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You have won a lottery have been offered (1) \$0.5 million, or (2) a
gamble in which you would receive a \$1 million if a head were flipped and \$ 0 if a tail came
up.

a. What is the expected value of the gamble?
b. Would you take the sure \$0.5 million or take the gamble? Why?
c. If you choose the sure \$0.5 million are you a risk taker or risk averter?
d. Assume that you actually take the sure \$0.5 million; you can invest it in either a US Treasury
bond that will return \$537,500 at the end of a year or a common stock that has a 50&#8725;50 chance of being either worthless or worth \$1,150,000 at the end of the year.

(1) Calculate the expected dollar profit on the stock investment. (The expected profit on
the US Treasury bond is \$37,500.)
(2) Calculate the expected rate of return on the stock investment. (The expected rate of
return on the US Treasury bond is 7.5%.)
(3) Would you invest in the bond or the stock? Why?
(4) Exactly how large would the expected profit (or 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 of 100 stocks with \$5,000 invested in each stock? Each
of these 100 stocks has the characteristics as the one stock - that is, a 50&#8725;50 chance of being
worth either \$ 0 or \$11,500 at year end. Would the correlation between these stocks
matter? Explain.

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#### Solution Preview

Greetings!
<br>
<br>a) The expected value is found by taking the expected outcome and multiply by the percent possibility of it happening. In the case of coin flipping, either outcome has a 50% chance. So, the expected value is (\$1 million X .50 and \$0 X .50) which total to exactly \$500,000 the same as the sure thing.
<br>
<br>b) I think it obvious one should take the sure thing as the expected value is the same for both.
<br>
<br>c) If you take the ...

#### Solution Summary

calculating a return on a portfolio based on risk

\$2.49