4 questions pertaining to bonds(basis points, duration, convexity...)

1. Suppose an investor can purchase a 10-year, 4% coupon bond that pays interest semiannually and the price of this bond is $100. The yield to maturity for this bond is 4% on bond-equivalent basis. Assume the investor can reinvest the coupon payments at 5% compounded semiannually. a. Compute the following for this bond: total coupon interest = total reinvestment income= total dollar return= b. What is the total return on a bond equivalent basis if it held to maturity? 2. Consider a 4% coupon 30-year option-free bond selling at 72.3244 and yielding 6%. If the yield is decreased by 20 basis points, the price would increase to 74.5492. If the yield increases by 20 basis points, the price would decrease to 70.1988. a.Calculate the modified duration. b. what does this number tell us c. What would be the approximate dollar price change for a 50 basis point change in yield? d. What is the convexity measure for this bond? e. Suppose yields change by 200 basis points, what is the percentage price change using duration by itself? What is the percentage price change due to convexity? Draw a graph illustrating these two percentage price changes? 3. Consider a 7% coupon 8-year bond with a maturity value of $100 currently valued at $106.36. Suppose that the first call date is 3 years from now and the call price is $103. a. Using the numbers above and the bond pricing formula, explain how the yield to the first call date is calculated. No calculation is required. b. Suppose the yield to first call on a bond-equivalent basis is 5.6%, under what assumptions can this be interpreted as a measure of the bond's potential return? 4. Suppose an investor can purchase a 5-year, 7% coupon bond that pays interest semiannually and the price of this bond is $104.27. The yield to maturity for this bond is 6% on bond-equivalent basis. Assume the investor can reinvest the coupon payments at 4% compounded semiannually. a. What are the total future dollars generated on this bond if it is held to maturity? b. Compute the following for this bond: coupon interest = reinvestment income= total dollar return= c. What is the total return on this bond if it held to maturity