You are an analyst at Edward Jones $($EJ$),$ an investment firm based in the US$.$ EJ has a

portfolio focused on interest rate$-$sensitive assets, including government bonds, corporate

bonds, and interest rate swaps. The firm aims to optimize returns while managing risks

associated with fluctuating interest rates.

Portfolio Details $($as of January $1,2024)$

$(1)100,000$ Government Bond $($GovBondA$)$:

Face Value: $100$ USD

Coupon Rate: $3\mathrm{.}5\%($paid semi$-$annually$)$

Time to Maturity: $2$ years

$(2)50,000$ Corporate Bond $($CorpBondB$)$:

Face Value: $100$ USD

Coupon Rate: $5\%($paid semi$-$annually$)$

Time to Maturity: $2$ years

Assume the first coupon on the above two bonds is exactly one period from today.

$(3)$ Interest Rate Swap $($SwapC$)$:

Notional Principal: USD $200,000,000$

Pay Fixed Rate: $4\%$ per annum, payable semi$-$annually

Receive Floating Rate: $6-$month SOFR. Interest payments made semi$-$annually

Time to Maturity: $1\mathrm{.}25$ years

The $6-$month SOFR at the last payment date: $5\%$ per annum

There are several fixed$-$income instruments actively traded in the market:

The cash prices of six$-$month and one$-$year Treasury bills with face value USD $100$ are

USD $95\mathrm{.}0$ and USD $90\mathrm{.}0.$ A $1\mathrm{.}5-$ year Treasury bond that pays coupons semi$-$annually with

a coupon rate of $8\%$ and face value USD $100$ currently sells for USD $95\mathrm{.}91.$ A two$-$year

Treasury bond that that pays coupons semi$-$annually with a coupon rate of $10\%$ and face

value USD $100$ currently sells for USD $97\mathrm{.}77.$

The credit spread for corporate bonds is $5\%$ per annum with continuous compounding.

$($Hint: Corporate zero curve $=$ Treasury zero curve $+$ credit spread$).$