Two securities have the following payoffs in two equally likely states of nature at the end of one year:
Security j costs $8 today, whereas k costs $9, and your total wealth is currently $720.
a) If you wanted to buy a completely risk-free portfolio (i.e., one that has the same payoff in both states of nature), how many shares of j and k would you buy? (You may buy fractions of shares.)
b) What is the one-period risk-free rate of interest?
c) If there were two securities and three states of nature, you would not be able to find a completely risk-free portfolio. Why not?