Question

Suppose you won the lottery and had two options: (1) receiving $1.3 million or (2) taking a gamble in which, at the flip of a coin, you receive $2.6 million if a head comes up but receive zero if a tail comes up.

A. 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

B. Would you take the sure $1.3 million or the gamble?

__________

C. If you chose the sure $1.3 million, would that indicate that you are a risk averter or a risk seeker?

___________

D. Suppose the payoff was actually $1.3 million - that was the only choice. You now face the choice of investing it in a U.S. Treasury bond that will return $1,404,000 at the end of a year or a common stock that has a 50-50 chance of being worthless or worth $2,730,000 at the end of the year.

1. The expected profit on the T-bond investment is $104,000. 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.

$_________

2. The expected rate of return on the T-bond investment is 8%. What is the expected rate of return on the stock investment? Round your answer to two decimal places.

__________%

3. Would you invest in the bond or stock? _____ (A, B, or C)

A|Bond B| Stock C| This depends on the individuals degree of risk evaluation

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 8% return on the bond? Round your answer to two decimal places. If no exact answer can be obtained, enter 0.

________%

5. How might your decision be affected if, rather than buying one stock for $1.3 million, you could construct a portfolio consisting of 100 stocks with $13,000 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 $27,300 at year-end.

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

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

III. The situation would be unchanged.

Would the correlation between returns on these stocks matter? (Yes or No)

________

Answer 1

1.

a.

in flip of coin there is two outcome, either head or tell.

Expected value of Gamble = (50% × $2.60) + (50% × 0)

= $1.30 million.

Expected value of Gamble is $1.30 million.

b.

Expected value of Gamble is $1.30 million and sure value is $1.30 million. So you should choose first option that is receiving $1.3 million for sure.

c.

If you chose the sure $1.3 million, rather than taking a gamble, it mean you are risk adverse.

d.

Expected value of investment in equity = ($2,730,000 × 50%) + ($0 × 50%)

= $1,365,000 + $0

= $1,365,000.

Expected value of investment in equity is $1,365,000.

investing it in a U.S. Treasury bond that will return $1,404,000 at the end of a year which is higher than Expected value of investment in equity is $1,365,000. So you should invest in US treasury bond.