You observe that the current three-year discount factor for default-risk free cash flows is 0.68. Remember, the t-year discount factor is the present value of $1 paid at time t, i.e. = (1 + ), where is the t-year spot interest rate (annual compounding). Assume all bonds have a face value of $100 and that all securities are default-risk free. All cash flows occur at the end of the year to which they relate.

1) Suppose you decide to purchase a 1-year zero-coupon bond today and also contract today to re-invest the proceeds from the bond for the following two years at 16.5% per year. Show that this arrangement presents an arbitrage opportunity. Demonstrate how you would take advantage of this opportunity.

2) Consider discount factors such that d1 < d2 < d3. Explain why it would be odd to observe such a situation in a competitive market.