ADMS4504-Midterm-Sample1-Sol

ADMS4504-Midterm-Sample1-Sol - AP/ADMS4504A Fixed Income...

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AP/ADMS4504A Fixed Income Securities and Risk Management Midterm Exam Solutions Fall 2009 October 24, 2009 Type A Exam Numerical questions (4 points each) 1. (Q. 5 in B) Consider a Treasury coupon bond with $100 par, 6% coupon payable semiannually, 3 years of maturity, yielding at 4.915075% on a bond- equivalent basis. Which of the following is the price quote of this bond? Please keep at least 4 decimal places in both your calculations and your final answers for this question . A) 102 12 1/4 B) 102 19 1/8 C) 102 28 3/8 D) 102 31 ¾ E) 103 02 15/16 Answer D First, we calculate the bond price: FV = 100, N = 6, PMT = 3, I/Y = 4.915075 / 2 = 2.457538, CPT PV = $102.9922. Since the price of a Treasury bond is quoted in percent and 32nds of one percent of par value (of $100), the five price quotes given above can be converted to dollar prices of $102.3828 (A), $102.5977 (B), $102.8867 (C), $102.9922 (D), and $103.0918 (E), respectively. 2. (Q. 6 in B) A Treasury inflation protection security (TIPS) has an original principal of $50,000. Today’s semiannual nominal interest rate and semiannual real interest rate are 4% and 2%, respectively. We expect the semiannual nominal rate and semiannual real rate to rise to 5% and 2.5% in six months from now, respectively. What will be the principal of this TIPS at the end of one year from today? A) $50,000 B) $52,224 C) $52,275 D) $54,600 E) $55,020 1
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Today’s semiannual inflation rate is given by: [(1 + 4%) / (1 + 2%)] -1 = 1.9608%. Likewise, the semiannual inflation rate six months from today is: [(1 + 5%) / (1 + 2.5%)] -1 = 2.4390%. The inflation-adjusted principal of this TIPS at the end of one year from now is: $50,000 × (1 + 1.9608%) × (1 + 2.4390%) = $52,223.82 or about $52,224. 3. (Q. 7 in B) A firm has two $1,000 par value bonds both selling for $701.22. The first bond has a coupon rate of 8% and 20 years of maturity. The second bond has the same yield as the first bond but only 5 years of maturity. Both bonds pay coupons annually. What is the annual coupon payment on the second bond? A) $18.56 B) $28.65 C) $35.18 D) $37.12 E) $38.24 Answer D The YTM on the first bond is: 80(PMT), 1,000(FV), 20(N), -701.22(PV), CPT (I/Y) YTM = 12%. This is also the YTM on the second bond. So the price of the second bond is calculated as: . 12 . 37 $ ] ) 12 . 1 ( 12 . 0 1 12 . 0 1 [ ) 12 . 1 ( 000 , 1 $ 22 . 701 $ coupon ) 12 . 1 ( 000 , 1 $ ] ) 12 . 1 ( 12 . 0 1 12 . 0 1 [ coupon 22 . 701 $ 5 5 5 5 = × = + × × = 4. (Q. 8 in B) Compute the price of the following Treasury bond: $600 par, 5% coupon payable semiannually, and a maturity of 3.5 years. The T-bill rates at 6 months and 1 year are 3.2% and 3.6%, respectively. The Treasury spot rates at 1.5 years, 2 years, 2.5 years, 3 years, and 3.5 years are 3.7%, 4%, 3.8%, 4.2%, and 4.5%, respectively. All the interest rates are reported on a bond-equivalent basis. A) $585.87
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ADMS4504-Midterm-Sample1-Sol - AP/ADMS4504A Fixed Income...

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