Bond Bond A B Coupon Rate 5% 5% Par/Face/Princ $1000 $1000 Years to Maturity 2 3 If the Yield to maturity of the two bonds is 5%, what is the price of both bonds. Find the Modified Duration of both bonds. Find the Modified Convexity of both bonds. Estimate the price of bond B using the Tayor Series Expansion if interest rates rise to 6% for the Yield to Maturity.
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Please answer 6D.
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- The following information about bonds A, B, C, and D are given. Assume that bond prices admit noarbitrage opportunities. What is the convexity of Bond D?Cash Flow at the end ofBond Price Year 1 Year 2 Year 3A 91 100 0 0B 86 0 100 0C 78 0 0 100D ? 5 5 105Calculating 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?…7. Given the two bonds below, answer the following questions. Bond Bond A Coupon Rate B 5% Par/Face/Princ $1000 Years to Maturity 2 5% $1000 a. If the Yield to maturity of the two bonds is 5%, what is the price of both bonds. b. Find the Modified Duration of both bonds. c. Find the Modified Convexity of both bonds. d. Estimate the price of bond B using the Tayor Series Expansion if interest rates rise to 6% for the Yield to Maturity. 3
- B. Directions: Compute for the following given statement and justify your answer. 1. Consider two bonds. Bond A has a face value of P100,000 and a stated rate of 12%. Bond B has a face value of P100,000 and a stated rate of 8%. Both bonds have the same maturity. Which bond has the greatest interest rate risk? 2. Consider two bonds. Bond X has a face value of P100,000 and five years remaining to maturity. Bond Y has a face value of P100,000 and ten years remaining to maturity. Both bonds have the same stated rate of 12%. Which bond has the greatest interest rate risk?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: DurationExplain 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 $1,000.00
- 4- Calculate the equilibrium interest rate of a 1-year discount bond with a face value of 1000. The demand and supply curves for this bond are represented by the following equations: ( B4: Price = -0.8 * Quantity + 1160 B": Price = Quantity +720Comment 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: 100.923Consider two bonds. Bond A has a face value of ₱100,000 and a stated rate of 12%. Bond B has a face value of ₱100,000 and a stated rate of 8%. Both bonds have the same maturity. Which bond has the greatest interest rate risk? Provide a computation
- 5. Look at the following data: i l-year bond, ti" t+1 5 percent premium = 0 i't +2 i't +3 5.78 percent 5.88 percent 5.65 percent premium = 0.10 premium = 0.22 premium = 0.33 Based on the data, do the following: a. Compute the interest rate on a 2-year, 3-year, and 4-year bond using expectations theory and then draw the corresponding yield curve. b. Compute the interest rate on a 2-year, 3-ycar, and 4-year bond using preferred habitat theory and then draw the corresponding yield curve.c) Suppose you observe the following three bonds. Assume that all bonds are denominated at $100 face value per contract and that they pay their coupons annually. Price Coupon Maturity (years) Bond A 111.42 15 3 Bond B 108.33 15 Bond C 116.61 15 1 i) Compute the spot rates r0,1, r0,2 and r0,3. ii) Compute the forward rates r1,2 and r2,3.Compute for the following given statement and justify your answer. 1. Consider two bonds. Bond A has a face value of ₱100,000 and a stated rate of 12%. Bond B has a facevalue of ₱100,000 and a stated rate of 8%. Both bonds have the same maturity. Which bond has thegreatest interest rate risk?