Question

Suppose you won the lottery and had two options: (1) receiving $2 million or (2) taking a gamble in which at the flip of a coin you receive $4 million if a head comes up but receive zero if a tail comes up

What is the expected value of the gamble? Round your answer to two decimal places. Enter your answer in millions. For example, an answer of $550,000 should be entered as 0.55.
________ million

Suppose the payoff was actually $2 million - that was the only choice. You now face the choice of investing it in a U.S. Treasury bond that will return $2,130,000 at the end of a year or a common stock that has a 50-50 chance of being worthless or worth $4,800,000 at the end of the year.

The expected profit on the T-bond investment is $130,000. What is the expected dollar profit on the stock investment? Round your answer to two decimal places. Write out your answer completely. For example, 0.25 million should be entered as 250,000.
$ _____________

The expected rate of return on the T-bond investment is 6.5%. What is the expected rate of return on the stock investment? Assume a correlation between stocks of less than 1. Round your answer to two decimal places.
% _____

Exactly how large would the expected rate of return have to be on the stock investment to make you invest in the stock, given the 6.5% return on the bond? Assume a correlation between stocks of less than 1. Round your answer to two decimal places. If no exact answer can be obtained, enter 0. ________
%

Answer 1

The Expected value of Gamble = 0.5 * $4 million + 0.5 * $0 = $2 million. ( Answer = 2)

In the next case:
Expected dollar profit from stocks = 0.5 * (4,800,000 - 2,000,000) + 0.5 * (0 - 2,000,000) = $400, 000

expected rate of return on the stock investment = $400,000/$2,000,000 = 0.2 = 20%

expected rate of return on the stock investment should be atleast 6.5%

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