6. Suppose you have an opportunity to invest in a company that is working on an important research project, C.B., a cure for cancer. If you invest, you have to put up $1 million. If the project is successful, your $1 million investment yields a $6 million return, for a net return of 85 million. If the project is unsuccesful, your return is 0), so you lose your $1 million investment. The probability of success is 1/5. ) Draw the game in extensive form including Nature as a player, (ii) Compute the expected pay-off in the event you choose to invest. Assuming you are risk neutral, do you choose to invest or not invest? STA 2422 W1-2-60-1-6 (iii) Reconsider your answer to part (b) assuming you have the utility function U(X) = VX+1,000,000, where X is your net return from the investment. Would you be willing to make the investment in this case? give a reason for your decision. (9 marks) marks) (b) Suppose you have an opportunity to invest in a company that is working on an important research project. If you invest, you have to put up $1 million. If the project is successful, your $1 million investment yields a $6 million return, for a net return of $5 million. If the project is unsuccessful, your return is 0, so you lose your $1 million investment. The probability of success is 1/5. (i) Draw the game in extensive form including Nature as a player. [2 marks] (ii) Compute the expected pay-off in the event you choose to invest. Assuming you are risk neutral, do you choose to invest or not invest? [3 marks] (iii) Reconsider your answer to part (b) assuming you have the utility function U(X) = VX +1,000,000, where X is your net return from the investment. Would you be willing to make the investment in this case? give a reason for your decision. (4 marks) 6. Suppose you have an opportunity to invest in a company that is working on an important research project, C.B., a cure for cancer. If you invest, you have to put up $1 million. If the project is successful, your $1 million investment yields a $6 million return, for a net return of 85 million. If the project is unsuccesful, your return is 0), so you lose your $1 million investment. The probability of success is 1/5. ) Draw the game in extensive form including Nature as a player, (ii) Compute the expected pay-off in the event you choose to invest. Assuming you are risk neutral, do you choose to invest or not invest? STA 2422 W1-2-60-1-6 (iii) Reconsider your answer to part (b) assuming you have the utility function U(X) = VX+1,000,000, where X is your net return from the investment. Would you be willing to make the investment in this case? give a reason for your decision. (9 marks) marks) (b) Suppose you have an opportunity to invest in a company that is working on an important research project. If you invest, you have to put up $1 million. If the project is successful, your $1 million investment yields a $6 million return, for a net return of $5 million. If the project is unsuccessful, your return is 0, so you lose your $1 million investment. The probability of success is 1/5. (i) Draw the game in extensive form including Nature as a player. [2 marks] (ii) Compute the expected pay-off in the event you choose to invest. Assuming you are risk neutral, do you choose to invest or not invest? [3 marks] (iii) Reconsider your answer to part (b) assuming you have the utility function U(X) = VX +1,000,000, where X is your net return from the investment. Would you be willing to make the investment in this case? give a reason for your decision. (4 marks)
