# Question

Suppose you won the Florida lottery and were offered a choice of $500,000 in cash or a gamble in which you would get $1 million if a head were flipped but $0 if a tail came up.

a. What is the expected value of the gamble?

b. Would you take the sure $500,000 or the gamble?

c. If you choose the sure $500,000, are you a risk averter or a risk seeker?

d. Suppose you take the sure $500,000. You can invest it in either a U.S. Treasury bond that will return $537,500 at the end of one 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.

(1) What is the expected dollar profit on the stock investment?

(The expected profit on the T-bond investment is $37,500.)

(2) What is the expected rate of return on the stock investment?

(The expected rate of return on the T-bond investment is 7.5 percent.)

(3) Would you invest in the bond or the stock?

(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 percent return on the bond?

(5) How might your decision be affected if, rather than buying one stock for $500,000, 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 either $0 or $11,500 at year-end. Would the correlation between returns on these stocks matter?

a. What is the expected value of the gamble?

b. Would you take the sure $500,000 or the gamble?

c. If you choose the sure $500,000, are you a risk averter or a risk seeker?

d. Suppose you take the sure $500,000. You can invest it in either a U.S. Treasury bond that will return $537,500 at the end of one 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.

(1) What is the expected dollar profit on the stock investment?

(The expected profit on the T-bond investment is $37,500.)

(2) What is the expected rate of return on the stock investment?

(The expected rate of return on the T-bond investment is 7.5 percent.)

(3) Would you invest in the bond or the stock?

(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 percent return on the bond?

(5) How might your decision be affected if, rather than buying one stock for $500,000, 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 either $0 or $11,500 at year-end. Would the correlation between returns on these stocks matter?

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