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.


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.




*please show how to derive answer, thanks!

Explanation / Answer

Expected returns and what we would actually do aren't always the same.
For the lottery option (1) is, or course $0.5 million.
Option (2) is (1/2)*$0.5million + (1/2)*$0 = $0.5
So, the expected return on your $500,000 is $0
It is your choice whether to keep the money or to flip the coin, economics can't give you any guidance there.

c. Now the investments: $37,500 profit for the T-bond
Stock expectation is
(1/2)*($1,150,000 - $500,000) + (1/2)*($0 - $500,000)= (1/2)*$650,000 -(1/2)($500,000)

expected profit = $325,000.00 - $250,000 = $75,000
So the stock investment has a larger expected profit.
ANSWER $75,000.00

Note:
Usually when we round an answer to two decimal places we are talking dimes and pennies. If we round to two digits we have $75,000 If we round to one digit we would have $80,000 (science: rounding keeps or makes last significant digit even if there is a five - this way half the time you round up and half the time you round down when there is a five) and $80,000 (IRS: always rounds last digit up if there is a five). Here the two methods agree, but scientists would round $85,000 to $80,000 and most economists would round it to $90,000.
If the odds were different than 50:50, we would multiply by the given fractions instead of by (1/2)

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