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)