### What is the expected value of each option

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Question: Suppose you have \$90 to invest or store in a safe deposit box. Your only alternative to storing is a stock which sells for \$90. The stock is an initial public offering for a company with a risky idea that is projected to triple in value in a year if the idea works. The history of such ventures is that 80% of the time they fail and you lose your money. The other 20% of the time they triple your money in a year.

a. What is the expected value of each option at the end of the year? = \$54

b. Which option would you take if your utility function for money is u(M) = M2 ? = 14,580 so buy stock

c. Which option would you take if your utility function for money is u(M) = M1/2 ? = 9.49 so money stored

d. Using calculus, characterize your risk preferences (risk adverse, risk lover, or risk neutral) in parts b and c above

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