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A corporation buys $100 million (par value) of a 10-year coupon bond that pays a 5% semiannual coupon. The corporation is worried about the losses that its portfolio may suffer from an upward shift in the term structure of interest rates. Consider the following hedging strategy:

Hedging strategy 1: The corporation enters into a position with "phi" units of a 2-year zero coupon bond.

Hedging strategy 2:The corporation enters into a position with "phi" units of a 2- year zero coupon bond and into a position "alpha" units of a 10-year zero coupon bond.

Assume you are given the following discount factors.

Calculate the price of the bond, the duration, total value of this portfolio; the price, duration and convexity of the bond in hedging strategy 1, and tell what is the position phi that the corporation should take in the hedging strategy 1, such that the portfolio is insensitive to a parallel shift in the yield curve? Compute the change in the hedged portfolio 1 given dr = 0.1% and given dr = 2%. What do you observe?

Compute the price, duration and convexity of the new bond added in hedging strategy 2. What is the position phi and alpha that the corporation should take in the hedging strategy 2, such that the portfolio is insensitive to a parallel shift in the yield curve? compute the change in the hedged portfolio 2 given dr = 0.1% and given dr = 2%. What do you observe?

\begin{tabular}{llll} \hline Maturity & Z(0,Ti) & Maturity & Z(0,Ti) \\ \hline 0.50 & 0.9778 & 5.50 & 0.7808 \\ 1.00 & 0.9560 & 6.00 & 0.7634 \\ 1.50 & 0.9347 & 6.50 & 0.7464 \\ 2.00 & 0.9139 & 7.00 & 0.7298 \\ 2.50 & 0.8936 & 7.50 & 0.7136 \\ 3.00 & 0.8737 & 8.00 & 0.6977 \\ 3.50 & 0.8543 & 8.50 & 0.6822 \\ 4.00 & 0.8353 & 9.00 & 0.6670 \\ 4.50 & 0.8167 & 9.50 & 0.6521 \\ 5.00 & 0.7985 & 10.00 & 0.6376 \\ \hline \end{tabular} \begin{tabular}{llll} \hline Maturity & Z(0,Ti) & Maturity & Z(0,Ti) \\ \hline 0.50 & 0.9778 & 5.50 & 0.7808 \\ 1.00 & 0.9560 & 6.00 & 0.7634 \\ 1.50 & 0.9347 & 6.50 & 0.7464 \\ 2.00 & 0.9139 & 7.00 & 0.7298 \\ 2.50 & 0.8936 & 7.50 & 0.7136 \\ 3.00 & 0.8737 & 8.00 & 0.6977 \\ 3.50 & 0.8543 & 8.50 & 0.6822 \\ 4.00 & 0.8353 & 9.00 & 0.6670 \\ 4.50 & 0.8167 & 9.50 & 0.6521 \\ 5.00 & 0.7985 & 10.00 & 0.6376 \\ \hline \end{tabular}

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