Unformatted text preview: Week 12 In‐Class Quiz: Duration: 30 mins, Format: Two questions with parts, covers Weeks 9 and 10; one question on duration, convexity and/or immunization and one question on options trading strategies and/or options‐like securities. Some sample practice questions: 1. Explain why a collateralized loan is similar to a covered call option. ANSWER: BKM P697‐9. You can see it from the bank manager’s perspective. The bank manager is long the asset (the collateral, e.g., the house) and sell a call option on the asset to the mortgagee. See Figure 20.13 P699. 2. Explain why levered equity and risky debt is similar to a covered call option. ANSWER: BKM P698‐9. You can see it from the debt holders perspective. The debt holder is long the company and sell a call option on the company to the equity holders. The equity holders retain a call option on the company. You need to draw a graph similar to Figure 20.13 to explain. The “Payoff to Lender” in Panel A should now be “Payoff to debt holders” and the “Payoff to call with exercise price L” in Panel B should now be “Payoff to call with exercise price D”, where D is total value of debt. 3. Explain why callable bond is similar to a covered call option. ANSWER: BKM P693‐4. See Figure 20.11 P694. 4. Explain why convertible bonds are option‐like securities. ANSWER: BKM P693‐5. See Figure 20.12 P695. 5. Explain why puttable bond is similar to a protective put option. ANSWER: BKM P449. Draw a graph similar to Figure 20.11 P694 but for a protective put for the puttable bond. 6. (a) Calculate the modified duration and convexity of a bond that pays 4% coupon annually, a yield to maturity of 5% per annum, and has 2‐years to maturity. (b) Use the modified duration and convexity to approximate the percentage change in the bond price when its yield changes by 25 basis points. ANSWER: Use the spreadsheet “2Y Annual Coupon Bond” in the file “FINS5513 L9 Duration and Convexity Examples.xls” to check the answers to your calculations. Try to do a few other examples by changing the coupon rate, yield to maturity and change to its yield. 7. Illustrate, with a numerical example, how one would implement a short strangle options trading strategy. What are the breakeven points? What are the maximum loss and/or maximum profit of this options trading strategy? Graph the payoff and profit this options trading strategy. Explain under what market condition one would take this position. ANSWER: Refer to the web site www.theoptionsguide.com . Try to do a few other examples using the other options trading strategies listed in the Week 10 Summary. See question 13 for a similar type of question. 8. See the sample questions in “L10 Options Trading Exercises.pdf” Use the following information for Questions 9‐14: The following is a list of prices for zero coupon bonds with different maturities and par value of $1,000: Years to Maturity 1 Price of Zero 9. (a) Calculate the modified duration and convexity of the zero‐coupon with 7 years to maturity. (b) Use the modified duration and convexity to approximate the percentage change in the price of the 7‐year zero when its yield changes by 25 basis points. ANSWER: Use the spreadsheet “Zero Coupon Bond” in the file “FINS5513 L9 Duration and Convexity Examples.xls” to check the answers to your calculations. 10. Calculate the modified duration and convexity of a portfolio that consists of two 4‐year zeroes, three 6‐year zeroes and five 8‐year zeroes. ANSWER: Use the same weighting method for calculating the portfolio duration. Calculate the PV for each zeroes and calculate the current value of the portfolio. 11. Construct a bond portfolio using only the 3‐year and 8‐year zero coupon bonds that would immunize a payment of $125 million in 6.54 years time and the yield is 4.75%. Note: This is an example of a target date immunization. 12. Construct a bond portfolio using only the 3‐year and 8‐year zero coupon bonds that would immunize a liability portfolio of two payments, a payment of $100 in 5 years time and another payment of $300 million in 7 years time. Note: This is an example of net‐worth immunization. 13. You manage a portfolio for Mr. G, who has instructed you to be sure her portfolio has a value of at least $500,000 at the end of eight years. The current value of Mr. G's portfolio is $400,000. You can invest the money at a current interest rate of 5% but you have decided to use a contingent immunization strategy. a. Suppose that four years have passed and the interest rate is 6%. What is the trigger point for Mr. G's portfolio at this time? Answer: $396046.83 b. What should you do if the portfolio value is at or below that trigger point? Answer: Implement the target date immunization. Duration is 4 years, future target value is $500,000 with a PV of $396046.83. Buy a 4‐year zero‐coupon bond with a face value of $500,000 and a price of $396046.83. $971 2 $935 3 $889 4 $840 5 $800 6 $760 7 $720 8 $677 14. You manage a portfolio for Mr. G, who has instructed you to be sure her portfolio has a value of at least $500,000 at the end of eight years. The current value of Mr. G's portfolio is $400,000. You can invest the money at a current interest rate of 5% but you have decided to use a contingent immunization strategy. a. Suppose that three and a half years have passed and the interest rate is 