Imagine that there are 2 securities trading. The first pays $1 in 6 months if Manchester United win the English Premier League (which, of course, we all know will happen). The second pays $1 in 6 months if Manchester United do NOT win the Premier League. The prices of these 2 securities are $0.80 and $0.18, respectively.

a. Assuming no transaction costs for buying or selling any securities, what must be the price of a 6-month, zero coupon bond with a face amount of $1,000?

b. If a 6-month, zero coupon bond sells for $985, what is the arbitrage strategy (again assuming no transaction costs)? What is the profit today per $1,000 face amount of zero coupon bonds?

c. If it costs $0.01 to buy or sell each of the Manchester United securities, what restrictions does the no arbitrage condition put on the price of a 6-month zero coupon bond?