Suppose you won the lottery and had two options: (1) receiving $1.5 million or (

Question

Suppose you won the lottery and had two options: (1) receiving $1.5 million or (2) taking a gamble in which, at the flip of a coin, you receive $3 million if a head comes up but receive zero if a tail comes up.

a) 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.

b) Suppose the payoff was actually $1.5 million - that was the only choice. You now face the choice of investing it in a U.S. Treasury bond that will return $1,590,000 at the end of a year or a common stock that has a 50-50 chance of being worthless or worth $3,300,000 at the end of the year.

1. The expected profit on the T-bond investment is $90,000. 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.

2. The expected rate of return on the T-bond investment is 6%. What is the expected rate of return on the stock investment? Round your answer to two decimal places.

3. Exactly how large would the expected profit (or the expected rate of return) have to be on the stock investment to make you invest in the stock, given the 6% return on the bond? Round your answer to two decimal places. If no exact answer can be obtained, enter 0.

Explanation / Answer

a. Probability of heads or tails is 50%.

Expected value of gamble= (Payoff when head comes * Probability of heads) + (Payoff when tail comes * Probability of tails) = $3 million*0.5 + 0*0.5 = $1.5 million

b. 1. Expected value of stock investment at the end of one year = $3.3 million*0.5 + 0*0.5 = $1.65 million

Expected dollar profit on stock investment = $1.65 million - $1.5 million =$0.15 million = $150,000

b. 2. Expected rate of return on stock investment = Expected dollar profit / Amount invested = $0.15 million/ $1.5 million = 10%

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.