Use the following information as your reference. There are five notes and one bond. Theoretical on$-$the$-$run Treasury yields for the settlement date of $02/11/25$ are provided based on maturity. Assume all securities are priced at par.

Portfolio Weights: Instructions:

$1.$ Calculate the modified duration, approximate duration, and approximate convexity $($in years$)$ using the approximation methods from the notes and textbook. Apply a $10-$basis$-$point $(\backslash (0\mathrm{.}10\backslash \%\backslash ))$ increase and decrease in yield for the calculations. Verify your duration result using the $=$MDURATION function in Excel.

$2.$ Calculate the weighted average yield, approximate and modified duration, and approximate convexity for both the Bullet and Barbell portfolios using the duration and convexity measures from Step $1.$

$3.$ Compute the returns for the Bullet and Barbell portfolios over a $6-$month holding period, including one coupon payment in the return calculation, for the two nonparallel shift scenarios below.

a$.$ Identify which scenario performs better under each portfolio with comparison to their returns $($just state "Scenario $1"$ or "Scenario $2")$

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|\}$

$\backslash$hline & $\backslash$begin$\{$tabular$\}\{$c$\}$

Scenario $1$: $\backslash \backslash$

Steepening Shift

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Scenario $2$: $\backslash \backslash$

Flattening Shift

$\backslash$end$\{$tabular$\}\backslash \backslash$

$\backslash$hline Note$/$Bond & Delta Y & Delta Y $\backslash \backslash$

$\backslash$hline $2-$Year Note & $\backslash (-2\mathrm{.}00\backslash \%\backslash )$ & $\backslash (1\mathrm{.}50\backslash \%\backslash )\backslash \backslash$

$\backslash$hline $3-$Year Note & $\backslash (-1\mathrm{.}50\backslash \%\backslash )$ & $\backslash (1\mathrm{.}25\backslash \%\backslash )\backslash \backslash$

$\backslash$hline $5-$Year Note & $\backslash (-1\mathrm{.}00\backslash \%\backslash )$ & $\backslash (1\mathrm{.}00\backslash \%\backslash )\backslash \backslash$

$\backslash$hline $7-$Year Note & $\backslash (-0\mathrm{.}50\backslash \%\backslash )$ & $\backslash (0\mathrm{.}50\backslash \%\backslash )\backslash \backslash$

$\backslash$hline $10-$Year Note & $\backslash (0\mathrm{.}00\backslash \%\backslash )$ & $\backslash (0\mathrm{.}25\backslash \%\backslash )\backslash \backslash$

$\backslash$hline $\backslash (30-\backslash )$ Year Note & $\backslash (+0\mathrm{.}50\backslash \%\backslash )$ & $\backslash (-0\mathrm{.}50\backslash \%\backslash )\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}4.$ Explain the differences in portfolio returns across the various parallel shift scenarios. Your response should discuss the impact of portfolio duration, convexity, and average coupon, referencing the calculations from the previous steps for support $($refer to the textbook for additional guidance$).$