Amy is figuring out her budget for two periods, t∈1,2 . In each period, she has an income yt with y1=200 and y2=0 . ct denotes her consumption level at period t . Amy decides to spend half of her first period income immediately, so c1=100 , and invest the other half ( $100 ). Amy has two investment options. One option is to buy stocks from company B . Each share costs $1 at t=1 . At t=2, the stock price is uncertain. There is a 10 % chance the stock price increases to $4 per share, a 50 % chance the stock price increases to $2.25 per share, and a 40 % chance the company B goes bankrupt and the stock price falls to $0 per share. Amy's other option is to invest all $100 in a savings account. But at t=2 , there is also a random shock to the savings account. There is a 50 % chance the bank operates normally and the interest rate is r=44 % and a 50 % chance the interest rate falls to 0 (but Amy can still get her $100 principal back). 1. If Amy invests $ 100 in stocks at t=1 , what is the expected value of her second period wealth? 2. If instead, she invests $100 in savings at t=1 , what is the expected value of her second period wealth? 3. If Amy is risk neutral, as a financial advisor, would you
Amy is figuring out her budget for two periods, t∈1,2 . In each period, she has an income yt with y1=200 and y2=0 . ct denotes her consumption level at period t . Amy decides to spend half of her first period income immediately, so c1=100 , and invest the other half ( $100 ).
Amy has two investment options. One option is to buy stocks from company B . Each share costs $1 at t=1 . At t=2, the stock
Amy's other option is to invest all $100 in a savings account. But at t=2 , there is also a random shock to the savings account. There is a 50 % chance the bank operates normally and the interest rate is r=44 % and a 50 % chance the interest rate falls to 0 (but Amy can still get her $100 principal back).
1. If Amy invests $ 100 in stocks at t=1 , what is the expected value of her second period wealth?
2. If instead, she invests $100 in savings at t=1 , what is the expected value of her second period
wealth?
3. If Amy is risk neutral, as a financial advisor, would you suggest she invest in her savings or in
stocks?
4. As before, assume without proof that at t=1 , she still consumes $100 and invests the remaining $100. If Amy’s utility function is U (c1, c2) = sqrt(c1) + sqrt(c2), what is Amy’s lifetime expected utility from investing purely in stocks? Do not include consumption at t=1.
5. Assuming the same utility function in the previous question, what is Amy’s lifetime expected utility from investing purely in savings? Do not include consumption at t=1.
6. Based on your answers to the previous two questions, what would you recommend Amy do: invest the $100 in savings or in stocks?
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