Consider the limits to arbitrage model with three types of agents (noise, investors, and arbitragers) and three periods. In period 3 the value of the asset is V, and arbitragers know this (so p3 = v). Noise traders receive a signal in periods 1 and 2 (S1, S2) that may cause them to be pessimistic. Investors supply funds to arbitragers, and they base their decisions on past performance. Let the demand for the asset on the part of noise traders be QN(t) = V-St/Ptat t=1 abitragers know S1, but not S2. In particular, there is some chance that S 2 >S1The supply of the asset is one for simplicity. Let Ftbe the resources available to arbitragers in ?.
(a) Given that markets clear show that the P2 depends positively on V and F2 and negatively on S2. What does P1 depend on? Explain.
(b) If arbitragers had access to unlimited funds what will P2 equal?
(c) Suppose that the supply function of funds to investors is given by
F2= F1G [(D1/F1)p2/p1+F1-D1/F1]
G(1) = 1, G" = 1, G" = 0. (1)
where D1 is the amount invested by arbitragers in period 1, and G" measures the sensitivity of F2 to the term in the brackets. If p 2 = p1 what happens to p2? What happens if p2 1? Explain why this could be important.
(d) What does G" > 0 imply about the nature of arbitrage? Explain. If G" is larger are arbitragers more likely to succeed or more likely to fail in offsetting noise traders signals in period 2?