Suppose you won the lottery and had two option: (1) receiving $0.5 million or (2

Question

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 head comes 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 $5000 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 $ 11,500 at year-end. Would the correlation between returns on these stocks matter ? Explain.

Explanation / Answer

a) 0.5 that is 50% is the chance to get gamble. because here probability of chance 2 those are 1.head and 2.Tail b) here also 50% chances ,as because of here have 2 options c) it indicates the me a risk averter. because if I would go for option 2 ,there is a chance to get 100 % amount ,since if I satisfy with first option with 0.5 million dollars ,it is meaning that risk avertion. d) 1. if expected profit on T-bonds 375000 the expected profit on stock = 0*100% + 1150000 = $1150000 2.if expected return on bonds 7.5% since ( 37500/500000),then expected return on stock = 650000/500000 =30% 3.If its for my personal purpose ,if I am avarage risk seeker ,then I WOULD like to invest into stock . becasuse the avarage return in Bonds is 7.5% ,where in stock[ (0+30) / 2 ] = 15% so the avarage return from stock 15% is higher than the bonds. 4. 30% 5.porfolio with 100 numbers can be diverese .where if 0.5 million invest into 1 stock ,there is no chance to divert.so it should 't be equal proposals forever...

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