Suppose you won the lottery and had the option of receiving (1) $0.5 million or

Question

Suppose you won the lottery and had the option of receiving (1) $0.5 million or (2) a gamble in which you would receive $1 million if a head were flipped but zero if a tail came up.

a. What is the expected value of the gamble? Round your answer to two decimal places.
_________________________ million


Suppose the payoff was actually $0.5 million - that was the only choice. You now face the choice of investing it in either a U.S. Treasury bond that will return $537,500 at the end of a year or a common stock that has a 50-50 chance of being either worthless or worth $1,150,000 at the end of the year.

c. The expected profit on the T-bond investment is $37,500. What is the expected dollar profit on the stock investment? Round your answer to two decimal places.


d. The expected rate of return on the T-bond investment is 7.5%. What is the expected rate of return on the stock investment? Round your answer to two decimal places.
____________________ %


*please show how to derive answer, thanks!

Explanation / Answer

(a) For the gamble,

P(winning $1 million) = P(getting a head) = 0.5

Expected value of gamble = P(head)*$1 million + P(tail)*$0

= (0.5 x $1,000,000) + (0.5 x 0)

= $500,000

= $ 0.5 million

(c) Given, that a payoff of $ 0.5 million is the only choice,

For the common stock, the probability of getting $650,000 profit is 0.5 (50-50 chance) and the probability of getting nothing is 0.5

Expected profit for the common stock

= (0.5 x $650,000) + (0.5 x 0)

= $325,000

= $ 0.325 million

(d) Now, in the part (c), we calculated that the expected profit for the stock investment is $325,000 on an investment of $500,000

Expected rate of return = (325000/500000) * 100 = 65 %

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