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APS 502 Financial Engineering 1 Winter 2015, March 12 Instructions: Closed book and closed notes except for one side of a 3 by 5 inch notecard. Only a simple scienti…c non-…nancial calculator with no programming capability is allowed. Please write neatly as this will aid in providing maximum partial credit. IMPORTANT: Interpretation of the exam questions is part of the exam and so no questions will be taken that ask for clari…cation of the question. You must turn in this question sheet with your answer booklet or else your exam will NOT be marked. Problem 1 (18 points, 6 points each) An internet company i-Money is o¤ering a savings account with a nominal annual interest rate of 4.75%. What is the e¤ective annual interest rate o¤ered by i-Money if the compounding is (a) Annual (b) Monthly (c) Continuously Problem 2 (15 points) You are considering buying a car whose price is $30,000. The car salesman, who is eager to sell the car, o¤ers you an attractive …nancing (loan) package: you need to make a down payment of $3,500 and pay the rest over 5 years in equal annual payments at an annual interest rate of 2%. The o¤ered interest rate of 2% is not necessarily the market interest rate. (a) (7 points) What is the annual payment to the care salesman? (b) (8 points) The car salesman o¤ers you a second option: you pay cash for the car, but get a $2,500 rebate. Which is better for you getting the loan or paying cash? Assume the market annual interest rate is constant at 5%. Problem 3 (18 points, 6 points each) Suppose you are given the following information about three zero coupon bonds: Bond Maturity Price A 1 95.92 B 2 92.01 C 3 87.00 (a) Compute the implied spot rates s1 ; s2 ; s3 (b) Compute the implied forward rate between years 2 and 3 i.e. f2;3 : (c) Compute the yield of a 2 year bond with coupon rate of 4.25% and annual coupon payments. The face value of the bond is $100. Problem 4 (24 points, 8 points each) You have an obligation (liability) of $1 million per year for the next 20 years (a liability payment is due at the end of each year), and you wish to invest now to meet that obligation. You can invest in the following two zero coupon bonds: Bond A Bond B maturity 5 years 20 years 1 (a) What is the duration of your obligations(liabilities)? (b) What dollar amount of bonds A and B should you invest in so that you immunize against changes in interest rates while meeting the liabilities? Assume the annual interest rate is constant at 4%. Show all work. (c) What should be the face value of each bond? Problem 5 (25 points) Consider the following two risky assets: asset expected return standard deviation 1 20% 20% 2 15% 25% also the correlation between the returns of assets 1 and 2 is 0:04. (a) (5 points) Suppose you invest 70% of your wealth in asset 1 and 30% in asset 2. What is the expected return of this portfolio? (b) (5 points) What is the standard deviation of portfolio returns for the portfolio in part (a)? (c) (5 points) Would anyone ever be interested in investing in asset 2? Why or who not? Explain BRIEFLY. (d) (10 points) Using the information of the 2 assets above …nd the portfolio that minimizes variance. SHOW ALL WORK i.e. you must show all steps in computing the portfolio and not just plug into some formula to get the weights directly (any such formula must be derived). What is the expected return and variance of the portfolio obtained in part (c). 2