Four years later, the Insurance company undertakes a review of all its holdings and wants to know

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Question:

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: P/P = -D*y + C (y)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?