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Week 12 InClass Quizz Answers Updated June 10

# Week 12 InClass Quizz Answers Updated June 10 - FAMILY NAME...

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FAMILY NAME: ____________________ OTHER NAMES: ____________________ STUDENT ID: ______________________ SIGNATURE: _______________________ FINS5513 INVESTMENTS AND PORTFOLIO SELECTION Week 12 In-Class Quiz Paper 01 Time Allowed: 30 minutes Question 1: [5 marks] (a) Explain why risky debt together with levered equity is similar to a covered call option. [2 marks] (b) Use a numerical example to construct a long strap and draw a graph that shows its payoff at expiration. Be sure to label the axes and all other relevant features of the graph, such as all breakeven points and all maximum profits/losses. [3 marks] Answer: See http://www.theoptionsguide.com/strap.aspx Question 2: [5 marks] The following is a list of yields to maturities (YTM) for zero coupon bonds with different maturities and par value of \$1,000: Years to Maturity 1 2 3 4 5 6 7 8 YTM of Zero 0.025 0.029 0.034 0.038 0.042 0.045 0.05 0.06 (a) Calculate the modified duration and convexity of the zero-coupon with 6 years to maturity. [1 mark] Modified duration=6/(1.045)=5.74 Convexity=(6+6^2)/(1.045)^2=42/1.092025=38.4607 (b) Use the modified duration and convexity to approximate the percentage change in the price of the 6-year zero when its yield changes by 25 basis points. [2 marks] Percentage change=-5.74*0.0025+0.5*38.46*0.0025^2=-0.01423 or -1.42% for an increase of 25 basis points, and Percentage change=5.74*0.0025+0.5*38.46*0.0025^2=0.01447 or 1.45% for a decrease of 25 basis points

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(c) Construct a bond portfolio using only the 2-year and 7-year zero coupon bonds that would immunize a liability portfolio of two payments, a payment of \$200 million in 4 years time and another payment of \$400 million in 6 years time. [2 marks] Current liability portfolio value=200m/(1.038)^4+400m/(1.045)^6 =172.2823m+307.1583m=479.441m Portfolio Duration=(4*172.2823+6*307.1583)/479.441=5.281 years Find the weight, w, such that w*2+(1-w)*7=5.281. The value of w=0.3437 and the portfolio should consists of \$164.8m (174,498 units) in the 2-year ZCB with a unit price of \$944.4289 and \$314.64m (442,729 units) in the 7-year ZCB with a unit price of \$710.6813. Paper 01
FAMILY NAME: ____________________ OTHER NAMES: ____________________ STUDENT ID: ______________________ SIGNATURE: _______________________ FINS5513 INVESTMENTS AND PORTFOLIO SELECTION Week 12 In-Class Quiz Paper 02 Time Allowed: 30 minutes Question 1: [5 marks] (a) Explain why a collateralized loan is similar to a covered call option. [2 marks] (b) Use a numerical example to construct a short strangle and draw a graph that shows its payoff at expiration. Be sure to label the axes and all other relevant features of the graph, such as all breakeven points and all maximum profits/losses. [3 marks] Answer: See http://www.theoptionsguide.com/short-strangle.aspx Question 2: [5 marks] The following is a list of yields to maturities (YTM) for zero coupon bonds with different maturities and par value of \$1,000: Years to Maturity 1 2 3 4 5 6 7 8 YTM of Zero 0.025 0.029 0.034 0.038 0.042 0.045 0.055 0.06 You manage a portfolio for Mr. G, who has instructed you to be sure her portfolio has a value of at least \$5 million at the end of seven years. The current value of Mr. G's portfolio is \$4 million. You can invest the money at a current interest rate of 5.5% but you have decided to use a contingent immunization strategy.

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(a) Calculate the duration and convexity of the zero-coupon with 7 years to maturity. [1 mark] Duration=7 (No calculation required) Convexity=(7+7^2)/(1+0.055)^2=56/(1.055)^2=50.31 (b) Suppose that three and a half years have passed and the interest rate is 5%.
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Week 12 InClass Quizz Answers Updated June 10 - FAMILY NAME...

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