Question $2(26\%)$

Today is November $7,2023.$ The closing prices of five Canadian government bonds are listed in

the following table:

Maturity dates are stated using the MM$/$DD$/$YYYY format. All bonds pay semi$-$annual coupons

and accrued interest is based on actual$/$actual day count.

a$)(4\%)$

Calculate yield to maturity for each of the five bonds $($APR with semi$-$annual compounding$).$

b$)(12\%)$

Calculate each bond's Macaulay duration, modified duration and convexity.

c$)(5\%)$

You plan to invest $$100,000$ in a portfolio of Bonds #$2,$ #$3$ and #$4$ that has a Macaulay duration

of $5\mathrm{.}5($years$)$ and convexity of $40(yea{r}^2).$ What is the face value of each bond you should

purchase in order to construct the portfolio?

d$)(5\%)$

If yields on all bonds decrease by $25$ basis points right after you purchase the portfolio $($in c$)$

above$),$ what is the percentage increase in the value of your portfolio? Estimate the increase

using both duration and convexity. How accurate is that estimate?Question $2(26\%)$

Today is November $7,2023.$ The closing prices of five Canadian government bonds are listed in

the following table:

Maturity dates are stated using the MM$/$DD$/$YYYY format. All bonds pay semi$-$annual coupons

and accrued interest is based on actual$/$actual day count.

a$)(4\%)$

Calculate yield to maturity for each of the five bonds $($APR with semi$-$annual compounding$).$

b$)(12\%)$

Calculate each bond's Macaulay duration, modified duration and convexity.

c$)(5\%)$

You plan to invest $$100,000$ in a portfolio of Bonds #$2,$ #$3$ and #$4$ that has a Macaulay duration

of $5\mathrm{.}5($years$)$ and convexity of $40(yea{r}^2).$ What is the face value of each bond you should

purchase in order to construct the portfolio?

d$)(5\%)$

If yields on all bonds decrease by $25$ basis points right after you purchase the portfolio $($in c$)$

above$),$ what is the percentage increase in the value of your portfolio? Estimate the increase

using both duration and convexity. How accurate is that estimate?