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There are two equally likely states of nature that can occur at date t + 1, either there is in an expansion or there is a recession. An investor has preferences over consumption at dates f and t +1 that can be represented by the utility function U (Ct, Ct+1) = log(Ct) + BEp (log(Ct+1)) where ß € (0,1). The investor can trade a risk-free bond and shares of a firm in a competitive market. Let på and på denote the price of a bond and a share of a firm in period t, respectively. A risk-free bond issued at date t is a promise to pay 1 unit at date t+1. The payoff of a share at date f + 1 is p²+1 + dt+1, where d₁+1 are the firm's dividends at t +1. The optimal consumption plan for this investor is such that the growth rate of consumption takes values μ+σ in an expansion and µ – o in a recession, and the investor does not face any binding borrowing constraint. (a) Use the consumption based model to derive the basic pricing equation for any payoff. Justify your answer. (10 marks) (b) Find pt as a function of μ, o and B. (10 marks) (c) How does the risk-free rate changes as μ, ß and σ changes? What is the economic intuition? Justify your answer. (10 marks) dt (d) Suppose the growth rate of dividends, +1, is equal to the growth rate of the investor's consumption plan. Show that p=d. (10 marks) (e) Which basic facts of asset returns the model in this exercise can explain and which ones it cannot? Explain your answer carefully. (10 marks) There are two equally likely states of nature that can occur at date t + 1, either there is in an expansion or there is a recession. An investor has preferences over consumption at dates f and t +1 that can be represented by the utility function U (Ct, Ct+1) = log(Ct) + BEp (log(Ct+1)) where ß € (0,1). The investor can trade a risk-free bond and shares of a firm in a competitive market. Let på and på denote the price of a bond and a share of a firm in period t, respectively. A risk-free bond issued at date t is a promise to pay 1 unit at date t+1. The payoff of a share at date f + 1 is p²+1 + dt+1, where d₁+1 are the firm's dividends at t +1. The optimal consumption plan for this investor is such that the growth rate of consumption takes values μ+σ in an expansion and µ – o in a recession, and the investor does not face any binding borrowing constraint. (a) Use the consumption based model to derive the basic pricing equation for any payoff. Justify your answer. (10 marks) (b) Find pt as a function of μ, o and B. (10 marks) (c) How does the risk-free rate changes as μ, ß and σ changes? What is the economic intuition? Justify your answer. (10 marks) dt (d) Suppose the growth rate of dividends, +1, is equal to the growth rate of the investor's consumption plan. Show that p=d. (10 marks) (e) Which basic facts of asset returns the model in this exercise can explain and which ones it cannot? Explain your answer carefully. (10 marks)
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Answer rating: 100% (QA)
a The basic pricing equation in the consumptionbased model is derived using the principle of noarbitrage According to the model investors evaluate assets based on their ability to improve future consu... View the full answer
Related Book For
Financial Theory and Corporate Policy
ISBN: 978-0321127211
4th edition
Authors: Thomas E. Copeland, J. Fred Weston, Kuldeep Shastri
Posted Date:
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