Chapter 7 Questions

Chapter 7 Questions - (b Calculate the implicit(martingale...

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THE ECONOMICS OF FINANCIAL MARKETS R. E. BAILEY Exercises for Chapter 7 Arbitrage 1. What is the arbitrage equilibrium price of asset C in the example below? (Explain) Asset A Asset B Asset C State 1 9 0 12 State 2 4 8 6 Price 5 4 ? 2. Use the information in question 1 to calculate (a) the implicit risk-free interest rate; (b) the implicit (martingale) probabilities; and (c) the state prices. 3. This exercise illustrates circumstances in which the arbitrage principle is satisfied with fewer assets than states of the world — circumstances that typically imply that the state prices are not unique. The following information is provided for an asset market, with two assets A and B , and three states of the world: Asset A Asset B State 1 4 1 State 2 0 5 State 2 15 10 Price 5 3 (a) Show that the following state prices, q 1 = 1 2 , q 2 = 1 10 , q 2 = 1 5 are compatible with the arbitrage principle, i.e. that these three state prices could hold for a market equilibrium in which there are no arbitrage opportunities (in frictionless markets).
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Unformatted text preview: (b) Calculate the implicit (martingale) probabilities, the implicit discount factor and the im-plicit risk-free rate associated with these state prices. (c) Show that there exist other state prices compatible with the given information and the absence of arbitrage opportunities. Given an example. (d) Together with the given information, suppose that a portfolio is formed by selling 6 units of asset A and buying 10 units of asset B . Is this an arbitrage portfolio? Is the portfolio consistent with the absence of arbitrage opportunities? 4. Explain and assess the role of the arbitrage principle in the determination of asset prices. [Answers to this question require a knowledge of the material in EFM chapter 8, together with a general awareness of the role of arbitrage in finance.] *****...
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