Question A

Ipen, a pension fund, computes the duration of its liabilities, currently valued at $$1\mathrm{.}97$ billion, and comes to a figure of $34\mathrm{.}5.$ Assuming parallel shifts in the yield curves, what is the $\%$ change in the value of their liabilities given a $10$ basis point change in yields?

To hedge against interest rate risks, Ipen decides to invest their money in $30-$yr zeros currently trading at a tm of $8\%$ p$.$a$.$ How much of the $30-$yr zeros will Ipen have to buy so that when combined with their liabilities, the duration of the combined portfolio will be zero?

$($Hint: think of liabilities as negative of assets, i$.$e$.$ a position in liabilities is the same as a short position in assets$)$