You invest $1 in Alphabet Inc. stock in year 1. In each subsequent year, you exp

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Question

You invest $1 in Alphabet Inc. stock in year 1. In each subsequent year, you expect the value of your portfolio to double with probability p = 0.45 or to decrease by half with p = 0.55. For example, if you have $100 in your portfolio at the end of year 9, then in year 10, you expected to have $200 with p = 0.45 and $50 with p = 0.55.
a) How much would you expect to have at the end of year 50, when you wish to retire? b) Use a standard normal variable to approximate the likelihood that your portfolio will be greater than the starting value of $1 at the end of year 50. You invest $1 in Alphabet Inc. stock in year 1. In each subsequent year, you expect the value of your portfolio to double with probability p = 0.45 or to decrease by half with p = 0.55. For example, if you have $100 in your portfolio at the end of year 9, then in year 10, you expected to have $200 with p = 0.45 and $50 with p = 0.55.
a) How much would you expect to have at the end of year 50, when you wish to retire? b) Use a standard normal variable to approximate the likelihood that your portfolio will be greater than the starting value of $1 at the end of year 50. a) How much would you expect to have at the end of year 50, when you wish to retire? b) Use a standard normal variable to approximate the likelihood that your portfolio will be greater than the starting value of $1 at the end of year 50.

Explanation / Answer

At the end of year 50, Expected value = 1 * 2^(50*0.45) * (1/2)^(50*0.55) = 1/2^5 = 1/32

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You invest $1 in Alphabet Inc. stock in year 1. In each subsequent year, you exp

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