Suppose you won the lottery and had two options: $(1)$ receiving $$0\mathrm{.}7$ million or $(2)$ taking a gamble in which, at the flip of a coin, you receive $$1\mathrm{.}4$ million if a head comes up but receive zero if a tail comes up$.$

What is the expected value of the gamble? Enter your answer in millions. For example, an answer of $$500,000$ should be entered as $0\mathrm{.}5.$ Round your answer to one decimal place.

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million

Would you take the sure $$0\mathrm{.}7$ million or the gamble?

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If you chose the sure $$0\mathrm{.}7$ million, would that indicate that you are a risk averter or a risk seeker?

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Suppose the payoff was actually $$0\mathrm{.}7$ million $-$ that was the only choice. You now face the choice of investing it in a U$.$S$.$ Treasury bond that will return $$766,500$ at the end of a year or a common stock that has a $50-50$ chance of being worthless or worth $$1,750,000$ at the end of the year.

The expected profit on the T$-$bond investment is $$66,500.$ What is the expected dollar profit on the stock investment? Round your answer to the nearest dollar.

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The expected rate of return on the T$-$bond investment is $9\mathrm{.}5\%.$ What is the expected rate of return on the stock investment? Round your answer to the nearest whole number.

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Would you invest in the bond or stock?

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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 $9\mathrm{.}5\%$ return on the bond? Round your answer to the nearest whole number. If no exact answer can be obtained, enter $0.$

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How might your decision be affected if$,$ rather than buying one stock for $$0\mathrm{.}7$ million, you could construct a portfolio consisting of $100$ stocks with $$7,000$ 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 $$17,500$ at year$-$end.

Investing in a portfolio of stocks would definitely be a deterioration over investing in the single stock.

Investing in a portfolio of stocks would definitely be an improvement over investing in the single stock.

The situation would be unchanged.

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Would the correlation between returns on these stocks matter?

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