Consider three zero-coupon bonds with 2, 10, and 30 years to maturity and with required yields 4%, 7%, and 9%, respectively.
a. Calculate the price and modified duration of the three bonds using annual compounding.
b. How can a trader use convexity to set up a profitable trade in case she expects the yield curve to move in a parallel way? (Hint: assume a short position of 100 10 year bonds and then solve the system of two linear equations in two unknowns)