Given how sensitive the Sleeping Beauty bonds are to changes in interest rates, we want to hedge against interest rate movements. Suppose you own $100 worth of Sleeping Beauty bonds and there are two other bonds that we can use to hedge interest rate shifts:

2-year zero coupon bond with a 5% yield (semi-annually compounded, so a 2.5% semi-annual yield)

10-year zero coupon bond with a 6% yield (semi-annually compounded, so a 3% semi-annual yield)

Assume a $100 par value throughout.

Then, assuming you have $x in the 2-year zero-coupon bond and $z in the 10-year zero-coupon bond, write down the price changes of your positions in the Disney bonds, the 2-year zero-coupon bond, and the 10-year zero-coupon bond, respectively, exactly as we practiced in the lecture.

Finally, simply set the Modified Duration Equation (the Delta_y part) and the Convexity Equation (the (Delta_y)² part equal to zero. That means, you set the modified duration of your long position equal to the modified duraiton of your short position and you set the convexity of your long position equal to the convexity of your short position. This gives you two equations with two unkowns, exactly as in the example in the lecture. The values you get for x and z are the answers to this question.

1)(4 points) What is the overall value of your portfolio (i.e. the portfolio consisting of the Disney bond, and the two- and the ten-year zero-coupon bonds)? Round to the nearest cent.

2)(4 points) What is the face value of your positions in the 2-year bond? Round to the nearest cent.

3) (4 points) What is the face value of your positions in the 10-year bond? Round to the nearest cent.

4) (4 points) Calculate the market value of your portfolio if all (annual) yields increased by three percentage points. Round to the nearest cent.