p (the probability of an upward price movement). Find the appropriate value of p in this case. Suppose Linze decides on buying a European call option that expires in two months, instead. Use the characteristics mentioned above, a monthly price increases of 10% are possible, a monthly price decreases of 5% are possible, 0 a strike price of 29, and o the same interest rate given above, to answer the following. Please turn over e. [3 marks] Draw a contingent cash flow diagram representing the payoffs associated with this call option. f. [3 marks] Calculate the price of this call option. Cease writing in your sixth booklet Please turn over a Open your seventh examination booklet QUESTION 7 [11 marks] Consider the following floating rate bond: it has a face value of $100. Each half year it 'pays a coupon based on the current market returns over the half year that has just ended. That is, if the market returns 6% from 15 January to 15 July then the bond pays $6. ‘ The bond matures in 10 years’ time, at which point the $100 face value is returned to the purchaser. a. [2 marks] How much would you pay for this floating rate bond? Why? Carsten had a serious motorcycle accident a number of years ago, greatly reducing his earning capacity. Shortly afterwards, he invested his savings in a floating rate bond. While he is confident the issuer is solvent, he is concerned that the bond returns may be low and volatile over the next eight years. He wants stable returns over the next eight years to ensure he can pay his annual bills (electricity, water, council rates and so on). o The current annual term structure of interest rates (3'1 rates) is (0.024, 0.025, 0.026, 0.028, 0.029, 0.030, 0.031, 0.032). 0 An eight year AAA corporate bond paying annual coupon (5h rate) at 3% pa. is currently priced at $98842 per $100 nominal. What stable rate of return could Carsten enjoy over the next eight years with an interest rate swap? In answering this question ensure you do the following. b. [3 marks] Draw a cash flow diagram indicating how the interest rate swap works. c. [6 marks] Write out, and solve, anequation of value for the desired stable rate of return (to two decimal places). Relate your equation of value to your cash flow diagram. Cease writing in your seventh booklet . End of paper 10 ...
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