Consider a corporate bond with 10 years until maturity, trading at par (M=100,000), with semi-annual yield to maturity 3.5% (the semi-annual coupon rate is also 3.5%). Also consider a Treasury bond with 7 years until maturity, also trading at par (M=100,000), with semi-annual yield to maturity 3% (the semi-annual coupon rate is also 3%).

1. Suppose you want to buy the corporate bond and hedge it with a short position in the Treasury bond. What is the market value of the short position? How many Treasury bonds should you sell short?
2. Now assume that the Treasury yield increases to 3.5%, but the corporate yield only increases to 3.75%. Use durations to calculate the change in the net value of the portfolio.