##### Question

# Expected return.

Suppose you won the lottery and had two option: (1) receiving $0.5 million or (2) taking a gamble in which at the flip of a coin you receive $1 million if a headcomes up but receive zero if a tail comes up.

a) What is the expected value of the gamble ?

b) Would you take the sure $0.5 million or the gamble ?

c) If you chose the sure $0.5 million, would that indicate that you are a risk averter or a risk seeker?

d) Suppose the payoff was actually $0.5million – 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) The expected profit on the T- bond investment is $37,500. What is the expected dollar profit on the stock investment ?

2) The expected rate of return on the T- bond investment is 7.5%. What is the expected rate of return on the stock investment ?

3) Would you invest in the bond or the stock ? Why ?

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 7.5%return on the bond ?

5) How might your decision be affected if, rather than buying one stock for $0.5million, you could construct a portfolio consisting of 100 stock with $5000invested 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 $ 11,500 at year-end.Would the correlation between returns on these stocks matter ? Explain.