This question is about the price and welfare effects of financial innovation when not all future outcomes are equally salient to investors. Consider an economy over three dates t = 0, 1, 2 with two assets B and A, which pay off at t = 2. B pays R > 1 for sure, while A pays yi with probability i where i indexes the three possible states of the world at t = 2, which are: g (growth), d (downturn), r (recession). Assume that yg > 1 > yd > yr and that g > d > r. At t = 0 both assets, which are in unit supply, are owned by a patient risk-neutral intermediary with preferences max E [C0 + C1 + C2] . The economy also has an infinitely risk-averse investor with initial wealth w and preferences max E [C0 + C1 + min (C2g, C2d, C2r)] where > 1. At t = 0 financial claims are traded and prices set. At t = 1 a signal s {sL, sH} observed, claims are re-traded and new prices set. Here sH is a "good signal" which raises the probability of state g and reduces that of r, while sL is a "bad signal" which raises the probability of r and reduces that of d. The exact signal distribution will not be important for answering the questions. At t = 2 returns are realized and distributed. Assume that both actors are price-takers and that asset prices are determined to equate demand and supply. Part A Assume that both actors are rational, and that the financial claims traded, which we label the bond and the share, coincide with the basic assets B and A. (a) Show that at t = 0 the investor's reservation price is R for the bond and yr for the share. What is the intermediary's reservation price for these two financial claims? From now on, assume that yr < E1 [y|sL]. Argue that this condition implies that there is no trade in shares. (E1 [.|.] denotes conditional expectations at t = 1.) (b) To solve for the equilibrium in the bond market at t = 0, plot the demand curve of the investor and the supply curve of the intermediary in a diagram where the vertical axis is the bond price and the horizontal axis is the bond quantity. Recalling that the investor may be constrained by her total wealth, show that demand is first horizontal then decreasing, and compute the point at which is starts to decrease. Explain why supply is a step function. Assuming that w is large enough, what is the equilibrium bond price pB,0? Indicate the area in the diagram which measures the gains from trade. (c) What is the bond price at t = 1 after the signal is realized? Why? Part B Now we introduce financial innovation. Both actors are still rational, but now the intermediary can repackage some of the payoffs of A to obtain a new synthetic safe bond which promises to pay R with certainty at t = 2. The synthetic bond is a perfect substitute for the true bond and can be sold to the investor, while the intermediary keeps the residual risky claim. (d) What is the maximum amount of synthetic bonds that the intermediary can create from the unit supply of A(e) Assume that w is large enough. Draw the new demand and supply curves in the combined market for both types of bonds at t = 0. How does the supply curve of bonds change? What is the bond price? How do the gains from trade change? Is the financial innovation Pareto-improving? What is the bond price at t = 1 after the signal is realized?

Part C Now we explore financial innovation in the presence of a behavioral bias called local thinking. We assume that on each date, both actors only pay attention to the two most likely states of the world, and neglect the least likely state. (f) Given that at t = 0 the least likely state is r, what is the total amount of the synthetic bond the intermediary will issue? Are synthetic bonds perfect substitutes of real bonds now? Are they perceived as perfect substitutes by the two actors? (g) Draw the demand and supply curves in the bond market at t = 0. Assuming that w is in the range that with the new bonds the price falls below your answer in (e), derive an expression for the equilibrium bond price. (h) Assume the signal structure is such that after sL both actors think about states g and r (and neglect d). Suppose that sL is realized at t = 1. Compute the investor's new reservation prices for the synthetic bond and for the true bond. Show that the intermediary reservation prices are h PrL (yr|sL) (yr/yd) + PrL (yg|sL) i R (which we denote LR) for the synthetic bond and R for the true bond, where PrL (.|.) denotes conditional probabilities for the local thinker. Explain why the markets for the synthetic and true bond segment in this event. (i) Draw the demand and supply curves for the old bond at t = 1 after sL is realized. Maintaining all of the above assumptions, what will be the price of the old bond? How does it change relative to t = 0? Assuming that R (yr/yd) < LR, also draw the demand and supply curves of the synthetic bond in this event at t = 1. Who sells and who buys this security now? How does the amount of capital available to the intermediary affect the price of the synthetic bond? (j) What aspects of events in the mortgage bond market in 2007 and in the market for money market funds in 2008 are consistent with this model? (k) In this model, would incentive-based policies reduce the size of the price drop in the synthetic bond market? What other policies might be effective?