acst201-12s2 - MACQUARIE UNIVERSITY 0 SESSION 2...

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Unformatted text preview: MACQUARIE UNIVERSITY 0))! SESSION 2 EXAMINATIONS—NOVEMBER 2012 ACST 201 FINANCIAL TECHNIQUES, INSTRUMENTS 81 MARKETS 1. TIME ALLOVVEDi?) hours plus 10 minutes reading time TOTAL NUMBER OF QUESTIONS—6 full response questions TOTAL MARKS AVAILABLE—100 YOU MAY REFER TO THE SINGLE A4-SIZE SHEET OF PAPER (WITH ANYTHING YOU LIKE HAND-WRITTEN ON BOTH SIDES) THAT YOU BROUGHT WITH YOU TO THE EXAM. YOU MAY TAKE THESE NOTES WITH YOU AT THE END OF THE EXAM. 5. PAPER-BASED TRANSLATION DICTIONARIES PERMITTED 6. NON~PROGRAMMABLE CALCULATORS (NO TEXT RETRIEVAL CAPACITY) PERMITTED +99!” SPECIAL INSTRUCTIONS 7. TI IE EXAMINATION HAS TWO PARTS. ANSWER ALL QUESTIONS IN EACH PART 8. ANSWER EACH PART IN A SEPARATE BOOK 9. BEGIN EACH OF THE 6 QUESTIONS ON A NEW PAGE Please turn over 0 Answers should be written in the first examination booklet provided QUESTION 1 [15 marks] a. Liz purchased a 180 day $1 000 bank bill 50 days ago for $995. She sold it to Jim today and received $999. (i) [5’ 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 Jim accepts a lower yield. (iii) [2 marks] Calculate capital gain or capital loss component of Liz’s investment (to two decimal places). (iv) [4 marks] Assuming Liz borrowed to purchase the bond, 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 10 basis points higher than the break—even rate, explain whether Liz will end up with a cash surplus or cash deficit. b. A company wants to raise $270 000 by issuing 180 day bank bills with a face value of $1 000. The current yield on such bank bills is 6.7% p.a. The company is required to pay $11 000 of fees and charges associated With this financing activity. (i) [2 marks] Calculate the real cost of borrowing if fees and charges are paid on the date of issue. Express the cost as a rate of simple interest, as a percentage, rounded to 2 decimal places. (ii) [2 marks] Calculate the real cost of borrowing if fees and charges are paid on the maturity date. Express the cost a rate simple interest, as a percentage, rounded to 2 decimal places. Please turn over QUESTION 2 [19 marks] a. A 15—year 9% Treasury bond will mature on 15 September 2020. (i) [2 marks] Calculate the price on 15 September 2013 to allow for a jg = 7.5% p.a. yield. Assume a face value of $100 and ignore tax. (ii) [2 marks] Calculate the price on 12 September 2013 to allow for a jg = 7.5% p.a. yield. Assume a face value of $100 and ignore tax. (iii) [2 marks] Without any calculations, rank the prices of this bond from the lowest to the highest at the following dates. Briefly explain your ranking. 0 2 September 2013 o 12 September 2013 o 15 September 2013 (iv) [3 marks] Allowing for 30% tax on interest and 15% tax on capital gains, recalculate the price of this bond on 15 September 2013. (v) [2 marks] Suppose tax on both interest and capital gains are de— ferred by 6 months. Without any calculation, state whether the price will be higher or lower than the result in the last question. Explain why. b. A ten—year corporate bond pays 9.6% p.a. interest semi—annually. The probability of default of this bond in any given half—year is 0.000 5. Assume that, if the company defaults, no further coupon payments will be made. The current risk-free rate of interest is jg = 6% p.a. (i) [2 marks] Draw a contingent cashflow diagram representing these circumstances. (ii) [4 marks] Calculate the price of the bond (per $100 face value). c. [2 marks] As a financial consultant, you have advised a client that the appropriate price for a corporate bond to earn a yield of jg = 7.5% p.a. is $94.53 (per $100 face value). The corporate bond will mature (at par) at the end of 5 years, and pays half-yearly interest at 8.2% p.a. Your client says he doesn’t understand how the price can be below par (i.e., below $100 per $100 face value) when the required yield (jg = 7.5% p.a.) is below the coupon rate (jg = 8.2% p.a.). You have not made a mistake. Write an explanation to your client of why the price you recommended is below par, even though the required yield is below the coupon rate. Please turn over QUESTION 3 [16 marks] An investor bought a 3-year 6% Treasury bond on 15 April 2012 at a yield of jg = 8% pa Coupons can be reinvested at jg = 6.8% p.a. The bond will be redeemed at par on the maturity date (face value $100). a. [2 marks] Calculate total accumulated value generated by this bond if the investor holds it to maturity. b. [2 marks] Calculate total realised compound yield (TRCY) of this bond. c. [2 marks] Decompose the total accumulated value generated by this bond into: original purchase price, coupons, interest on coupons, and capital gain/loss. d. [2 marks] If the investor holds the bond for 2 years and sell it for a yield of jg = 8.7% p.a., calculate the holding period yield (HPY). e. [4 marks] Calculate duration of this bond if it is held to maturity. f. [2 marks] Use the concept of modified duration to estimate the price of the bond if the yield to maturity increases to jg = 8.1% p.a. immedi— ately after the investor buys the bond. g. [2 marks] What are two major factors affecting duration? In which direction do they affect duration? End of part A Cease writing in your part A booklet Please turn over 0 Answers should be written in the second examination booklet provided QUESTION 4 [10 marks] Mr. Smith, aged 60, is considering buying a life insurance policy which pays $100 000 (at the end of the year) in the event of his death during the next year. An insurance company