2 Question 2 (20 marks) Consider an investor with $130 budget who has access to the stock that currently trades at $5 and who can buy or write call options on this stock. The investor is not affecting the price of the stock or the option by his deals. The call option is currently priced at $.5 (50 cents) and has the strike price of $5. Tomorrow the option expires and the investor believes that the stock will be priced either at $7 or at $4 with equal probabilities. Suppose further that the investor values his wealth w according to vw) = lnw. a. (2 marks) What are the financial assets here? Write their payoff matri? 6. (1 mark) Further denote with s the number of stocks and with c the number of call options purchased. Write the investor's budget constraint? c. (1 marks) Write the state contingent levels of wealth that are feasible to achieve by holding a portfolio (s, c)? d. According to the investor's preferences what is the optimal portfolio? Write this as an optimization problem with the Lagrangean (2 marks). Solve it, that is find the optimal portfolio (5.c). (4 marks). E. (3 marks) Suppose the investor is so risk-averse that she wants to perfectly insure herself against the stock market fluctuations. How many stocks and how many options does she have to hold (or write) to achieve this? Your answer, should, of course, respect the budget constraint. 9. (5 marks) What are stochastic discount factors (SDF) in general and what role do they play? Calculate the stochastic discount factors for the two states. Hint: you need to recover the connection between the SDFs and Arrow security prices. h. (2 marks) Your answers in d. and in e. are hopefully different. Explain why they should be different using your answer in g. 2 Question 2 (20 marks) Consider an investor with $130 budget who has access to the stock that currently trades at $5 and who can buy or write call options on this stock. The investor is not affecting the price of the stock or the option by his deals. The call option is currently priced at $.5 (50 cents) and has the strike price of $5. Tomorrow the option expires and the investor believes that the stock will be priced either at $7 or at $4 with equal probabilities. Suppose further that the investor values his wealth w according to vw) = lnw. a. (2 marks) What are the financial assets here? Write their payoff matri? 6. (1 mark) Further denote with s the number of stocks and with c the number of call options purchased. Write the investor's budget constraint? c. (1 marks) Write the state contingent levels of wealth that are feasible to achieve by holding a portfolio (s, c)? d. According to the investor's preferences what is the optimal portfolio? Write this as an optimization problem with the Lagrangean (2 marks). Solve it, that is find the optimal portfolio (5.c). (4 marks). E. (3 marks) Suppose the investor is so risk-averse that she wants to perfectly insure herself against the stock market fluctuations. How many stocks and how many options does she have to hold (or write) to achieve this? Your answer, should, of course, respect the budget constraint. 9. (5 marks) What are stochastic discount factors (SDF) in general and what role do they play? Calculate the stochastic discount factors for the two states. Hint: you need to recover the connection between the SDFs and Arrow security prices. h. (2 marks) Your answers in d. and in e. are hopefully different. Explain why they should be different using your answer in g