6%. What is the trigger point for Mr. G's portfolio at this time? Answer: $384674.69 b. What should you do if the portfolio value is at or below that trigger point? Assume only 4‐year zero coupon bonds with YTM of 5.8% and 5‐year zero coupon bonds with YTM of 6.3% are available. Answer: Implement the target date immunization. Duration is 4.5 years, future target value is $500,000 with a PV of $384674.69. The prices of the 4‐year and 5‐year zeroes are $798.10 and $736.77, respectively. Buy $192337.34 worth of 4‐year zeroes and $192337.34 worth of 5‐year zeroes. That is, buy 241 4‐year zeroes and 261 5‐year zeroes. Use the following information for Questions 15‐20: 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 YTM of Zero 15. (a) Calculate the modified duration and convexity of the zero‐coupon with 7 years to maturity. (b) Use the modified duration and convexity to approximate the percentage change in the price of the 7‐year zero when its yield changes by 25 basis points. ANSWER: Use the spreadsheet “Zero Coupon Bond” in the file “FINS5513 L9 Duration and Convexity Examples.xls” to check the answers to your calculations. 16. Calculate the modified duration and convexity of a portfolio that consists of two 4‐year zeroes, three 6‐year zeroes and five 8‐year zeroes. ANSWER: Use the same weighting method for calculating the portfolio duration. Calculate the PV for each zeroes and calculate the current value of the portfolio. 17. Construct a bond portfolio using only the 3‐year and 8‐year zero coupon bonds that would immunize a payment of $125 million in 6.54 years time and the yield is 4.75%. Note: This is an example of a target date immunization. 18. Construct a bond portfolio using only the 3‐year and 8‐year zero coupon bonds that would immunize a liability portfolio of two payments, a payment of $100 in 5 years time and another payment of $300 million in 7 years time. Note: This is an example of net‐worth immunization. 0.03 2 0.034 3 0.04 4 0.045 5 0.046 6 0.047 7 0.048 8 0.05 19. You manage a portfolio for Mr. G, who has instructed you to be sure her portfolio has a value of at least $500,000 at the end of eight years. The current value of Mr. G's portfolio is $400,000. You can invest the money at a current interest rate of 5% but you have decided to use a contingent immunization strategy. a. Suppose that four years have passed and the interest rate is 6%. What is the trigger point for Mr. G's portfolio at this time? Answer: $396046.83 b. What should you do if the portfolio value is at or below that trigger point? Answer: Implement the target date immunization. Duration is 4 years, future target value is $500,000 with a PV of $396046.83. Buy a 4‐year zero‐coupon bond with a face value of $500,000 and a price of $396046.83. 20. You manage a portfolio for Mr. G, who has instructed you to be sure her portfolio has a value of at least $500,000 at the end of eight years. The current value of Mr. G's portfolio is $400,000. You can invest the money at a current interest rate of 5% but you have decided to use a contingent immunization strategy. a. Suppose that three and a half years have passed and the interest rate is 6%. What is the trigger point for Mr. G's portfolio at this time? Answer: $384674.69 b. What should you do if the portfolio value is at or below that trigger point? Assume only 4‐year zero coupon bonds with YTM of 5.8% and 5‐year zero coupon bonds with YTM of 6.3% are available. Answer: Implement the target date immunization. Duration is 4.5 years, future target value is $500,000 with a PV of $384674.69. The prices of the 4‐year and 5‐year zeroes are $798.10 and $736.77, respectively. Buy $192337.34 worth of 4‐year zeroes and $192337.34 worth of 5‐year zeroes. That is, buy 241 4‐year zeroes and 261 5‐year zeroes. Question 21: A) Use a numerical example to construct a long straddle and draw a graph that shows its payoff at expiration. Be sure to label the axes and all other relevant features of the graph. B) Use a numerical example to construct a short straddle and draw a graph that shows its payoff at expiration. Be sure to label the axes and all other relevant features of the graph. C) Use a numerical example to construct a long 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. D) 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. E) 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. F) Use a numerical example to construct a short 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. G) Use a numerical example to construct a long strip and draw a graph that shows its payoff at expiration. Be sure to label the axes and all other relevant features of the graph. H) Use a numerical example to construct a short strip and draw a graph that shows its payoff at expiration. Be sure to label the axes and all other relevant features of the graph. I) Use a numerical example to construct a collar and draw a graph that shows its payoff at expiration. Be sure to label the axes and all other relevant features of the graph. ANSWER: Refer to the web site www.theoptionsguide.com . See question 7 for a similar type of question. ...
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 Three '10
 WangJianxin
 Options, coupon bonds, numerical example, Mr. G, trigger point, contingent immunization strategy.

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