roblem 8-18 -18 C EXPECTED RETURNS 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 What is the expected value of the gamble? E (gamble) = 0.5 (1) +0.5(0) - 500,000 b. Would you take the sure $0.5 million or the gamble? Sume 0.5 millon If you chose the sure $0.8 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) poster 75, dollar protit on the stock investment? 0.510) + 6.5L1,150,-) (2) The expected rate of return on the T-bond inveytment is 7.5%. What is the expected 15% (3) Would you invest in the bond or the stock? Why? (4) Exactly how large would the expected profit for the expected rate of rotuun) have to be on the stock Investment to make you invent in the stock. given the 7.5% return on the bond? (5) How might your decision be affected it, 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 were or $11,500 at year end. Would the correlation between returns on these stocks matter? Explain