Final_Examination,_Fall,_2006

# Final_Examination,_Fall,_2006 - Final Examination Economics...

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Final Examination Economics 466Y Bruce C. Dieffenbach December 20, 2006 Total time: 120 minutes. On the cover of the bluebook, please write the numbers of the questions answered. Part I. Please answer the following 2 questions. Question 1 a) Define arbitrage . b) Suppose that an investor judges that an asset is overvalued. Explain how the investor might nevertheless buy this asset to obtain an arbitrage profit. c) What is a call option ? What is the striking price ? What is the expira- tion date ? d) Consider two call options on the same stock, with the same expira- tion date but with different striking prices. The first option has striking price 50 and has price 3, and the second option has striking price 55 and has price 5. Explain how these prices create an opportunity for arbitrage profit. Describe specifically the arbitrage strategy. Question 2 Consider a stock for which each period the dividend D t either rises or falls. With probability two thirds, there is good news, and the dividend rises 30%. With probability one third, there is bad news, and the dividend falls 45%. Consequently, each period the dividend rises by 2 3 × 30% + 1 3 × ( - 45% ) = 5% , on average. The expected future dividend is E ( D t + n ) = ( 1 . 05 ) n D t . Assume that the price of the stock is the present value of expected divi- dends, P t = E ( D t + 1 ) 1 + R + E ( D t + 2 ) ( 1 + R ) 2 + E ( D t + 3 ) ( 1 + R ) 3 + ··· . The interest rate R = . 10 is constant. a) Calculate the current stock price P t as a function of the current divi- dend D t , by evaluating an infinite geometric sum. b) Calculate the rate of return from time t to time t + 1, D t + 1 + P t + 1 - P t P t . Calculate the rate of return when there is good news and when there is bad news. Show that the efficient-market theory applies: show that the expected rate of return equals R , and show that the rate of return is greater or less than R depending on whether there is good news or bad news.

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