1. What is time value of money? Give a real world example.
2. How do interest rate changes affect bond prices?
3. What is a riskless arbitrage? Setup an arbitrage strategy if applicable, to take advantage of any mispricing.
Data: Interest rates are 4%, 10% and 16% in the first, second and third years respectively.
4. Computethe present values of 1, 2, 3 years zero coupon bonds that pays $100 at the end of the first, second and third years respectively.
5. Compute the present value of a 3-year coupon bondwith a coupon interest rate equal to 10% and a face value of $100.
6. Construct the yield curve. What is the type of this yield curve?
7. Suppose the following trading strategy: short one1 and 2-year zero coupon bonds and eleven 3-year zero coupon bonds and simultaneously, long ten 3-year coupon bonds. Compute the net cash flows. Is there any arbitrage trade? If applicable,compute the profit from this trading strategy.
8. Suppose the 1-year zero coupon market is open and trading at 96.15385, the 2-year zero coupon bond is trading at 87.41259 and the 3-yearzero coupon bond is trading at 75.3568 (relative to a 100 face value) when the 3-year 10% coupon bond (i.e., coupon rate = 10% and assume coupons are paid once a year relative to a 100 facevalue) is trading at 101.24789
a. Is this set of prices arbitrage free? Explain.
b. Construct a synthetic one year zero coupon bond, which consists of:
- Short 10 3- yearcoupon bonds.
- Long one 2-year zero coupon bond.
- Long 11 3-years zero coupon bond.
Compute the net cash flows.
c. Consider the following position: Buy 1-year zerocoupon bond at its spot price and sell synthetic 1-year zero coupon bond. Compute the net cash flows. Is there arbitrage trade? If applicable, compute the profit from this trading strategy?