The following information about bonds A, B, C, and D are given. Assume that bond prices admit no arbitrage opportunities. What is the convexity of Bond D? Cash Flow at the end of Bond Price Year 1 Year 2 Year 3 A 91 100 0 0 B 86 0 100 0 C 78 0 0 100 D ? 5 5 105
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The following information about bonds A, B, C, and D are given. Assume that
arbitrage opportunities. What is the convexity of Bond D?
Cash Flow at the end of
Bond Price Year 1 Year 2 Year 3
A 91 100 0 0
B 86 0 100 0
C 78 0 0 100
D ? 5 5 105
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- You are given the following prices and cash flows associated with bonds. CF stands for cash flow. Bond Price Today CF Year 1 CF Year 2 CF Year 3 A 105.185 10 10 110 B 90.371 100 0 0 C 91.784 5 105 0 D X 15 15 115 What is the current price of Bond D as per the no-arbitrage principle? In other words, what is the value of X?This first table describes prevailing market interest rates. Market Data Yield 0.05 Required: Using the yield above and the information contained in the table below, please calculate the price and duration of the bond as well as all necessary steps. (Use cells A5 to B5 from the given information to complete this question.) Time Until Payment Payment Discounted Payment Weight Time × Weight 1.00 $30.00 2.00 $30.00 3.00 $30.00 4.00 $1,030.00 Price: DurationCalculating the risk premium on bonds The text presents a formula where (1+1) = (1-p)(1 +i+x) + p(0) where i is the nominal interest rate on a riskless bond x is the risk premium p is the probability of default (bankruptcy) If the probability of bankruptcy is zero, the rate of interest on the risky bond is When the nominal interest rate for a risky borrower is 8% and the nominal policy rate of interest is 3%, the probability of bankruptcy is %. (Round your response to two decimal places.) When the probability of bankruptcy is 6% and the nominal policy rate of interest is 4%, the nominal interest rate for a risky borrower is %. (Round your response to two decimal places.) When the probability of bankruptcy is 11% and the nominal policy rate of interest is 4%, the nominal interest rate for a risky borrower is %. (Round your response to two decimal places.) The formula assumes that payment upon default is zero. In fact, it is often positive. How would you change the formula in this case?…
- How do investors calculate the net present value of a bond? If a bond's coupon payment is C, the interest rate is R, and the bond's coupon payment is made in each period for T years at which time the original principal, P, is repaid, then the bond's present discounted value (PDV) is C A. PDV = + (1 + R) (1 + R? (1 + R)T B. PDV = C(1 + R) + C(1 + R)2 - + C(1 + R)T + P(1 + R)T + C P OC. PDV = - + R R2 RT RT C D. PDV = P + C C (1 + R) (1+R)2 (1 + R)T C E. PDV = + + + + (1 + R) (1+ R)2 (1 + R)T (1 + R)T If the interest rate is 9 percent, what is the present value of a perpetuity that pays $50,000 each year, forever? The perpetuity's value is $ (Enter a numeric response rounded to two decimal places.)Suppose that y is the yield on a perpetual government bond that pays interest at the rate of $1 per annum. Assume that y is expressed with simply com- pounding, that interest is paid annually on the bond, and that y follows the process dy = a(y0 −y)dt + oydWt, where a, y0, and o are positive constants and dWt is a Wiener process. (a) What is the process followed by the bond price? (b) What is the expected instantaneous return (including interest and capital gains) to the holder of the bond?еВook Problem Walk-Through Last year Carson Industries issued a 10-year, 13% semiannual coupon bond at its par value of $1,000. Currently, the bond can be called in 6 years at a price of $1,065 and it sells for $1,200. a. What are the bond's nominal yield to maturity and its nominal yield to call? Do not round intermediate calculations. Round your answers to two decimal places. YTM: % YTC: % Would an investor be more likely to earn the YTM or the YTC? -Select- -Select- ent yield and to Table 7.1) Round your answer to two decimal places. b. Since the YTM is above the YTC, the bond is likely to be called. Since the YTC is above the YTM, the bond is likely to be called. Since the YTM is above the YTC, the bond is not likely to be called. Since the YTC is above the YTM, the bond is not likely to be called. Since the coupon rate on the bond has declined, the bond is not likely to be called. I. If the bond is called, the capital gains yield will remain the same but the current yield will be…
- Explain what you see from the pricing calculations. How do the two bonds differ? Bond C Bond Price = PV(rate,nper,pmt,fv) Given: n = Period which takes values from 0 to the nth period = 0,1,2,3 & 4 Cn = Coupon payment in the nth period = 10%*$1,000 = $100 YTM = interest rate or required yield = 9.6% P = Par Value of the bond = $1,000 Bond Z Bond Price = PV(rate,nper,pmt,fv) Given: n = Period which takes values from 0 to the nth period = 0,1,2,3 & 4 Cn = Coupon payment in the nth period = 0%*$1,000 = $0.00 YTM = interest rate or required yield = 9.6% P = Par Value of the bond = $1,000 years Bond A Bond Z 4 $1,012.79 $693.04 3 $1,010.02 $759.57 2 $1,006.98 $832.49 1 $1,003.65 $912.41 0 $1,000.00 $1,000.007-42 Spreadsheet Problem You have a portfolio of three bonds. The long bond will mature in 19 years and has a 5.5% coupon rate. The midterm bond matures in 9 years and has a 6.6% coupon rate. The short bond matures in only 2 years and has a 4% coupon rate. a. Construct a spreadsheet that shows the value of these three bonds and the portfolio when the discount rate is 5%. The spreadsheet can look something like this: A B D E 1 Now Change to 2 Interest rate = 5.00% 5.50% 3 Bonds Bond Price Now Price After Change Change in $ Change in % 4 Long bond 5 Midterm bond 6 Short bond 7 Total = $0.00 $0.00 図The forward rate f(t1,12) of a bond, is the implicit interest rate in a future period between time t1 and t2. For example, assuming continuous time returns, if the discount rate from period 0 to t1 is: exp(-r t1), and from period 0 to 12 (greater than t1) is: exp(-r t2), then the forward rate f from t1 to t2 maintains the following no arbitrage relationship: exp(-r t1) exp(-f (t2-t1) exp(-r t2)). Suppose we observe the prices of a 14-year zero-coupon bond (with a face value of $93.31), where P(t1,t2) regans the price of the bond between t1 and 12, and a year 7-to-14 forward rate as follows:P(0.14) - $86.5496905000 and f(7,14) - 0.6074704253 %. Calculate the price of a 7-year zero-coupon, with face value $99.27: $82.9604 $96.0778 ✓(25 %) $96.2349 $82.1804
- The time value of money is used in calculating bond prices because: Group of answer choices A - The company might choose to repay the bonds prior to their maturity date B - Bond investors receive future payments and purchase bonds with current dollars C - The amount to be repaid at maturity will change as market rates change D - Cash interest payments to bondholders will change as market rates changeFor a bond that is currently selling for par value (i.e., $1000). which one of the following relationships is correct (note: assume that all factors, other than the one mentioned, remain constant)? O 1) if the coupon rate increases, the bond price will remain the same. 2) if the coupon rate increases, the bond price will decrease. 3) if the yield to maturity decreases, the bond price will decrease. O 4) if the term to maturity increases, the bond price will remain the same. O 5) if the yield to maturity increases, the bond price will remain the same.Comment on the attractiveness of the bonds in two ways: a) How does the yield compare to the benchmark? Market YTM: 3.62% YTM of bond: 3.72% b) How does the current price compare to the benchmark-yield implied price? Price: 100.875 Implied price: 100.923