Question

Once upon a time, the treasurer of  “Mighty Corporation” (MCO) decided to issue a bond (hereafter: The bond) The bondwould have a 20-year life and promised that the holder of the bond would receive:

• 20 annual payments of $80,
• Along with the 20^thpayment, MCO promised to return the principal of $1,000. In other words, the final payments received at maturity would be ($1000+$80) = $1080.

Four years later, the Insurance company undertakes a review of all its holdings and wants to know what the price risk is associated with its bonds.  It ‘stress tests’ them by estimating what the effect of a 2 percentage point increase in YTM maturity would be.  

• Key formula: ΔP/P = -D*Δy + ½ C (Δy)²

Summary: the bond now has 15 years to maturity, a coupon of $80, a par value of $1000 and is trading with at YTM of 6%.  Its Macaulay Duration is 9.75 years

• A) Calculate the modified duration
• B) Using the modified duration, estimate in percentage terms how much the price would drop if the YTM rose from 6% to 8%.
• C) Convexity for the bond would be 116.8.  In percentage terms, how much would convexity reduce the loss estimated in (B) if rates rose to 8%?
• D) Adding the modified duration and the convexity effects together, calculate an estimate of the dollar value of the loss that would result if rates rose to 8%, (i.e. multiply your percentage answers to (B) and (C) times the price of the bond when YTM is 6%)
• E) Calculate accurately using either a spreadsheet or the bond function keys on your calculator what the actual price change would be if the YTM rose from 6% to 8%.
• F) If interest rates rose by 2 percentage points, what is the percentage loss that the insurance company would suffer on The Bond.  In other words, what percentage price loss does your answer to (E) show?

Answer 1

Once upon a time, the treasurer of  “Mighty Corporation” (MCO) decided to issue a bond (hereafter: The bond) The bondwould have a 20-year life and promised that the holder of the bond would receive: