Suppose you won the lottery and had two options: (1) receiving $0.8 million or (

Question

Suppose you won the lottery and had two options: (1) receiving $0.8 million or (2) taking a gamble in which, at the flip of a coin, you receive $1.6 million if a head comes up but receive zero if a tail comes up. What is the expected value of the gamble? Round your answer to two decimal places. Enter your answer in millions. For example, an answer of $550,000 should be entered as 0.55. million Would you take the sure $0.8 million or the gamble? If you chose the sure $0.8 million, would that indicate that you are a risk averter or a risk seeker? Suppose the payoff was actually $0.8 million - that was the only choice. You now face the choice of investing it in a U.S. Treasury bond that will return $868,000 at the end of a year or a common stock that has a 50-50 chance of being worthless or worth $1,680,000 at the end of the year. The expected profit on the T-bond investment is $68,000. What is the expected dollar profit on the stock investment? Round your answer to two decimal places. Write out your answer completely. For example, 0.25 million should be entered as 250,000. $ The expected rate of return on the T-bond investment is 8.5%. What is the expected rate of return on the stock investment? Round your answer to two decimal places. % Would you invest in the bond or stock? 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 8.5% return on the bond? Round your answer to two decimal places. If no exact answer can be obtained, enter 0. % How might your decision be affected if, rather than buying one stock for $0.8 million, you could construct a portfolio consisting of 100 stocks with $8,000 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 $16,800 at year-end. Investing in a portfolio of stocks would definitely be an 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. Would the correlation between returns on these stocks matter?

Explanation / Answer

Part I

Expected Pay off from the gamble = 0.5 * 0 + 0.5 * 1.6 million = 0.8 million (since the probability of heads and tails in coin toss is 0.5 each). Since the expected return is same as certain payment of 0.8 million (option 1) we would choose to take the certain payment of 0.8 million.

Part II

Return on bond = 868000 - 800000 = 68000

Expected return on the stock = (0.5*0 + 0.5*1680000) - 800000 = 40000

The expected return on stock in % = 40000/800000 = 5% which is less than the bond return.

The stock expected return has to be higher than the bond return for it to be a viable option. Hence the return will have be higher than 8.5% or in dollar terms it will have to increase by atleast 28000 . At this level an investor should be equivocal between the two choices and as the expected return on the stock increases beyond this level, it becomes more attractive. However exact level of profit required is dependent on the risk function of investor.

Part III

Even at the portfolio level, the expected return will remain unchanged :

Expected return of each stock = 0.5*0 + 0.5 * 16800 = 8400 which when multiplied by 100 gives us the same answer. Hence the situation will be unchanged . If we have all uncorrelated assets also, then in a random sample half would have profit of 16800 and other half would be zero and total sum would be same result. Hence no change in the situation.

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