Consider a $5-$year, $11\%$ annual coupon bond priced at $86\mathrm{.}59138$ per $100$ per to yield $15\%$ to maturity.

a$.$ If its YTM increases by $50$ basis points, its price will decrease to $85\mathrm{.}09217.$ If its YTM decreases by $50$ basis points, its price will increase to $88\mathrm{.}12721.$ Calculate the approximate convexity of the bond.

b$.$ We have calculated the modified duration to be $3\mathrm{.}50$ and the convexity of the bond to be $16\mathrm{.}9.$ Estimate the new price of the bond if its yield decreases by $50$ basis points.

c$.$ For the bond in the previous examples, calculate the money duration and money convexity of a $$10$ million par position in the bond and estimate the new price of the bond for a $50-$basis point decrease in yield. Recall that the modified duration of the bond is $3\mathrm{.}50$ and its convexity is $16\mathrm{.}9.$

Calculate the following in each:

a$.$: V$-$; V$+$; V$0$; $\backslash$Delta YTM; the approximate convexity

b$.$: modified duration; $\backslash$Delta YTM; duration effect; convexity of the bond; convexity effect; new price of the bond

c$.$: the market value of the position; money duration of the position; money convexity of the bond; duration effect; convexity effect; the expected change in the bond price; new price of the bond

Solve the questions in Excel. Use functions $($indicate when and detail them$)$ and elaborate on every other equation utilised during the solution as well.

Addition:

money convexity $=$ annual convexity $*$ full price of the bond position

change in full price of bond $=-($MoneyDur $*\backslash$Delta YTM$)+(0\mathrm{.}5*$ MoneyCon $*\backslash$Delta YTM$^2)$