interest theory final time: 70 min

Act 2120 University Of Manitoba Actuarial Club – 2016/2017 Interest Theory Final – Time: 70 min 1) A company must pay a benefit of $1000 to a customer in two years. To provide for this benefit, the company will buy one-year and three-year zero-coupon bonds. The one-year and three-year spot rates at 8% and 10%, respectively. The company wants to immunize itself from small changes in interest rates on either side of 10% (Redington Immunization). What amount should it invest in the one -year bonds? 2) An investment will return $1,000 in two years and $5,000 in five years. Determine the ratio of the convexity of the payments to their modified duration, evaluated at i = 7.5%. 3) Two bonds are purchased for the same price to yield 5%. Bond X has 4% annual coupons and matures for its face value of $100. Bond Y has annual coupons of $3 and matures for 180. Both bonds mature at the end of n years. Calculate n. 4) A common stock pays annual dividends at the end of each year. The earnings per share in the year just ended were J. Earnings are assumed to grow 10% per year in the future. The percentage of earnings paid out as a dividend will be 0% for the next 5 years, and 50% thereafter. Calculate the theoretical price of the stock to yield the investor 21%. 5) You are given the following information about two bonds that will mature in four years at par: Bond A Bond B Par Value $750 $1,000 Annual Coupon Rate 4% 2% Price $500 $700 Determine the four-year spot rate. 6) A company has the following projected liability cash flows: Year 1 2 3 4 5 Liability Cash Flow 179 679 144 3144 824 There are three assets available for investment: x 2-year bond with annual coupons of 7% x 4-year bond with annual coupons of 4% x 5-year bond with annual coupons of 3% Each bond has a par value of $100. The annual effective yield rate on all three bonds is 5%. The company has decided to pursue a dedication strategy. Determine the amount of each bond to be purchased, and calculate the cost of establishing the asset portfolio.

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Act 2120 University Of Manitoba Actuarial Club – 2016/2017

Interest Theory Final – Time: 70 min

1) A company must pay a benefit of $1000 to a customer in two years. To provide for this benefit, the company will buy one-year and three-year zero-coupon bonds. The one-year and three-year spot rates at 8% and 10%, respectively. The company wants to immunize itself from small changes in interest rates on either side of 10% (Redington Immunization). What amount should it invest in the one -year bonds? 2) An investment will return $1,000 in two years and $5,000 in five years. Determine the ratio of the convexity of the payments to their modified duration, evaluated at i = 7.5%. 3) Two bonds are purchased for the same price to yield 5%. Bond X has 4% annual coupons and matures for its face value of $100. Bond Y has annual coupons of $3 and matures for 180. Both bonds mature at the end of n years. Calculate n. 4) A common stock pays annual dividends at the end of each year. The earnings per share in the year just ended were J. Earnings are assumed to grow 10% per year in the future. The percentage of earnings paid out as a dividend will be 0% for the next 5 years, and 50% thereafter. Calculate the theoretical price of the stock to yield the investor 21%. 5) You are given the following information about two bonds that wil l mature in four years at par: Bond A Bond B

Par Value $750 $1,000 Annual Coupon Rate 4% 2% Price $500 $700 Determine the four-year spot rate. 6) A company has the following projected liability cash flows: Year 1 2 3 4 5

Liability Cash Flow 179 679 144 3144 824 There are three assets available for investment:

x 2-year bond with annual coupons of 7% x 4-year bond with annual coupons of 4% x 5-year bond with annual coupons of 3%

Each bond has a par value of $100. The annual effective yield rate on all three bonds is 5%. The company has decided to pursue a dedication strategy. Determine the amount of each bond to be purchased, and calculate the cost of establishing the asset portfolio.

Page 2: Interest Theory Final Time: 70 min

Act 2120 University Of Manitoba Actuarial Club – 2016/2017

7) You are given the following spot rates: S(2)

0.5 = 12.00% S(2)

1.0 = 13.50% S(2)

1.5 = 14.66% S(2)

2.0 = 16.00% Calculate the 1-year implied forward rate for the second year, expressed as a rate that is effective over 6 months. 8) A perpetuity-immediate has annual payments of 1.05, 1.052, 1.053,… Determine the duration of this perpetuity at an effective rate of 10%. 9) A twenty-six week Treasury bill maturing for $10,000 is bought at a discount to yield 2.51% annually. For the same purchase price, a zero coupon bond maturing for $50,000 at the end of 20 years is available. The nominal yield rate convertible semi-annually on this bond if i %. Calculate i. Disclaimer: this exam is not one that has actually been previously tested in Interest Theory. This was

an exam created by UMAC in order to provide students with a more recent realistic representation of

what one may expect on both Interest Theory Exams, and Exam FM. There is a strong possibility that

this exam is of easier difficulty than what will be tested in Interest Theory.

- Sergiu Buda