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Suppose there are three equally likely states of nature s ∈{1, 2, 3} that might occur at date
t + 1, the assumptions of free portfolio formation and the Law of One Price hold. There are
three assets whose prices at date t and payoffs, as a function of the states of nature at date
t + 1, are given by the following table:

                                        State
Asset                        Price 1 2 3
Stock                         1.10 1 2 1
State 1 Arrow Security 0.30 1 0 0
State 2 Arrow Security 0.60 0 0 1

(a) Find the set of stochastic discount factors for this economy.
(b) Obtain the prices at date t for a European put option on the stock with strike price
equal to 1 that matures at t + 1 (Hint: Recall that a European put option on the stock
that matures at t + 1 gives the right to sell the stock at date t + 1 at the strike price).

(c) Find the risk-free rate.
(d) Use the stochastic discount factor you found in (a) to value two projects with payoffs
x1 = (2, 1, 0.50) and x2 = (0.50, 1, 2). Does the value of these projects reflect any
compensation for risk? Explain.

(e) A wealth management company advertises a portfolio with expected (gross) return of 2
and standard deviation of 1. Is it possible to form such a portfolio with the existing
assets?

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