y showing your calculations of Macaulay duration, justify which bond will be less sensitive to interest rate changes: Bond A Bond B Par value £,1,000 £,1,000 Term to maturity 10 years 10 years Annual coupon rate 5% 5% Frequency of coupon payment per year Once Twice Annual yield of bonds in similar risk class 3% 3%
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By showing your calculations of Macaulay duration, justify which bond will be less sensitive to interest rate changes:
|
|
Bond A |
Bond B |
|
Par value |
£,1,000 |
£,1,000 |
|
Term to maturity |
10 years |
10 years |
|
Annual coupon rate |
5% |
5% |
|
Frequency of coupon payment per year |
Once |
Twice |
|
Annual yield of bonds in similar risk class |
3% |
3% |
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- Bonds have a maturity risk premium that can be modeled as the following:MRP = (t-1) 0.3%were t represents the years to maturity. What is the Maturity risk premium of a bond that matures in 8 years? answer in % without the symbolQ2. Duration and Convexity Bond A has face value at $1,000, coupon rate of 6% paid semi-annually, 5 years to maturity, and a yield to maturity of 7%. a. Using the bond pricing formula, calculate the price of the bond and duration. ABC b. Calculate the convexity of the bond. c. Using the calculations from above, what is the "approximated bond price change" using duration and convexity, if the interest rate increases by 1%? d. What is the actual change in the bond price if the interest rate increases by 1%? e. Based on c) and d) above, discuss the roles of duration and convexity in estimating the price change. Which risk measure plays a bigger role? f. Suppose you have two bonds with the same maturity date but one bond has a 10% coupon rate while the other has a 5% coupon rate. Which of these two bonds would have a higher duration?Problem: You are given the following data for two bonds with semiannual payments (A and B) Bond Settlement Date B 2/15/2020 2/15/2020 Maturity Date Coupon rate 2/15/2040 2/15/2040 4% 8% Similar bonds with 20 year to maturity sell for 9% coupon rates in the market. a) Calculate the bond value for bond A and B b) Calculate the YTM for bond A and B Bond Valuation Settlement Date 2/15/2020 2/15/2020 Maturity Date Coupon rate Required return Redemption Value Frequency Basis Calculate the PV of the bond in U.S. S 2/15/2040 2/15/2040 8% 4% 4.50% 4.50% 100 100 2 a) Use the Price Function B) Use the Yield Function
- Q2. Duration and Convexity Bond A has face value at $1,000, coupon rate of 6% paid semi-annually, 5 years to maturity, and a yield to maturity of 7%. Using the bond pricing formula, calculate the price of the bond and duration. Calculate the convexity of the bond. Using the calculations from above, what is the “approximated bond price change” using duration and convexity, if the interest rate increases by 1%? What is the actual change in the bond price if the interest rate increases by 1%? Based on c) and d) above, discuss the roles of duration and convexity in estimating the price change. Which risk measure plays a bigger role? Suppose you have two bonds with the same maturity date but one bond has a 10% coupon rate while the other has a 5% coupon rate. Which of these two bonds would have a higher duration?K Assume that a bond will make payments every six months as shown on the following timeline (using six-month periods): 0 2 5 Period $19.53 a. What is the maturity of the bond (in years)? b. What is the coupon rate (as a percentage)? c. What is the face value? Cash Flows View an example Get more help. ★ a. What is the maturity of the bond (in years)? The maturity is years. (Round to the nearest integer.) A 6 1 MacBook Pro & 7 $19.53 * 8 9 C 59 $19.53 60 $19.53+$1,000 Clear all BUB 0 {You are given the following data for two bonds with semiannual payments (A and B) Bond Years to Maturity Coupon rate 20 20 8% 4% Similar bonds with 20 year to maturity sell for 9% coupon rates in the market. Calculate the bond value for bond A and B What happends if the coupon rate of similar bonds drops to 6%? Calculate the bond value for bond A and B Bond Valuation Required Return Coupon 4.50% 4.50% 80 40 Par-value 1000 1000 Frequency 2 Basis Yield Bond 1 Bond 2 4.5% Price Change Percentage Change List the main bond theorems you derive from the above calculation
- Annual payment bond with a $1,000 par has 5% quoted coupon rate 6% promised YTM, and six years to maturity. What is the bond's duration and modified duration? How to use a financial calculator to solve this? explain the input in the calculatorQ. a.Estimate the interest rate that should be quoted for a 4-year maturity, zero coupon bond bought 6 years from today? The yield curve for a bond of comparable credit quality is speci ed below: Maturity YTM Maturity YTM Maturity YTM 1 year 8.00% 7 year 9.15% 13 year 10.45% 2 year 8.11% 8 year 9.25% 14 year 10.65% 3 year 8.20% 9 year 9.35% 15 year 10.75% 4 year 8.50% 10 year 9.47% 16 year 10.95% 5 year 8.75% 11 year 9.52% 17 year 11.00% 6 year 8.85% 12 year 9.77% 18 year 11.25%Consider the following bonds. Bond A B с D Coupon Rate (annual payments) 0.0% 0.0% 3.5% 7.8% Maturity (years) 10 15 15 10 Which of the bonds A to D is most sensitive to a 1% drop in interest rates from 6.7% to 5.7%? Which bond is least sensitive? Provide an intuitive explanation for your answer.
- Which bond is more sensitive to an interest rate change of 1 percent? Bond A: Yield to maturity = 4.00%, maturity = 8 years, coupon = 6% or £60, face value = £1,000. OR Bond B: Yield to maturity = 3.50%, maturity = 5 years, coupon = 7% or £70, face value = £1,000. A. Bond A B. Bond B C. Cannot be determined D. Both are equally sensitive.Consider following characteristic of a bond Time to Maturity: 5 years Coupon Payment: Semi-ainual Coupon Rate: Par Value: YTM (in annual): 3.5% 6.2% $1,000 15. What the Macaulay's duration and modified duration for 1% yield change for this bond given the information? 国2. Consider a bond with a 7.5% annual coupon rate and a face value of $1,000. Calculate the bond price and duration & show your work. Years to Maturity Interest rate Bond Price Duration 4 6. 6. 9. What relationship do you observe between yield to maturity and the current market value? What is the relationship between YTM and duration?