Consider a corporate bond with 7 years until maturity, tradingat par (M = 100, 000), with yield to maturity y_c = 2.5% (y_c: semi-annual rate). Also, consider a Treasury bond with 8 yearsuntil maturity, also trading at par (M = 100, 000), with yieldto maturity y = 2% (y: semi-annual rate).

Suppose you want to buy the corporate bond and hedge it with a short position in the Treasury bond. What is the dollar amount of the short position, and how many Treasuries do you need to short?

Now, assume that the corporate rate decreases to 2.00% and the Treasury rate decreases to 1.75%. Use durations to calculate the change in the net value of the portfolio.