Assets, returns, and Arrow securities. Consider a two-period event tree. At date 0, we purchase one unit

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Assets, returns, and Arrow securities. Consider a two-period event tree. At date 0, we purchase one unit of asset (or security, the words are interchangeable) j for price qj . At date 1, we get dividend (or payoff) dj(z), which depends on the state z. Let us say, specifically, that there are two assets and two states. We will label Asset 1 as a "bond" and Asset 2 as an "equity". The date-1 payoffs of the two assets in each of the two states is given by Asset State 1 State 2 1 ("bond") 1 1 2 ("equity") 9 15 The prices of the assets are q1 = 0.95 (bond) and q2 = 11.50 (equity). (a) In an arbitrage-free environment, what is the price of a bond that pays 100 in each state? Or one that pays 1,000 in each state? Does the return from investing in the bond depend on these different payoffs? (b) What are the state-contingent returns on the equity asset? (c) An Arrow security has a payoff of 1 in a specific state, and 0 in all other states. Here we have two states, hence there are two Arrow securities. Their payoffs are

Security State 1 State 2 Arrow1 1 0 Arrow 2 0 1 What quantities of the two assets (bond, equity) when held in combination - which we can call a portfolio - reproduce the payoff of the first Arrow security? How about the second Arrow security? In an arbitrage-free environment, what are the prices of the two Arrow securities? Interpret the difference in these two portfolios and their respective prices. (d) All assets can be thought of as collections or portfolios of Arrow securities. If we know the prices of Arrow securities, in an arbitrage-free environment we can then find the prices of all other assets by adding up the prices of their state-specific payoffs. Use the prices of the Arrow securities computed above to find the prices of the bond and equity assets. (Hint: this is just reversing the logic of part c.)