Suppose you won the lottery and had two options: (1) receiving$0.5 million or (2) taking a gamble in which, at the flip of a coin, you receive $1 million if ahead comes up but receive zero if a tail comes up.a. What is the expected value of the gamble?b. Would you take the sure $0.5 million or the gamble?c. If you chose the sure $0.5 million, would that indicate that you are a risk averter or arisk seeker?d. Suppose the payoff was actually $0.5 million—that was the only choice. You nowface the choice of investing it in a U.S. Treasury bond that will return $537,500 at theend of a year or a common stock that has a 50–50 chance of being worthless or worth$1,150,000 at the end of the year. 1. The expected profit on the T-bond investment is $37,500. What is the expected dollarprofit on the stock investment?2. The expected rate of return on the T-bond investment is 7.5%. What is the expectedrate of return on the stock investment?3. Would you invest in the bond or the stock? Why?4. Exactly how large would the expected profit (or the expected rate of return) have tobe on the stock investment to make you invest in the stock, given the 7.5% returnon the bond?5. How might your decision be affected if, rather than buying one stock for $0.5 million,you could construct a portfolio consisting of 100 stocks with $5,000 invested in each?Each of these stocks has the same return characteristics as the one stock—that is,a 50–50 chance of being worth zero or $11,500 at year-end. Would the correlationbetween returns on these stocks matter? Explain.
Suppose you won the lottery and had two options: (1) receiving
$0.5 million or (2) taking a gamble in which, at the flip of a coin, you receive $1 million if a
head comes up but receive zero if a tail comes up.
a. What is the expected value of the gamble?
b. Would you take the sure $0.5 million or the gamble?
c. If you chose the sure $0.5 million, would that indicate that you are a risk averter or a
risk seeker?
d. Suppose the payoff was actually $0.5 million—that was the only choice. You now
face the choice of investing it in 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 worthless or worth
$1,150,000 at the end of the year.
1. The expected profit on the T-bond investment is $37,500. What is the expected dollar
profit on the stock investment?
2. The expected
rate of return on the stock investment?
3. Would you invest in the bond or the stock? Why?
4. 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 7.5% return
on the bond?
5. How might your decision be affected if, rather than buying one stock for $0.5 million,
you could construct a portfolio consisting of 100 stocks with $5,000 invested in each?
Each of these stocks has the same return characteristics as the one stock—that is,
a 50–50 chance of being worth zero or $11,500 at year-end. Would the correlation
between returns on these stocks matter? Explain.
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