analyses Mr. Smith’s profile and estimates the probability of death of Mr. Smith within the next year as 0.0025. The risk— free rate of return in the market is currently 6% pa. a. [3 marks] Calculate the actuarially fair insurance premium. b. [4 marks] If the insurance company pays $350 in administration fees per policy (payable when the policy is issued) and wants to make 3% profit at the end of the year, what is the premium for the policy? c. [3 marks] Ms. Jordan, aged 65, is willing to pay $1000 for an identi— cal insurance policy. The insurance company is just breaking even by accepting Ms. Jordan. Assume no administration fees or profit load— ing. What is the probability of death of Ms. Jordan? Explain whether this is the lowest or the highest probability of death for the insurance company to accept Ms. Jordan. Please turn over QUESTION 5 [21 marks] Use the spot rates in the table for the this question. These spot rates are currently available in the market and are spot yields of zero coupon bonds derived from the corporate bond market. Term (years) Spot rate (jl) % pa. 1 5.4 2 5.6 3 5.9 4 6.3 5 6.7 a. [4 marks] Use the arbitrage-free pricing principle to find the for- ward rate (3'1) which should be used to price a 3-year zero coupon bond with a face value of $100 to be purchased two years from to- day. (Give your answer as a percentage rounded to three decimal places.) (ii) [4 marks] Consider a 3—year corporate bond paying annual interest coupons at 7.5% p.a. (assume face value is $100 and redemption is at par). By pricing an equivalent portfolio of zero coupon bonds, find the fair price of this corporate bond. You can assume that zero coupon bonds are available with whatever term to maturity and whatever face value you may require. (Give your answer rounded to three decimal places.) (iii) [4 marks] Suppose the actual price of the 3—year 7.5% corporate bond today is $103 (per $100 face value). List and explain all the steps that you would need to take in order to make an arbitrage profit. Make sure you outline all that needs to happen on all relevant future dates, as well as today. (iv) [2 marks] How much profit (per $100 face value) will you make, if you carried out all steps in your answer to the previous question? b. Company XYZ wants a forward contract to buy 30 metric tons of cop— per in six months’ time. The current price of copper is $7800 per metric ton. The current interest rate for the six months loan is 8.0% p.a. (simple interest). The carrying cost of 30 metric tons of copper for 6 months is $5 000 (payable today). (i) [3 marks] Use the arbitrage—free pricing principle to calculate the fair forward price for copper per metric ton, rounded to the nearest dollar. Please turn over (ii) [4 marks] Suppose company XYZ agrees with the $8 300 contract price per metric ton, and suppose the spot price of copper after 6 months is $8415 per metric ton. If the contract is settled by cash, what payment will be made? Will company XYZ pay its counterparty or receive payments from its counterparty? QUESTION 6 [19 marks] a. [2 marks] What are the differences between Eur0pean Options and Amer- ican options? What factors affect option prices? b. [I mark] Suppose investor A has a long position in a European call op- tion and investor B is short an identical option. If price of the under— lying asset increases on the option expiry date, which of the following statement is correct? (i) It is investor B’s right to buy the underlying asset from A. (ii) It is investor B's obligation to buy the underlying asset from A. (iii) It is investor B’s right to sell the underlying asset from A. (iv) It is investor B’s obligation to sell the underlying asset from A. c. You are thinking of buying a European call option on shares in a com- pany called Triple R. The current price of one Triple R share is $30, and over the next month the share price will either increase to $36 (if there is a positive progress report on Triple R’s latest mineral exploration project) or decrease to $27 (if there is no positive report). The European call option will expire at the end of one month. The strike price is $32. The share will not pay any dividends during the next month. You can borrow money today for one month at the rate of 3'12 = 9% pa. (i) [2 marks] Suppose you estimate the probability of a positive progress report to be 65%. Use the contingent payments method to find the amount you would be willing to pay today (i.e., the Option premium) for the call option. (ii) {4 marks] Consider the replicating portfolio (i.e., the investment strategy which will give identical payoffs, at the end of one month, to the call option), that involves buying it shares in Triple R today, and borrowing $3 for one month. Find the values of h and B. 7 Please turn over (iii) (iv) (v) (vi) [2 marks] What is the initial cost (1.6., net outlay) today of invest— ing in the replicating portfolio? [I mark] What is the fair price (premium) for the call option, using the arbitrage—free pricing method? [3 marks] The contingent payments method will give the same option value as the arbitrage pricing method, as long as the ap— propriate value is used for p (the probability of an upward price movement). Find the appropriate value of p in this case. [4 marks] Suppose there was a dividend (of known amount $13) to be paid on Triple R shares, halfway through the next month. Explain how you would allow for this when using the replicating portfolio and the arbitrage—free pricing method to find the option premium. ...
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