Question

2. Expected returns Suppose you won the lottery and had two options: (1) receiving $1 million or (2) a gamble in which you would receive $2 million if a head were flipped but zero is a tail came up. a. What is the expected value of the gamble? b. Would you take the sure $1 million or the gamble? c. If you chose the sure $1 million, would that indicate that you are a risk averter or a risk seeker? d. Suppose the payoff was actually $1 million that was the only choice. You now face the choice of investing it in either a U.S. Treasury bond that will return $1,050,000 at the end of a year or a common stock that has a 50-50 chance of being either worthless or worth $3,000,000 at the end of the year. (1) The expected profit on the T-bond investment is $50,000. What is the expected dollar profit on the stock investment? (2) The expected rate of return on the T-bond investment is 5%. What is the expected rate of return on the stock investment? (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 5 percent return on the bond? (5) How might your decision be affected if, rather than buying one stock for $1 million, you could construct a portfolio consisting of 100 stocks with $10,000 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 zero or $30,000 at year-end. Would the correlation between returns on these tocks matter?

Answer 1

You have asked a question with multiple sub parts, in the same post. In order to complicate the things even further, one of the sub parts have further sub parts. I have addressed the first three sub part and first sub sub part of the fourth sub part. Please post the balance sub parts separately.

Q - 2

Part (a)

Expected value of gamble = P(H) x 2 million + P(T) x 0 =1/2 x 2 + 1/2 x 0 = $ 1 million

Part (b)

I will choose the sure 1 million. It has the same expected value as the gamble but without any risk.

Part (c)

It would indicate that you are a risk averter. This is a sign of a risk averse person.

Part (d)

Sub part (1)

Expected value of the stock investment = 1/2 x 3 + 1/2 x 0 = 1.5 million

Hence, dollar profit = 1.5 - 1 = $ 0.5 million = 500,000