# Question

Ellie Daniels has $200,000 and is considering three mutual funds for investment—a global fund, an index fund, and an Internet stock fund. During the first year of investment, Ellie estimates that there is a .70 probability that the market will go up and a .30 probability that the market will go down. Following are the returns on her $200,000 investment at the end of the year under each market condition:

At the end of the first year, Ellie will either reinvest the entire amount plus the return or sell and take the profit or loss. If she reinvests, she estimates that there is a .60 probability the market will go up and a .40 probability the market will go down. If Ellie reinvests in the global fund after it has gone up, her return on her initial $200,000 investment plus her $25,000 return after 1 year will be $45,000. If the market goes down, her loss will be $15,000. If she reinvests after the market has gone down, her return will be $34,000, and her loss will be $17,000. If Ellie reinvests in the index fund after the market has gone up, after 2 years her return will be $65,000 if the market continues upward, but only $5,000 if the market goes down. Her return will be $55,000 if she reinvests and the market reverses itself and goes up after initially going down, and it will be $5,000 if the market continues to go down. If Ellie invests in the Internet fund, she will make $60,000 if the market goes up, but she will lose $35,000 if it goes down. If she reinvests as the market continues upward, she will make an additional $100,000; but if the market reverses and goes down, she will lose $70,000. If she reinvests after the market has initially gone down, she will make $65,000, but if the market continues to go down, she will lose an additional $75,000.

Using decision tree analysis, determine which fund Ellie should invest in and its expected value.

At the end of the first year, Ellie will either reinvest the entire amount plus the return or sell and take the profit or loss. If she reinvests, she estimates that there is a .60 probability the market will go up and a .40 probability the market will go down. If Ellie reinvests in the global fund after it has gone up, her return on her initial $200,000 investment plus her $25,000 return after 1 year will be $45,000. If the market goes down, her loss will be $15,000. If she reinvests after the market has gone down, her return will be $34,000, and her loss will be $17,000. If Ellie reinvests in the index fund after the market has gone up, after 2 years her return will be $65,000 if the market continues upward, but only $5,000 if the market goes down. Her return will be $55,000 if she reinvests and the market reverses itself and goes up after initially going down, and it will be $5,000 if the market continues to go down. If Ellie invests in the Internet fund, she will make $60,000 if the market goes up, but she will lose $35,000 if it goes down. If she reinvests as the market continues upward, she will make an additional $100,000; but if the market reverses and goes down, she will lose $70,000. If she reinvests after the market has initially gone down, she will make $65,000, but if the market continues to go down, she will lose an additional $75,000.

Using decision tree analysis, determine which fund Ellie should invest in and its expected value.

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