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AP/ADMS4504 midterm exam solutions Winter 2010 AP/ADMS4504 Fixed Income Securities and Risk Management Midterm Exam Solutions Winter 2010 Type A exam Numerical questions (4 points each) 1. (Q. 5 in B) A bond priced at par (\$1,000) has a duration of 6 and a convexity of 40. What happens to the bond’s price if interest rates rise by 30 basis points? The bond price goes to: A) \$980.00 B) \$982.00 C) \$982.36 D) \$1,018.00 E) \$1,018.36 Answer C The bond price decreases by -6 × (0.003) × 100 + 40 × (0.003) 2 × 100 = 1.764, or 1.764% to \$982.36. 2. (Q. 6 in B) A floating rate security has a market price of 98.6498 per \$100 of par value, a spread for life of 250.64 basis points, and a maturity of 12 years. What is the coupon rate on this floater if the reference T-bill rate is 2.5%? A) 4.68% B) 4.74% C) 4.80% D) 4.86% E) 4.92% Answer D The spread for life for this floater is calculated as follows: ). 6498 . 98 100 ( 12 ) 6498 . 98 100 ( 100 [ 64 . 250 × + × = = margin] Quoted life for Spread After some computations, we can solve the quoted margin to be 236 basis points. Then given the benchmark T-bill rate now stands at 2.5%, the current coupon rate on this floating rate security is: 2.5% + 236 basis points = 4.86%. 1

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Winter 2010 3. (Q. 7 in B) Bonds A and B are both callable and putable. Bond A : market price of \$895, face value of \$1,000, 8% coupon rate payable semiannually, 15 years to maturity, may be first called in 5 years at \$1,080, may be first called at par in 6 years, and finally may be first put in 8 years at par. Bond B : market price of \$454.65, face value of \$500, 8% coupon rate payable semiannually, 10 years to maturity, may be first called in 4 years at \$508, may be first called at par in 7 years, and lastly may be first put in 9 years at par. Calculate (the yield to worst on Bond A – the yield to worst on Bond B) in basis points. A) - 22 B) - 11 C) - 7 D) - 25 E) - 16 Answer B (We round the answers to the nearest two decimal places in the following.) Bond A: the YTM is 9.31%, and the yield to the first call, the yield to the first par call, and the yield to put are 12.07%, 10.40%, and 9.93%, respectively. So the yield to worst on Bond A is its YTM, 9.31%. Bond B: the YTM is 9.42%, and the yield to the first call, the yield to the first par call, and the yield to put are 11.20%, 9.82%, and 9.52%, respectively. So the yield to worst on Bond B is its YTM, 9.42%. It follows that (the yield to worst on Bond A – the yield to worst on Bond B) = 9.31% - 9.42% = - 0.11% or - 11 basis points. 4. (Q. 8 in B) The yield on a discount basis on a Treasury bill is 6.9964%. The settlement date is June 16 and the maturity date of the Treasury bill is September 5. Calculate the price of the T-bill per \$1 of face value ( please keep at least six decimal places in your answer ). A) 0.984064
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