Given the following fixed income portfolio, answer the questions below. Assume: (1) the settlement date for all securities is December 7, 2023. (2) we own the following portfolio and are worried the unemployment report (due to be released December 8, 2023) will cause interest rates to increase. (3) we wish to hedge our portfolio by shorting the UST-notes with a coupon rate of 4.500% and a maturity of November 15, 2028 Further, assume the yield curve, at the time of the hedge, is flat at 4.620% YTM for all four of these securities. (in other words, the YTM for all four securities is currently 4.620% ) Portfolio: $10,000,000 par amount of UST-notes with coupon rate of 4.000% and maturity of November 15,2033 , and $10,000,000 par amount of UST-notes with coupon rate of 4.7500% and maturity of November 15,2026 , and $10,000,000 par amount of UST-notes with coupon rate of 4.250% and maturity of November 15, 2030. Questions: I. What par amount of the UST hedge security must we short to hedge the total portfolio? (round to the nearest whole \$million par amount) II. What is the current market price for the UST hedge security? III. What are the total proceeds resulting from the sale of the UST hedge security? (round to the nearest whole dollar) Part 2 If, instead of hedging the bond portfolio above with the security maturing in November 2028, we want to use the CBOT's US Treasury 5 year futures ($100,000 notional value). If we know the March 2024 futures contract has a duration of 3.9 years and we can calculate the "dollar duraction" of the above portfolio, how many futures contracts should we sell if today is December 1,2023? Round your futures hedge down to the nearest whole futures contract. Assume the futures contract delivery date is March 1, 2024. Part 3 Assume at the time of the hedge, the futures contracts are currently trading 107-18 and have an initial margin of $ : maintenance margin of $2500 per contract. Then: I. What price must the futures contracts trade before you get a margin call? II. How large will the total futures margin call be at that price? Part 4 Assume, the day you purchased the portfolio, the US Treasury yield curve immediately experienced a parallel shift of a 20 basis points increase in yields